/ Program and Extended Abstracts International Conference on the Physics of X-ray Spectra August 30 - Sept. 2, 1976 National Bureau of Standards Gaithersburg, Md. Sponsored by: International Union of Pure & Applied Physics U.S. Dept. of Commerce National Bureau of Standards U.S. Naval Research Laboratory U.S. Army Research Office U.S. Energy Research & Development Admin. U.S. Office of Naval Research a, a- o a. o «/* PREFACE This International Conference on the Physics of X-ray Spectra at the U.S. National Bureau of Standards follows a sequence begun in Ithaca, New York, USA (1965) and followed biennially in Kiev, USSR (1968), Paris, France, (1970), Munich, Federal Republic of Germany (1972), and Helsinki, Finland (1974). The Conference is sponsored by the International Union of Pure and Applied Physics, the U.S. Energy Research and Development Administra- tion, the U.S. National Bureau of Standards, the U.S. Naval Research Laboratory, the U.S. Army Research Office and the U.S. Official Naval Research. The 1976 Conference provides a forum for the discussion of current work in the physics of X-ray spectra as obtained under a wide variety of conditions and from a diversity of points of view. Sessions have been arranged under the topics: Many-Body Effects in Metals, Hole State Dynamics, Continuum Oscillator Strength Distributions, Ion-Atom Collisions, X-rays from Astro- physical and Laboratory Plasmas, and X-ray Lasers. Other discussions are included in the areas of spectra from Molecules and Compound Solids, Metals and Alloys, and Synchrotron Studies of Extended Absorption Fine Structure. In addition to a considerable number of reports on related spectroscopies (APS, AES, XPS and Isochromats) , there will be papers concerning recent work on Compton and Raman Scattering. Finally, a session has been planned to permit exchanges of experience regarding Instruments and Methods. The organization of the Conference and its program has relied upon the functioning of its two principal committees: International Advisory Committee Program Committee o T. Aberg (Finland) M.A. Blokhin (USSR) J. Drahokoupil (Czechoslovakia) D.J. Fabian (United Kingdom) B.S. Fraenkel (Israel) S. Hagstrom (Sweden) R. Manne (Norway) W. Mehlhorn (Federal Republic of Germany) T. Sagawa (Japan) F.J. Wuilleumier (France) R.D. Deslattes R.C. Elton M.O. Krause R.E. LaVilla S.T. Manson D.J. Nagel P. R i chard S.E. Schnatterly H.W. Schnopper As is usually the case in any gathering such as this, the transition from an initial state of a conference that will take place to a final state that is a smoothly operating conference has been the result of much labor by a small number of people. R.E. LaVilla has borne the major part of the burden of arranging the sessions, communicating with authors about the mechanics of their contributions, and assembling this Proceedings volume. I am greatly indebted to him for dedicated efforts. I also extend my grateful thanks to Miss Robyn Hoy who did all the typing and record- keeping for the Conference. Finally, I appreciate the contributions of Dr. W.G. Schweitzer, Jr. and Mrs. Sara Torrence in handling administrative details. R.D. Deslattes August 1976 Gaithersburg, Maryland n INTERNATIONAL CONFERENCE ON THE PHYSICS OF X-RAY SPECTRA PROGRAM MONDAY, AUGUST 30, 1976 PAGE SESSION 1 - PREAMBLE AND MANY-BODY EFFECTS IN METALS Chairman - W.T. Oosterhuis 0900 Keynote Address - X-ray Physics After Eighty Years 1 Bernd Crasemann 0930 Many-Body Effects at X-ray Edges in Metals 7 G.D. Mahan 1000 Prediction of Many-Body Lineshapes Using Sum Rules 10 J.D. Dow 1020 Coffee 1040 Exchange Effects in the Li K Edge 13 S.M. Girvin and J.J. Hopfield 1100 Band Theory of Edge Shapes in Metals 16 R.P. Gupta and A.J. Freeman 1120 Photoabsorption and Photoyield Measurements of Li K-Edge 19 C. Kunz, H, Petersen and B, Sonntag 1140 Inelastic Electron Scattering Determination of Edge Shapes 23 in Simple Metals P.C. Gibbons, S.G. Slusky and S.E. Schnatterly 1200 Impurity Spectra and the Optical Threshold Profile in Metals 26 C.P. Flynn 1220 Understanding of X-ray Absorption Edges in Simple Metals 29 Using X-ray Photoemission P.H. Citrin, G.K. Wertheim, M, Schluter and Y. Baer 1240 Lunch SESSION 2a - HOLE STATE DYNAMICS Chairman - J, P. Br i and 1340 Categorization of Two-Electron Processes According to the 32 Major Many-Electron Interaction M.O. Krause 1410 Effects of Relaxation and Continuum Interaction on the Ne 35 KLL Auger Spectrum G. Howat, T. Aberg and 0. Goscinski i i i MONDAY, AUGUST 30, 1976 - continued PAGE 1430 Double L-vacancy States in the Electron Capture Decay of 181 W 38 P.V. Rao 1450 Multipolarity of Some Transitions in 231 TH By Application of 40 Gamma : X-rays Coincidence Technique E. Vano and L. Gonzalez 1510 Simplified Calculation of Autoionization Rates in Two and 43 Three-Electron Atoms D.R. Franschetti and D.L, Miller 1530 Theoretical X-ray and Autoionization Rates for Four-Electron 46 Ions with 2s n 2p Configurations M. Ahmed, S.C. Soong and C.P. Bhalla 1550 Tea SESSION 2b - MOLECULES AND COMPOUND S0LIDS-I Chairman - T. Sagawa 1340 Interpretation Schemes for Core Electron Excitation Spectra 49 of Small Molecules W.H.E. Schwarz 1410 An Ab Initio Calculation of a Vibrational Structure in X-ray 53 Spectra of Molecules L.N. Mazalov, F.K. Gel 'mukhanov, A.V. Kondratenko and V.I. Avdeev 1430 Soft X-ray Absorption of Molecular Alkali Halides 54 K. Radler, B. Sonntag and H.W. Wolff 1445 Interpretation of the X-ray Emission and Photoelectron 57 Spectra of Simple Solid Compounds G. Leonhardt, A. Kosakow, H. Sommer and M. Petke 1500 The Oxygen X-ray Emission Spectrum of Some Oxyanions 60 N. Kosuch, E. Tegeler, G. Wiech and A. Faessler 1520 X-ray Investigation of the Energy Level Structure of 63 Tetrahedrically Coordinated Transition Metal Atoms R. Szargan and A. Meisel 1535 On the 1 s-Absorption Line Spectra of Li in Lithium Halides 64 and of B in BC1 3 and BF 3 T. Hayasi and Y. Hayasi 1550 Tea iv MONDAY, AUGUST 30 , 1976 - continued II 1 ' — ■— . - ' ■■- I . . . ■ ! . . PAGE SESSION 3 - COMPTON AND RAMAN SCATTERING Chairman - Cully Sparks 1610 Resonant X-ray Scattering from Solids 67 Philip M. Platzmann 1640 Compton Spectroscopy 70 William Reed 1710 X-ray Inelastic Scattering - Relation Between Compton - 72 Raman- and Plasmon Scattering T. Suzuki TUESDAY, AUGUST 31, 1976 PAGE SESSION 4 - RESONANCE AND CONTINUUM OSCILLATOR STRENGTH DISTRIBUTION-I Chairman - R. Haensel 0900 Shape Resonance Effects in X-ray Absorption Spectra of 75 Molecules J.L. Dehmer and D. Dill 0920 Partial Photoionization Cross-Sections in the Soft X-ray 78 Region I. Lindau, P. Pianetta and W.E. Spicer 0940 X-ray Resonance Scattering by Atoms with A Partially Empty 81 Local ized Shell C. Bonnelle and R. Barchewitz 1000 Coffee SESSION 5 - EXTENDED ABSORPTION FINE STRUCTURE Chairman - A. Bienenstock 1020 White Lines and EXAFS: Complementary Effects 84 D E. Sayers, E.A. Stem and F.W, Lytle 1050 Extended Structure in X-ray Photoabsorption: Principles and 86 Applications P. Eisenberger, W.E. Blumberg, G S. Brown, P.H. Citrin, B.M. Kincaid, J. Reed and R.G. Shulman 1120 X-ray Photoabsorption Studies of Superconducting A15 Compounds 88 G.S. Brown and L. Testardi 1140 EXAFS in Photoelectron Yield Spectra: Comparison with 89 Photoabsorption and Determination of Electron Escape Depths R. Haensel, G. Martens, P. Rabe, N. Schwentner, M. Skibowski and A. Werner 1200 EXAFS of a Single Crystal of Galium 90 W.M. Weber 1220 Lunch SESSION 6a - APS, XPS AND ISOCHROMATS Chairman - M.A. Blokhin 1320 On Newer Developments in Isochromat Spectroscopy 92 K. Ulmer vi TUESDAY, AUGUST 31, 1976 - continued PAGE 1350 X-ray Continua Near the High Frequency Limit 95 R.J. Liefeld and A.F. Burr 1420 Bremmstrahlung Isochromat from Aluminum 98 P.E. Best and C.C. Chu 1435 Bremmstrahlung Isochromat of Tungsten at 16 eV 101 H. Humberg and H, Merz 1450 Studies of the 4f States in Ba and La by Electron and Photon 102 Excited APS J. Kanski, P.O. Nilsson and I. Curelaru 1505 Diffraction Effects in Appearance Potential Spectroscopy 105 M.L. den Boer, Y. Fukuda and R.L. Park 1520 X-ray Photoelectron Studies of the Heavy Rare-Earth Metals 108 and Their Oxides D.J. Fabian, W.C. Lang, P.R. Norris, B.D, Padalia and L.M. Watson 1540 Tea 1600 Determination of Empirical Atomic Continuum Charge Densities, 111 Phase Shifts, and Local Pseudo-Potentials from Angular- Dependent Photoemission Data for Rare Gases D.L. Miller and J.D. Dow 1615 Satellites in the Is and 2s XPS Spectra of Nickel Oxide 114 E.-K. Viinikka and P.S. Bagus 1630 Multiplet Splitting of Core 2p and 3p Photoelectron Lines of 116 Transition Metal Hal ides M. Okusawa, T. Ishii and T. Sagawa 1645 Importance of Relaxation Effect During Ionigation of Molecules 119 J.J. Pireaux, S. Svensson, E. Basilier, P. -A. Malmqvist, U. Gelius, R. Caudano and K. Siegbahn 1700 ESCA Studies of the Al kal i-Hal ides, LiF, LiCl and LiBr, and 122 of Li Metal L.I. Johansson, S.B.M. Hagstrom and S.-E. Karlsson 1715 X-ray Spectra of Transition Metal Alloys and Their 125 Interpretations E.Z. Kurmaev vn TUESDAY, AUGUST 31, 1976 - continued PAGE SESSION 6b - MOLECULES AND COMPOUND SOLIDS-II Chairman - A. Meisel 1320 Formation of Band Structures in Quasi One Dimensional 126 Molecules J.J. Pireaux, S, Svensson, E. Basil ier, P. -A. Malmqvist, U. Gelius, R. Caudano and K. Siegbahn 1340 Beryllium K Spectra of Beryllium Compounds 130 Yasuo Iguchi 1355 Characterization of Silicon Monoxide by X-ray Spectroscopy 133 M.T. Costa Lima and C. Senemaud 1410 The Effect of Temperature on X-ray Emission Spectra 136 J.B. Jones, M. Kasrai and D.S. Urch 1425 The Chemical Bonding in Spinel (MgAl 2 0j Studied by X-ray 139 Emissions and X-ray Photoelectron Spectroscopies D. Haycock, C.J. Nicholls and D.S. Urch 1440 An XES Study of the Structure of As-S Glasses 142 M, Lahdeniemi and E, Suoninen 1455 Investigation of the X-ray Emission and Photoelectric Yield 145 Spectra of Beryllium in Its Compounds M.A. Blokhin, E.G. Orlova and I,G. Schweizer 1510 Chemical Shifts of the K-Absorption Discontinuity of Cobalt 148 in Intermetall ic Systems C. Mande and V. Kondawar 1525 K-Absorption Spectra of Some Polynuclear Copper Complexes 151 J. Prasad, V. Krishna and H,L, Nigam 1540 Tea 1600 The K-Emission and Absorption of Gallium in GaP, GaAs and GaSb 154 J, Drahokoupil , H. Klokocnfkova and A. Simunek 1615 Effect on Chemical Environment on Sulfur Ka X-ray Spectra 157 G. Graeffe, H. Juslen and E.-K. Viinikka 1630 X-ray Emission Spectra of Rare Earth and Transition Elements 160 and Their Oxides S.I, Salem vm TUESDAY, AUGUST 30, 1976 - continued PAGE 1645 X-ray Spectroscopic Studies of Some CaCu 5 Type Intermetall ic 163 Compounds A.R. Chetal and P.R. Sarode 1700 Positron Annihilation and X-ray Spectroscopic Studies of 166 Heavy Rare Earth Elements S.N. Gupta and V.P. Vi jayavargiya 1715 X-ray Spectra of Transition Metal Disulfides: FeS 2 , CoS 2 , 168 and NiS 2 C. Sugiura, S. Nakai , T. Matsukawa, M. Obashi , J. Kashiwakura and Y. Gohshi IX WEDNESDAY, SEPTEMBER 1, 1976 PAGE SESSION 7 - ION ATOM COLLISIONS Chairman - E, Merzbacher 0900 Mul tielectron Transitions in K X-ray Spectra of Ion-Atom 171 Coll isions T. ftberg 0940 Measurement of Cross Sections for the Two-Electron One-Photon 174 Transitions in Heavy-Ion Collisions R. Schuch, G, Nolte, H. Schmidt-Bocking, R. Schule, W. Lichtenberg, K.E. Stiebing and I. Tserruya n+ 1000 Evidence for 2e-ly Transitions in CI Bombardment of KC1 177 W.W. Jacobs, B.L. Doyle, S.M. Shafroth, J. A. Tanis and A.W, Waltner 1020 Coffee 1040 Excitation of 2 Electron - 1 Photon K X-ray in Ni-Ni 180 Collisions J.S. Greenberg, P. Vincent and W. Lichten 1105 Effects of Collisional Quenching on the X-ray Yield from 183 Ion-Atom Collisions D. Matthews and R. Fortner N+ 1130 K X-rays and REC from CI Bombardment of Targets in the 186 Region 19 <_ Z <^ 35 J. A. Tanis, B.L. Doyle, W.W. Jacobs and S.M. Shafroth 1155 Ka Satellite Structure in Ion-Atom Collisions 189 R.L. Watson, B.I. Sonobe, A.K. Leeper, T. Chiao and F.E. Jenson 1220 Lunch SESSION 8a - VALENCE BAND STUDIES OF METALS AND ALLOYS Chairman - Derek Fabian 1320 Calculations of X-ray Band Spectra 192 D.A. Papaconstantopoulos 1350 Valence Band Structure of Diamond, Graphite and Amorphous 195 Carbon Obtained by X-ray and Photoelectron Spectroscopy G. Wiech 1405 Polarization and Anisotropy of the C K-Spectrum 198 J. Kieser WEDNESDAY r SEPTEMBER 1, 1976 - continued PAGE 1420 Calculation of the K-Absorption Spectrum of Aluminum 202 F. Szmulowicz and B, Segal 1 1435 Valence Band Spectra of Aluminum Noble-Metal Alloys 205 L.M. Watson, D.J. Fabian, J.C. Fuggle, E. Kallne and P.R. Norris 1450 SXS and XPS in the Investigation of Order in Alloys and 208 Liquid Metals C. Hague, J.M. Mariot, G. Dufour,and R.C. Karnatak 1505 A New Comparison Between Experiment and Theory for the X-ray 211 K-Absorption Edge of Nickel D.M. Pease and T.K. Gregory 1520 Application of Pt L Emission and Absorption Spectra for the 214 Investigation of Cluster Structures J. Finster, P. Muller, F. Thiel and A. Meisel 1540 Tea 1600 Configuration Interaction Interference Effects in the Core- 217 Electron Excitation Edges of Transition Metals R.E. Dietz and E.G. McRae 1615 Valence Band and Conduction Band Spectra of Transition-Metal 220 Compounds K. Tsutsumi , K. Ichikawa and 0. Aita 1630 Interpretation of the Rhenium L 3 Absorption Discontinuity in 223 Rhenium Metal and in Some of Its Compounds A.V. Pendharkar and C. Mande 1645 Coherent- Pseudopotential- Pair Calculation for X-ray 226 Photoemission Studies of Ag-Pd Alloys V. Srivastava and S.K. Joshi 1700 On the Electronic Structure of Palladium in the Pd-H System 229 E. Gil berg 1715 Characteristic and Continuous X-ray Emission Measurements on 232 TiNi H. Foil XI WEDNESDAY, SEPTEMBER 1, 1976 - continued PAGE SESSION 8b - INSTRUMENTS AND METHODS Chairman - R. Lief eld 1320 Resolution-Enhanced Cu and Co K04 i2 X-ray Emission Spectra 235 Obtained by the Deconvolution Method J, Kashiwakura, Y. Gohshi and I. Suzuki 1335 A New Computer Controlled Soft X-ray Spectrometer 238 H.-E. Goldstein, R. Pfliegl and H. Kirchmayr 1350 Ultra High Resolution Capabilities of a 5M Grating 240 Spectrometer in the 10 to 250 A Region G. Andermann, L. Bergknut, M. Karras and G. Griesehaber 1405 K-Absorption Spectra of Fluorine in Alkalihalide Crystals 241 S. Kiyono, Y. Hayasi and T. Muranaka 1420 A High-Resolution X-ray Spectrometer: Description and 243 Preliminary Experimental Results W.C. Sauder and R.E. LaVilla 1435 Holographic Transmission Gratings - A New Analyzer in the 245 X-ray Region E, Kallne, H.W. SchnopDer, L.P. Van Speybroeck, J. P. Delvaille, A. Epstein, R.Z, Bachrach, J.H. Dijkstra and L.J, Lantwaard 1450 Vapor X-ray Spectra of Rare-Earth Metals 248 I. A. Brytov, L.E. Mstibovskaya, N.I. Komyak and L.G. Rabinovitch 1505 Determination of the Depth of Impurity Atoms in Bulk Material 249 by Proton Induced X-rays 0. Benka, M. Geretschlager, A. Kropf, H. Paul and J. Kepler 1520 High Resolution L X-ray Emission Spectrum of Argon 250 J. Nordgren, H. Kgren, C. Nordling and K. Siegbahn 1540 Tea 1600 The Use of Long Wavelengths for Low-Angle Scattering 253 Y. Siota and M. Yokota 1615 X-ray Detection for Measurement of Inner Shell Ionization by 256 Relativistic Electron Impact H. Genz, D.H.H. Hoffmann, W. Low and A. Richter 1630 A New Type of Kossel -Borrmann Radiation from Germanium 260 Crystal K. Das Gupta xii WEDNESDAY, SEPTEMBER 1, 1976 - continued PAGE 1645 Theory and Measurement of X-ray Diffraction Several Acid 263 Phthalates D.M. Barrus, R.L. Blake and A.J. Burek 1700 A Spectrograph for Studies of High Speed Discharge 266 B. Sundbom and S.K. Handel 1715 X-ray Spectroscopic Investigation of Energy Bands Fine 269 Structure and the Interpretation of Conductivity Character of Phosphorous Compounds of Various Chemical Bond Types A.N. Gusatinski, M.A. Blokhin, G.I. Alperovich, M.A. Bunin and I. A. Topol SESSION 8c - MORE ION ATOM COLLISIONS Chairman - P. Richard 1320 Target K X-ray Production for Heavy Ions Moving in Thin Solid 272 Films T.J. Gray, P. Richard, R.K. Gardner, K.A. Jamison and J.M. Hall 1340 Ar Ka, Kg and K-REC X-ray Energies and Intensities vs. Ar +12 275 -*■ C-Foil Thickness F. Folkmann, K.-0. Groeneveld, P. Mokler, J, Schader and K.D. Sevier 1400 Absolute Measurements of L-Shell Excited Ar Projectiles 278 Emerging from Carbon Foils Between 100 and 800 keV P. Ziem, R. Baragiola and N. Stolterfoht 1420 Continuous Thermal X-ray Spectrom from Hot Plasmas, 281 Bremmstrahlung and Radiative Electron Capture Process CM. Lee and R.H. Pratt 1435 Relative Intensities of Ion-Induced Ka X-ray Satellite 284 Spectra of Si and Mg as a Function of the Chemical Environmental R.L. Kauffman, L.C, Feldman and P.J Silverman 1450 Impact Parameter Dependence of Non Characteristic Radiation 287 Emitted in CI -CI Collisions I. Tserruya, H. Schmidt-Bocking, R. Schule, R. Schuch, K. Bethge and H.J. Specht 1505 Angular Distribution and Projectile-Energy Dependence of the 289 Radiative Electron Capture X-rays R. Schule, H. Schmidt-Bocking and I. Tserruya xi n WEDNESDAY, SEPTEMBER 1, 1976 - continued PAGE 1520 Continuous X-ray Spectra Below 2 MeV in Relation with Nuclear 292 Resonance Y, Cauchois 1540 Tea xiv THURSDAY, SEPTEMBER 2, 1976 PAGE SESSION 9 - X-RAYS FROM ASTROPHYSICAL AND LABORATORY PLASMAS Chairman - H.W, Schnopper 0900 Solar X-ray Astronomy 293 A.S. Krieger 0930 K-Shell Excitation and X-ray Spectra in Hot Laboratory and 296 Astrophysical Plasmas L.P. Presnyakov 1000 X-rays from Tokomaks 298 W. Stodiek 1030 Coffee 1050 300 - 500 A Lasers and Possible Lasers of Shorter A 299 I. Sobelman 1120 Electron Temperature and Density Measurements from Laser Produced Plasmas T.C. Bristow 1135 K X-ray Emission Spectra from a High Power-Density Plasma 301 1150 Spatially Resolved Spectra from Exploded Wire Plasma 304 CM. Dozier, P.G. Burkhalter and D.J. Nagel 1205 Picosecond Proximity-Focused X-ray Streak Camera 307 A.J. Lieber, H.D. Sutphin and C.B. Webb 1220 Lunch SESSION 10a - RESONANCE AND CONTINUUM OSCILLATOR STRENGTH DISTRIBUTION II Chairman - H.P. Kelly 1320 Theoretical Investigations Concerning the Evolution of the 310 Atomic Effects Contribution in the Spectra (40 to 400 eV) F. Combet Farnoux and F. Keller 1340 Analytic Calculation of Screened Photoeffect Cross Sections J. McEnnan, S.-D. Oh and R.H. Pratt 1355 Low Energy Photoionization Cross Sections from Proton Induced 316 X-ray Spectroscopy A, Lurio, W. Reuter and J. Keller xv ■THURSDAY. SEPTEMBER 2, 1976 - continued PAGE 1410 Study of 4d Shell Excitations by Electron Scattering 319 C. Franck, P.C. Gibbons and S,E. Schnatterly 1425 Experimental Study of Photoabsorption in Gd and Dy in the 321 Vicinity of the 4d Ionization Threshold M. Cukier, P. Dhez and P, Jaegle 1440 Exact Numerical Calculation of Rayleigh Scattering 324 L. Kissel and R.H. Pratt 1455 Angular Correlation Between K and L X-rays in Platium 327 A.L. Catz 1510 Soft X-ray Photoionization of Xenon by Photoelectron 329 Spectroscopy with Synchrotron Radiation F. Wuilleumier, M.Y. Adam, V. Schmidt, N. Sandner and W. Mehlhorn 1540 Tea SESSION 10b - EMISSION SATELLITES Chairman - K. Tsutsumi 1320 About the La Satellite Spectrum - Can La Diagram Lines Be 332 Observed J. P. Briand, M. Frilley, P. Chevallier, A. Chetioui, A. Touati, M. Tavernier and J.P, Rozet A Direct Proof of the Shake Model: The Ka Satellite Spectrum 335 Following Electron Capture J.P. Briand, P. Chevallier, A. Chetioui, J.P. Rozet, M. Tavernier and A. Touati 1340 Rigorous Screening and Effective Principal Quantum Numbers 338 Z.J. Horak, M.N. Lewis and H. Rihova 1355 Contribution of Radiative and Auger Transition on Kg' 341 Satellite of Transition Elements T. Watanabe and C. Horie 1410 Theoretical X-ray Spectra for Double Vacancy in 2p Shell of 344 Argon C.P. Bhalla 1425 Systematics of X-ray Satellites 347 S. Rai xvi THURSDAY, SEPTEMBER 2, 1976 - continued PAGE 1440 On the Satellites of the Ka-Doublet of Fluorine in Lithium- 351 Fluoride Y. Hayasi 1455 Electron Excited K Series Spectra of Neon Gas 352 T. Tooman and R. Liefeld 1510 Plasmon Satellites in Auger Spectra of Metals 354 D, Chastenet and P. Longe 1525 Multiple Plasmon Excitation in Characteristic Energy Loss 355 Spectrum of Polycrystall ine AL K.S. Srivastava, S.P. Singh and R.L. Shrivastava 1540 Tea SESSION 11 - X-RAY LASERS Chairman - James M, Forsyth 1600 Review and Status of X-ray Laser Research 358 R.W. Waynant 1630 Time Resolved Negative Absorption of a Laser-Produced Plasma 361 G. Jamelot, A. Carillon, P. Jaegle and A. Sureau 1700 Population Inversion and the Measurement of Gain in Laser 364 Produced Plasmas W.T. Silfvast, O.R. Wood and J.M. Green 1715 Gain Calculation for Electron Collision Pumped X-ray Lasers 365 L.J. Pal umbo xvn X-RAY PHYSICS AFTER EIGHTY YEARS* Bernd Crasemann Department of Physics, University of Oregon, Eugene, Oregon 97403 Two days before Christmas, 1895, Wilhelm Conrad Rontgen in his chambers in the Physical Institute of the University, Wurzburg, recorded a radiograph of the hand of his wife, Bertha. The event marks the birth of our field of study, which is named after Rontgen 1 s rays. Yet radia- tive transitions play only a relatively minor role in the deexcitation of deep atomic vacancies, the preponderant majority of inner-shell tran- sitions being radiationless. The world had to wait another quarter of a century until Pierre Auger, ca. 1923, performed the ingenious cloud- chamber experiments that led to the unambiguous characterization of what the Germans called " strahlenlose Quantensprunge . " The close interplay between experiment and theory during the advent of wave mechanics, in the second half of the twenties, led to a basic understanding of atomic transitions [l] . In 1927, Wentzel formulated the ansatz through which Auger rates are being computed to this day, and in 1935, Coster and Kronig deduced from x-ray satellites the existence of an Auger process in which a vacancy bubbles up among subshells with the same principal quantum number--a kind of transition that is being studied intensely now. The physics of x rays came to be pursued vigorously in the United States as well. At Harvard, W. Duane and his students used a 43,000-v storage battery made from test tubes to measure Planck's constant. We recall the pioneering contributions of F. K. Richtmyer, L. G. Parratt, J. A. Bearden, and J. W. M. Du Mond, to name a few. At the present time, we are experiencing a resurgence of interest in the field of inner-shell atomic physics, of which x-ray physics is an integral and historically the oldest part. Modern experimental and theoretical techniques have made important problems accessible that were once intractable. Applications to astrophysics, solid-state and plasma physics, surface studies, and other areas of practical concern have stimulated work in this field. The high level of current activity in x- ray physics is well illustrated by the comprehensive scope of the pre- sent conference, and by that of the Second Inner-Shell-Ionization Con- ference held in Freiburg only five months ago. It is my task here to attempt to relate one person's assessment of the present status of the subject, to single out some problems and ac- complishments, and to try some crystal-ball gazing. This effort is bound to be very subjective, reflecting my own interests and limita- tions, for which I ask your forbearance. Of the many possible topics, I shall limit myself to commenting briefly on many-body effects, advances in the understanding of transitions among multiple-vacancy configura- tions, new work on energies, and some developments in technology and instrumentation. Many-electron interactions . If one were asked to identify a single feature of this field that is moving into the focus of activity and is likely to characterize much of our research in the near future, then, I believe, he would have to point toward the role of many-electron effects. Not only in connection 1 with solid-state physics (as exemplified by the following papers in this session) , but also in "pure" atomic physics some of the most significant recent work has been done in this direction: as the apex of refinement in relativistic HF independent single-particle calculations has been reached, increasing attention is being given to electron correlations and their effect on photoelectron spectra, partial photoionization cross sections, and multi-electron excitation. The simultaneous excitation of two atomic electrons, in particular, is a manifestation par excellence of a departure from independent- particle behavior; progress is being made in understanding shakeup and shakeoff in terms of contributions from core rearrangement, ground-state correlations, virtual Auger transitions, and final-state configuration interaction [2] . The converse process — the simultaneous deexcitation of two elec- trons — has only been discovered within the last year, through Wolfli's identification of two-electron transitions to an empty K shell, ac- companied by the emission of a single photon [3] , and through the work of Afrosimov et. ad. on the complementary three-electron Auger transi- tion, in outer shells [4], There has been intense activity in the search for the production of Wolfli lines in various ion-atom collision systems , and in the measurement and calculation of cross sections for their production. Perhaps some of the most astonishing manifestations of atomic many- body effects are found in connection with certain short-lived hole states, such as the 4p levels of Xe. Here the independent-particle model predicts super-Coster-Kronig transitions of extraordinary inten- sity: the hole lifetime is shortened so that ionization and decay pro- cesses can no longer be separated clearly, and the transition rate is such that perturbation theory may well be pushed beyond its limits. In- deed, the levels are wide — so wide, that the 4pi/2 "line" virtually dis- appears from the Xe photoelectron spectrum [5] . A combination of energy degeneracy and strong overlap between configurations, and of a wide exit channel, produces a situation in which the independent-particle model indeed appears to break down [2] : virtual super-Coster-Kronig transi- tions cause the hole to fluctuate with great strength. The level is broadened and redistributed as a result of many-electron interactions, so that the simple picture of a well-defined hole loses much of its meaning [6] . The arduous task is now being undertaken of formulating a description of atoms that sometimes seem to behave more like a breathing plasma than the traditional model, and of reformulating traditional transition theory that cannot be generalized to the many-electron case involving non-orthogonal orbitals [7] . Multiple inner-shell ionization, x-ray yields, and satellites . Already at the time of the Atlanta Inner-Shell Ionization Confer- ence in 1972, increased interest in the properties of atoms with several deep-lying holes had become apparent [8] . Rapid progress has taken place since then in the understanding of the deexcitation of multiply ionized atoms. Efforts in this area were primarily motivated by work on ion-atom collisions, where inner-shell excitation under quasi-adiabatic molecular conditions can result in gutting of a collision partner. But the significance of the insights gained here reaches much farther. In 2 the complex cascade of radiative and (mostly) radiationless transitions through which an atom with a single initial inner vacancy rids itself of its excitation energy, only the very first one or two steps constitute single-hole decay and have heretofore been treated theoretically with reasonable accuracy. Recent advances will make it possible to extend calculations to further steps in the cascade. The clue has been the im- proved understanding of the decay properties of multiplet states, and the development of computational techniques to treat transitions among multiplets [9], Unfortunately, the overwhelming complexity of these calculations has forced their limitation, so far, to a few cases of par- ticular practical interest. The drastic differences in decay properties of different multiplet states pertaining to one and the same vacancy configuration have inter- esting consequences. The fluorescence yield of the products of ion-atom collisions is profoundly affected by the distribution among final states, a fact that entails promising possibilities for diagnosing de- tails of collision mechanisms. Moreover, x-ray yields from ion-atom collisions in gases differ strikingly from those in solids. A notice- able decrease in x-ray yields from solids has been found to arise from collisional quenching — not only the quenching of vacancies through such processes as electron capture and vacancy transfer, but also quenching through redistribution among multiplet states. This phenomenon lends itself to a new approach to the study of the dynamics of ions traversing solid targets [10] . In x-ray spectra, the presence of multiple vacancies manifests it- self through satellite lines. Many satellites are as yet not well identified. The improved understanding of the properties of multi- vacancy states and better methods for calculating their energies now promise to resolve many of the difficulties in this area. On the exper- imental side, the use of coincidence counting techniques, long since em- ployed in the disentanglement of nuclear decay schemes, has been applied successfully to the characterization of definite multiple inner-shell vacancy states and to the study of their decay. This technique has per- mitted the identification of some La satellites. The finding that the radiative deexcitation of an L3 hole in the presence of an N vacancy leads to a satellite that is shifted by less than the natural width of the Lai li ne raises the spectre that indeed other diagram lines may be contaminated with satellites of nearly the same energy, distorting if not invalidating intensity determinations [11] . Energies . Progress in understanding the energetics of both radiative and radiationless transitions holds promise for very interesting applica- tion. Free-atom transition energies have been computed by several groups; semiempirical approaches to the calculation of transition energies have been refined [12] and even superseded by ab initio calculations of the energies of the pertinent hole states [13] . Relativistic effects are being included through the full Breit operator, not as corrections made a posteriori. Vacuum polarization and self energy are taken into ac- count. The importance of these QED corrections for heavy atoms can be considerable: in the case of hahnium (element 105), for example, vacuum 3 polarization lowers the Is level by ^190 eV (out of 161 KeV) , and self energy raises it by ^570 eV. Delicate tests of the QED calculations be- come possible, but first, a substantial effort toward extension and com- pletion of these calculations is called for. Thus, the effect of screening on the self energy, for example, has not yet been calculated, and no one has as yet worked out the self-energy shifts of levels above 2 Pl/2- One striking illustration of the importance of accurate high-Z energy calculations arose a few months ago in connection with the dis- covery of fluorescent x rays attributed to the L series of naturally occurring superheavy elements. A search for the corresponding K peaks, unsuccessful at the time of this writing, was seriously hampered by the lack of a reliable prediction of the expected energy. Aside from the familiar problems of finding a tractable yet fairly realistic atomic model and taking care of relativity and QED, the big uncertainty in the area of energetics appears to lie with the topic of relaxation . The adjustment of the electron cloud of one isolated atom (or even a molecule) to the removal of an inner electron can be ac- counted for by performing separate SCF calculations for the initial and final states. Such relaxed-orbital ("ASCF") calculations, while time- consuming, do adequately reproduce the redistribution of charge that represents the static monopole screening of the hole, including its self energy. It is more complicated to evaluate the result of interatomic re- laxation , the "solid-state effect." Mostly semi-empirical considera- tions have been brought to bear on this subject so far, although abso- lute measurements of changes in reorganization energy between related compounds have been performed and successfully interpreted [14] . It appears that a closer evaluation of the absolute values of interatomic relaxation energies is now becomig possible, due to two factors: (i) the increasing availability of theoretical free-atom transition ener- gies, and (ii) the possibility, with new techniques of comparing tran- sition energies in solids and vapors [15] . The solid-state effect shows itself in the widths of XPS lines, re- flecting the hole-state lifetimes, and in the intensities of x-ray satellites and the related Coster-Kronig electron peaks. The extreme sensitivity of Coster-Kronig and super-Coster-Kronig rates to the tran- sition energy, especially near threshold, appears to have great poten- tial for investigating extraatomic relaxation. On^ may speculate that the exploration of detailed features of the interatomic relaxation energy, once better understood, could grow to become a very useful technique in materials science. Technological developments . Many papers at this conference deal with advances in instrumenta- tion and techniques that are reaching ever increasing sophistication. The development of facilities for obtaining Auger and x-ray spectra from liquids [16] and vapors [15] will be of great help in checking free-atom calculations. Channel-cut crystals [17] and holographic gratings [18] imply a significant advance in diffraction techniques. Elaborate new spectrometers are being constructed in several laboratories [17, 19] . Auger-electron appearance potential spectra have been shown to 4 exhibit diffraction properties, not unlike those found in EXAFS, that may prove very valuable in surface studies [20] . Last but not least, the vast possibilities of synchrotron radiation are beginning to be exploited, though clearly only the surface is being scratched. Measurements of extended x-ray absorption fine structure are probably the most widely utilized application of synchrotron radiation to date, and EXAFS is now seen not only in absorption, but also in fluorescence and even in photoelectron yield spectra [21] , and is ob- served as a function of polarization [22]. The energy dependence of partial photoionization cross sections is being measured [23] , yielding information that is badly needed. The potential of synchrotron radia- tion, with its intensity, tunability, polarization, and time structure, is likely to lead to many important innovations yet. All considered, then, we may well be justified in concluding that the field of x-ray physics, after its first eighty years, is as stimu- lating and challenging as ever, and that we can look forward to con- tinued exciting work in the time ahead. *Work supported in part by the National Aeronautics and Space Adminis- tration, and by the U.S. Army Research Office. 1. E. Merzbacher, in Proceedings of the Second International Confer- ence on Inner-Shell Ionization Phenomena, Freiburg, 1976 (here- inafter referred to as 1976 Freiburg Proceedings ) , Invited Papers, ed. by R. Brenn and W. Mehlhorn (Fakultat fur Physik, Universitat Freiburg, 1976). 2. M. 0. Krause, in Photoionization and Other Probes of Many-Electron Interactions , ed. by F. Wuilleumier (Plenum, New York, 1976) , and this Conference. Wolfli et al . , Phys. Rev. Lett. 35, 656 (1975). Afrosimov et al. , JETP Lett. 21, 249 (1975) . Gelius, J. Electr. Spectr. 5_, 985 (1974). Wendin and M. Ohno, in 1976 Freiburg Proceedings . Howat, T. Aberg, and 0. Goscinski, in 1976 Freiburg Proceedings , and this Conference. 8. Proceedings of the International Conference on Inner-Shell Ioniza- tion Phenomena and Future Applications , ed. by R. W. Fink e_t al . (U.S. Atomic Energy Commission Report No, CONF-720404, 1973). 9. E. J. McGuire, Phys. Rev. A 10, 13 (1974) and 11, 1889 (1975); M. H. Chen and B. Crasemann, Phys. Rev. A 10, 2232 (1974) and 12, 959 (1975); C. P. Bhalla, Phys. Rev. A 12, 122 (1975) and this Conference. Matthews and R. Fortner, this Conference. P. Briand et_ al . , this Conference. P. Larkins, J. Phys. B: Atom. Molec. Phys. 9_, 37 (1976). , Briancon and J. P. Desclaux, Phys. Rev. A (in press); K.-N. Huang at al., At. Data Nucl. Data Tables (in press). J. Pireaux e_t al. , this Conference. A. Brytov et elI. , this Conference. Hague e_t al . , this Conference. C. Sauder and R. E. La Villa, this Conference. H. W. Schnopper et al. , this Conference. 3. W. 4. V. 5. u. 6. G. 7. G. 10. D. 11. J. 12. F. 13. Ch 14. J. 15. I. 16. C. 17. W. 18. H. 19. G. Andermann, et al. , this Conference. H.-E. Goldstein et al. , this Conference. I. den Boer e_t al . , this Conference. Haensel et al . , this Conference. M. Weber, this Conference. Lindau et al. , this Conference. 20. M. 21. R. 22. W. 23. I. MANY BODY EFFECTS AT X-RAY EDGES IN METALS G. D. Mahan Physics Department Indiana University Bloomington, IN 47401 Current practice ascribes the shape of the x-ray absorption edge in metals to four or five contributions. [1-4] The first of these are the normal one electron processes, which are determined by calculating wave functions in the suitable metallic environment . [5] Second is the Auger decay of the core hole, which gives a lorentzian broadening to the edge shape. [3] Third are the atomic vibrations — phonon contributions. They contribute a Poisson broadening to the distribution, which can usually be approximated by a gaussian. [6] Fourth is the exciton and many-elec- tron effects, which are described by MND theory. [6] Fifth are possible spin flip processes. [7] The early theories considered each of these processes as independent. Thus the final edge shape was constructed by a successive convolution of the shape of each contribution. This also seems to be the current experimental practice. In XPS analysis, lorent- zian contributions are labeled "Auger," and gaussian contributions are labeled "phonon." This successive convolution is equivalent to having each term a separate factor in the time response of the system A(w) = r dt e la,t A Q (t) exp[-r|t| - cf, p (t) - 4> el (t)] where A (t) is the fourier transform of the one electron spectra, while other factors are for Auger, phonon, and many electron contributions. This simple separation may not be valid. Recently Sunjic and Lucas [8] noted that the Auger decay may also effectively reduce the phonon matrix elements. It is possible that a similar modification takes place, as we shall discuss, for the electron-electron contribution. A. One Electron Theory Although this contribution is the one which everyone thinks they understand, it is by no means easy to calculate. This may be appreciated by reviewing the different theoretical methods of calculating atomic photoionization spectra of, for example, neon. [9] These different methods mostly vary the procedure for including exchange, correlation, and relaxation into the continuum wavef unctions. The same problems are encountered in the solid, with the additional necessity of including band structure. The theoretical formula for the absorption V») = tVl M £-l (W)2 + C £ + l M £ + l (w)2] 9(W " V (1) M £ = / ^ (f) g.p ^ (i) (2) The initial and final state wave functions which enter the matrix ele- ment are really Slater determinants of 10^3 orbitals of the solid. Generally these are replaced by one electron wave functions for the primary orbital in the transition. Atomic shake-up processes are very small, and the integrals over the other atomic orbitals provide typi- 7 cally a 5% reduction in the intensity. The conduction electrons provide a shake-up process which is discussed separately in D. The initial orbital is taken for a ground state potential V^(Z,R) where Z is the ion charge as viewed from outside of the atom. The final state orbital is evaluated for the potential Vf(Z+l,R). Both potentials should be calculated with the inclusion of the screening charge of con- duction electrons. These two potentials, if evaluated self consistently, are quite different, so that the two wave functions are not solutions of the same Hamiltonian. This is quite well known in atomic physics, and accounts for the different results obtained using the length, velocity, or acceleration forms of the transition matrix element. [9] In the solid, band structure effects must also be included, and are regarded as being important in even changing the edge shapes. B. Auger Decay In atoms of low atomic number, the core hole mostly decays by an Auger process. In metals, one possible event is where a conduction band electron falls into the core hole, while exciting another conduction electron to a state of high kinetic energy. The rate of this process is calculated by assuming the particles interact via the coulomb potential. It provides a lorentzian broadening to the spectra. The widths r are typically 0.1 eV or larger. [1-4] C. Phonon Nearly all electronic transitions in solids are accompanied by the emission or absorption of phonons. For coupling to a core hole, the form of D (t) is well known to be (f)p(t) = Z M(q) 2 [(N(q) +1) (1 - e ~ ±mt ) + N(q) (1 - e iwqt ) ] q At zero temperature this gives a Poisson distribution. Since it is usu- ally true that r >> oo q , then Wqt << 1 and the small time limit may be used, which is cf> p (t) -*- t 2 Z M(q) 2 (N(q) + 1/2). Thus this contribution usually provides gaussian broadening. Whether this process is important depends upon the size of the matrix element M (q) . There has been much debate over the size of this quantity. Sunjic and Lucas recently questioned the use of this simple formula. They argue that the energy denominator ajq 2 should be replaced by u)q 2 + T 2 . Since r >> ooq, this significantly reduces the effective coupling to phonons. We have derived a formula similar to the one they propose. We find that the reduction in phonon broadenings is only about a factor of two. This is, however, still a significant factor. D. Exciton and Electron-Electron The MND theory predicts in simple metals an edge shape of the form [6] 8 A(o>) = e(o)-o) T ) [C A-1 M £ _ 1 (w) 0)-03„ a £-1 + C £+1 M (a,) ia 03-0). £+1 ] (3) where C^ M£ are the normal one-electron amplitudes described above, and the exponents a = 26£/tt - Z (2£'+l) (So ' /tt) are obtained by calculating A 6o(kj>) for conduction electron scattering from the core hole. This for- mula applies just at threshold, and there have been several methods suggested to convolute the theory with a full spectrum. [10-11] There have been numerous calculations of the phase shifts, using either a screened point charge, or else a pseudopotential. [10-12] It would seem that Auger decay would affect this potential. One should use, as is commonly done in nuclear physics, a complex potential, wherein the imaginary part relates to the absorptive part of the potential: the electron can get absorbed by the core hole. The two terms in a^ arise from two processes: 26 ^/tt is from an exciton-type enhancement of the absorption edge, while the other is from shake-up processes involving the conduction band electrons. Our eqn. 3 for the MND theory is slightly different than the one we have used in the past. The difference is in the ordinary matrix elements. Previously we used matrix elements evaluated with ^(f)and ^(i) both cal- culated from V(Z,R), and the core hole potential V C (R) = V(Z+1,R)-V(Z,R) is treated as a perturbation which gives rise to the edge anomalies. As first suggested by Friedel, [13] and argued persuasively by Flynn,[14] the form in eqn. 2 is more correct. It can be derived by starting with a Kubo formula in which the current operator is expanded in final state basis set (eigenstates of Vf(Z+l,R)) instead of those of the initial state. One can derive the edge singularity in the standard fashion, except that it is obvious that the matrix elements should be those in eqn. 2. References 1. P. H. Citrin, G. K. Wertheim, Y. Baer, Phys. Rev. Letters 35_, 885 (1975). 2. J. J. Ritsko, S. E. Schnatterly, P. C. Gibbons, Phys. Rev. B 10, 5017 (1974). 3. L. Ley, F. R. McFeely, S. P. Kowalczyk, J. G. Jenkin, D. A. Shirley, Phys. Rev. B 11 , 600 (1975). 4. H. Neddermeyer, Phys. Rev. B 13 , 2411 (1976). 5. R. J. Gupta and A. J. Freeman, Phys. Rev. Letters 36 , 1194 (1976). 6. G. D. Mahan, Solid State Physics, Vol 29 (Academic Press, 1974) pg. 75. 7. Y. Onodera, J. Phys. Soc. Japan 39, 1482 (1975). 8. M. Sunjic and A. A. Lucas, preprint. 9. J. W. Cooper, Phys. Rev. 128, 681 (1962). 10. P. Longe, Phys. Rev. B 8 , 2572 (1973). 11. G. D. Mahan, Phys. Rev. B 11 , 4814 (1975). 12. P. Minnhagen, Phys. Letters 56A , 327 (1976). 13. J. Friedel, Comments Solid State Physics _2, 21 (1969). 14. C. P. Flynn, private communication. PREDICTION OF MANY-BODY LINESHAPES USING SUM RULES'* John D. Dow Department of Physics and Materials Research Laboratory- University of Illinois at Urb ana -Champaign Urbana, Illinois, U.S.A. 61801 Sinn rules, conservation laws, and other general theoretical rela- tions can be used (i) to predict many-body lineshapes with higher con- fidence and accuracy than straightforward computations, and (ii) to test existing theories of x-ray edges. Here we consider three general theo- ries: (A) The MND theory, which is the version of the Nozieres-de Dom- inicis (ND) theory [1], widely accepted three years ago, and discussed in Mahan's review article [2] (this theory includes the prediction that L2 3 edges should be peaked, Qq ^>0.4, whereas K edges should be rounded, .] Here 5^ are the phase shifts of a Fermi energy electron in the presence of a hole, and must satisfy several constraints. Chief among these is the constraint of charge conservation, which is embodied in Friedel's sum rule for a fully screened hole: CO 1 = jE n 2(2j+1)(6,/tt). J=0 J Moreover, reasonable phase shifts for alkali (noble) metals assign most of the screening to s- and p-electrons; 2 2(2j+1)(6 j ./tt) < z Q , where z < 0.3 (0.5) for alkalis (noble metals). Finally, to a very good approximation, the phase shifts 6* should be the same for L 2 o thresholds (a Q ) , K thresholds (»i), x-ray photoemission (XPS) asymme- tries (A), and impurity resistivity data. These constraints provide many useful relations among experimental data, which should be satisfied if the ND interpretation is valid. The data violate these restrictions [11]. Given one datum ( e.g ., a Q ) and various constraints, it is possi- ble to predict other data ( e.g . A, c^) with higher precision than they can presently be measured or calculated a priori ; however the predicted exponents generally disagree with the measured values, indicating that interpretation of the data in terms of a pure ND effect is not generally tenable . Nevertheless the L2 3 edge controversy lingers on. One reason for this is that the ND lineshape formula has several parameters, is very flexible, and can be well-fitted to data unrelated to the ND effect. Another reason is that recently virtually every conceivable exponent a Q has been computed by one theorist or another; and different experiments have likewise produced virtually every possible value of & . Hence every experiment agrees with at least one theory and every theory de- scribes at least one experiment -- even though the experimental results are not mutually compatible. This is an important point which should be kept in mind when analyzing data. Other important tests of the theory are experiments which produce inconceivable exponents: XPS lines which are unacceptably symmetric (A < 0.03) [11], and allowed absorption thresholds which are nearly linear (a Q = -0.9 + 0.1) [12]. 11 (C) OTHER THEORIES Sum rules and general constraints not only are capable of predicting ND lineshapes with high precision, they are also useful for indicating the form an improved theory must take; that is the principal purpose of this work. The relative importances of band-structure effects, exhange, and electronic recoil will be discussed, with attention paid to the general theoretical requirements. Particularly useful in this regard are the experiments of Flynn and coworkers [12], which suggest that general features of initial and final state charge distributions, not just the Fermi energy phase shifts 6*, strongly influence the edge shapes. * Research supported by the National Science Foundation under grants DMR-73-07661 and DMR-72-03026. [I] P. Nozieres and C. T. de Dominicis, Phys. Rev. 178, 1097 (1969). [2] G. D. Mahan, Solid State Phys. _29, 75 (1974). [3] J. D. Dow, J. E. Robinson and T. R. Carver, Phys. Rev. Lett. 3_1, 759 (1973). [4] D. R. Franceschetti and J. D. Dow, J. Phys. F. 4, L151 (1974). [5] A. J. McAlister, Phys. Rev. 186, 595 (1969). [6] J. D. Dow and D. L. Smith, J. Phys. F 3, L170 (1973). [7] B. F. Sonntag, J. Phys. F 3, L255 (1974). [8] C. Kunz, H. Petersen, and D. W. Lynch, Phys. Rev. Lett. 33, 26 (1974). [9] J. J. Ritsko, S. E. Schnatterly, and P. C. Gibbons, Phys. Rev. BIO , 5017 (1974); P. Citrin, G. K. Wertheim et.al ., Bull. Amer. Phys. Soc. [II] 21, 425 (1976); H. Neddermeyer, Phys. Rev. B13, 2411 (1976) [10] J. H. Slowik and F. C. Brown, Phys. Rev. BIO, 416 (1974). [II] J. D. Dow (to be published). [12] C. P. Flynn (these proceedings, and to be published); see also R. A. Tilton, D. J. Phelps, and C. P. Flynn, Phys. Rev. Lett. 32 , 1006 (1974). 12 EXCHANGE EFFECTS IN THE Li K EDGE S.M. Girvin and J.J. Hopfield Department of Physics Princeton University Princeton, New Jersey 08540 The Mahan, Nozieres, and De Dominicis [1,2] (MND) theory of x-ray edges in metals predicts a power law absorption shape whose exponent is determined by the phase shifts for the core hole potential. One feature of this potential which has been previously neglected is the exchange interaction. This is of particular importance in lithium where exchange produces a 0.5 ev splitting in the free ion. The edge exponent is given by the modified formula [3]: a , . = 26 , ,/tt - A (1) A = f J (2H+1)(6 /tt) 2 , (2) * £=0 a=±l * a where V and a' are the orbital and spin quantum numbers in the channel into which the core electron is injected. Since spin is unaffected by the optical transition, a' refers to the singlet orientation relative to the core. In the Born approximation, the diagonal part of exchange leads to a symmetric modification of the phase shifts by some amount u. : \± ' & l + -^ (3 > where 6^ is the phase shift without exchange and (±) refers to the spin orientation. Equations (1) and (2) become a l = (28 l h " A ° } + (2 V* ~ U) (4) 00 oo A = 2 I (2£+l)(S%) 2 (5) V = 2X I (2A+1) (y„/ir) (6) 1=0 * £=0 where X = 1. The effect of the off-diagonal part of exchange (spin flip scattering) may be included to lowest order by invoking rotational invariance which gives X = 3 . Note that u^ must be negative since the phase shift for the singlet orientation is reduced by exchange. Exchange decreases threshold exponents because the excitonic enhancement factor, 26 /it is reduced and because the orthogonality index, A is increased. The phase shifts obtained for lithium from a self-consistent model potential calculation are displayed in Table I along with results for sodium for comparison purposes. The lithium phase shifts differ substantially from those for a simple screened point charge [4], empha- sizing the importance of details of the core. The absence of ortho- gonality effects accounts for the anomalously large p phase shift in 13 lithium which is unique among the alkali metals for its lack of p core levels. The sodium results more closely resemble the point charge values . The phase shift correction, u& may be calculated by treating exchange as a local perturbation and adjusting the coupling constants to fit the atomic level splittings. The coupling constants in the metal are scaled by the metal to ion ratio of electron density inside the core radius. In addition, the electron-electron exchange interac- tion in the bulk contributes a factor of the ratio of the measured electronic susceptibility to the ordinary Pauli suseptibility. Calculation of the exchange corrections from the numerical lithium wave functions yields \xq =.24, \i\ = .07, and Vz^O. The threshold exponents corrected for exchange are displayed in Table II. Note that A is increased by some 50% and that the edge exponents are substantially reduced. The predicted value of A is smaller than that obtained by XPS [5,6] measurements by about 0.08 for both sodium and lithium. Exchange does increase the orthogonality index but is insufficient to prevent this important discrepancy. The best absorption edge test of the lithium results is a meas- urement of the difference between ag and a.\ . The point charge model predicts ag - 04 = + .58, while the present calculation yields a ~ a l = ".21. Inelastic electron scattering measurements [7] find that ao and a.\ are both close to zero with their difference probab- ly not exceeding 0.1 in magnitude. Calculations on lithium by Freeman and Gupta [8] show that band structure effects increase the value of ao and reduce the value of a\ which would be deduced from experiment. These effects appear to bring the present calculation into good agreement with the data. However, quantitative results for the band structure corrections to the exponents are not available at present. Exchange plays a fundamental role in the lithium K edge by re- ducing all the threshold exponents while at the same time increasing the orthogonality index — a possibility not otherwise allowed by the Friedel sum rule. This mechanism partially resolves the troubling paradox that the MND many-body effects appear only weakly in x-ray edge data but are strikingly large in x-ray photoemission. [1] G.D. Mahan, Phys. Rev. 163, 612 (1967). [2] P. Nozieres and C.T. DeDominicis, Phys. Rev. 178, 1097 (1969). [3] S.M. Girvin and J.J. Hop field, to be published. [4] George A. Ausman, Jr. and Arnold J. Glick, Phys. Rev. 183 (1969). [5] P.H. Citrin, G.K. Wertheim, and Y. Baer, Phys. Rev. Letters 35, 885 (1975) [6] Y. Baer, P.H. Citrin, and G.K. Wertheim, submitted for publication in Phys. Rev. Letters. [7] J.J. Ritsko, S.E. Schnatterly, and P.C. Gibbons, Phys. Rev. B10 , 5017 (1974). [8] Raju P.Gupta and A.J. Freeman, Bull. Am. Phys. Soc. 2JU 310 (1976). 14 Table I . Phase shifts 6 1 , fill with and without the core hole, the change in the phase shifts A6 , and the exponents a for lithium and sodium without exchange corrections. .II A6, -.375 -.115 +.260 1 +.126 +.516 +.390 2 -.001 + .026 +.027 -.011 + .607 +.618 1 -.001 +.249 +.250 2 +.003 +.043 +.040 +.059 +.141 -.089 Li A - .106 +.276 +.042 -.091 Na A = .117 I II Table II . Phase shifts S , 6 with and without the core hole, the change in the phase shifts A6 , and the exponents a* for lithium with exchange corrections .II AS, -.375 -.357 +,018 -.164 Li 1 +.126 +.451 +.325 +.044 A = .159 2 -.001 +.026 +.027 -.142 15 BAND THEORY OF EDGE SHAPES IN METALS * RAJU P. GUPTA, Physics Department and Materials Research Center, Northwestern University, Evanston, Illinois 60201. and A.J. FREEMAN, Physics Department, Northwestern University, Evanston, Illinois 60201, and Argonne National Laboratory, Argonne, Illinois 60439 The shapes of the observed threshold edges in simple metals are either sharp and peaked (e.g. L 9 ~ edges of Mg and Al) or broad and rounded (e.g. K edges of Li, Be, Mg, and Al) over energies « leV. Since these features cannot be explained using one-electron theory based on the free-electron model, efforts have been made by Mahan, Nozieres and de Dominicis (MND) [l] to explain them as many body effects in which conduction electron-core hole final state interaction effects play a dominant role. We have attempted to assess the importance of the generally ignored one-electron effects on both emission and absorption spectra.- of Mg, Na, and Li using the energy eigenvalues and wave functions obtained from aug- mented plane wave (APW) calculations. We have found that there are im- portant and significant departures from the behavior expected of free- electron metals, especially near the threshold and above it. To assure numerical accuracy of both the density of states (DOS) N(E) and the x- ray intensity 1(E) (the energy E is measured from the bottom of the va- lence band) , the ab initio Bloch eigenvalues and wavefunctions were cal- culated on a dense mesh (495 inequivalent points in the irreducible l/24th zone for Mg, and 285 inequivalent points in the irreducible l/48th zone each for Na and Li) . The x-ray emission or absorption intensity 1(E) in the one electron approximation is given by Fermi's Golden Rule I(E)Qf S Fd 3 k|| 2 6(E-E 7 + E ), (1) n J c n k nk c with transition matrix elements between core (ty c ) and Bloch states (ty 77) . Note from Eq.(l) that in the constant transition matrix elements approxi- mation, the intensity depends on the projected or partial DOS (associated with different angular momentum quantum numbers) because of the dipole selection rule and not cm the total DOS. Fig. 1 presents our DOS results for Mg. We first note that the DOS is remarkably parabolic over the bottom three-fourths of the occupied part of the band but at higher ener- gies (which is also the region of interest for the edge problem) some large peaks appear, including an important peak at the Fermi energy itself. Since we are concerned with transitions involving a 2p core state for the L~ „ spectrum we also show in Fig. 1 the projected DOS of s,p and d char- acter (only s and d will contribute to the L spectrum because of di- pole selection rules and only p to the K spectrum). Fig. 2 shows the results for the L „ emission/absorption spectra obtained entirely on the basis of the band model including the transition matrix elements calculat- ed from APW Bloch functions. The results of Fig. 2 show that essentially all features of the partial DOS (not the total DOS) are also t esent in the calculated x-ray spectrum. As discussed in ref [2], the L _ emission results are in very good agreement with experiment, band structure effects are significant in Mg at the x-ray edge and the L ? „ edge of Mg is a poor testing ground for many body threshold effects. ' 16 2.0 4.0 6.0 ENERGY (eV) Fig. 1 Fig. 3 shows the calculated L_ ~ x-ray spectrum for Na; for comparison we give the free elec- tron total and partial DOS in Fig. 4. We see that features in the APW x-ray spectrum (especially in absorption) are totally absent in the free-electron case. The po- sitions of the calculated absorp- tion peaks are in agreement with the experimental data of Crisp and Williams [3]. Note that if one includes the TME in the free- electron case using a s^ir^gle plane wave ( \|n w exp(ik»r)) then even the intensity ratio s/d will be wrong (=0.5 at all ener- gies) . We have also calculated the K spectrum of Li and the results are shown in Fig. 5. There is no peak below threshold in the calculated emission spectrum, indicating that an observed rounded peak would have to be associated either with a) broadening and emission-absorp- tion overlap or b) with an electron- hole scattering resonance (in which Fig. 2 CO 1 - T I_2,3 SPECTRUM Na i i (APW) EMISSION ABS0RPTI0N_ / \ TOTAL TOTAL 1 ^% i\\ / \ s "/E F =3.23eV 1 S<\ d j^"^ -a. — i i i 1.6 3.2 4.8 6.4 8.0 E(eV) Fig. 3 17 0.8 tn > cc - o o X ,CL C/) LJJ (/)LU °o | 2 fife - E 4 - -Kw) (2) e I ' f ' ' i ' ^ f i 3 q where , , is the macroscopic differential cross section for electron scattering, -fiq is the total momentum transfer, -nw is the energy loss and e is the dielectric constant. Y^ and Y-j_ are the initial and final states of the system. The major advantage of electron scattering over optical absorption or emission for the study of x-ray edges is the ability to vary momentum transfer independently of energy loss. We can then *Present address: Department of Physics, Washington University, St. Louis, MO. 63130 23 compare the energy loss spectrum at large momentum transfer to that at small momentum transfer. For core excitations, it is useful to expand the operator: e iq * r = 1 + iq-r - \ (q-r) 2 + ... (3) The first term does not contribute to the matrix element since V. and V. are orthogonal. When q is very small compared to the inverse of the relevant core radius, the second term dominates the series. Thus, for small q our count rates show a general 1/q depend- ence, and dipole transitions are being observed. As q is increased, the third term in the series becomes important and monopole and quad- rupole transitions are observed. Applied to x-ray edges, this means that different partial waves in the conduction band become available as the final state. For example, transitions from an s core state can only go to conduction band p-waves when q is small, but can also go to s-waves when q is large. The Mahan-Nozieres-De Dominicis (MND) theory of x-ray edges [3,4] predicts that transitions to different partial waves will have different threshold shapes. High angular momentum partial wave final states are expected to contribute more rounded threshold shapes than low ones. Thus electron scattering is well suited to the investigation of this problem and provides information not obtainable by optical measurements. In our analysis of our electron scattering data we include the effects of spectrometer resolution, lifetime and phonon broadening, Fermi surface thermal width, spin-orbit and exchange [5] interactions in the excited state and one-electron transition density in a simple approximation. Multiple scattering and background from low energy excitations are removed from the data before analysis. To date the threshold shapes of the K edge in Li [6] and the Lj-j- ,-£i-£ edge in Mg [7] have been studied in detail and the Lxj,jjj edge of Na has been subjected to some investigation. The Li, Mg, and Na samples studied were polycrystalline films evaporated within the vacuum chamber of the spectrometer onto thin carbon substrates. The lithium edge remained the same at momentum transfer up to 1.2 A , implying either that the MND theory doesn't apply at all to the Li K edge or that the threshold shapes characteristic of s and p wave final states are the same. The data showed that the edge shape was consistent with a simple step function convoluted with a Gaussian. The magnesium Ljj,jj-|- threshold is peaked at low momentum transfers. When momentum transfer is increased, the edge becomes 24 rounded as expected but by more than MND theory would predict. The general conclusion is that in Mg, some effect other than the MND theory influences the edge shape in a significant way. In preliminary results, the sodium Ln»xn threshold appears peaked at low momentum transfers and rounded at high momentum transfers. Most recently we have studied the potassium l>li»in anc * M-J--J- tij_i edges using a potassium film on a carbon substrate. Our ef- forts at improving sample preparation techniques were rewarded by a potassium sample which provided high count rates in the edge and very low carbon background rates. This eliminates the need for elaborate background subtraction schemes. The data thus obtained is, at this writing, in analysis. The spin-orbit splitting of the edge is large enough that we should be able to ascertain whether the two portions have different shapes. In addition, we have obtained spectra of the ^II'III e dge at a range of momentum transfers rather than only a high and low value. We have observed that the Mu,iii threshold shape changes with momentum transfer. It becomes less peaked as momentum transfer increases. We shall discuss these data in relation to the various mechanisms proposed to explain x-ray threshold shapes. References 1. P. C. Gibbons, J. J. Ritsko, and S. E. Schnatterly, Rev. Sci. Instr. 45, 1546 (1975). 2. J. R. Fields, Thesis (unpublished), Princeton University (1975). 3. G. D. Mahan, Phys. Rev. 163, 612 (1967). 4. P. Nozieres and C. T. De Domini cis , Phys. Rev. 178, 1097 (1969). 5. Y. Onodera, J. Phys. Soc. Japan 3£, 1482 (1975) and Y. Onodera and Y. Toyozawa, J. Phys. Soc. Japan 22, 833 (1967). 6. J. J. Ritsko, S. E. Schnatterly, and P. C. Gibbons, Phys. Rev. BIO , 5017 (1974). 7. S. G. Slusky, P. C. Gibbons, S. E. Schnatterly, and J. R. Fields, Phys. Rev. Lett., 36 326 (1976). 25 IMPURITY SPECTRA AND THE OPTICAL THRESHOLD PROFILE IN METALS AND ALLOYS C. P. FLYNN, Physics Department and Materials Research Laboratory, U. of Illinois, Urbana, 111. 61801 It would stretch the truth too far to call 10 eV photons x-rays. At first sight our work with 5 - -ft to - 12 eV therefore appears mis- placed among contributions dealing with keV x-rays . In fact , the "persistence" spectra [1] discussed here closely resemble those at high energy, and provide unusually rich information about the physics of photon-induced core processes in metals. Some of the specific results discussed here are: (1) the MND formula [2] makes qualita- tively incorrect predictions in some cases; (2) the shapes of the observed optical edges are determined by chemical properties of the active center; (3) in some cases the optical process in metals is decoupled from the electron gas and gives sharp lines . Persistence spectra characterize a single site in the lattice. They occur in metals whenever the hole localizes for times much longer than to ~1 (the reciprocal plasma frequency) . Conduction electrons can then screen the perturbation within a distance ~ kp , and the entire excitation is localized inside the cell it character- izes. This happens whenever the hole energy lies outside a band; it is invariably the case for deep levels but, for impurity atoms, may often occur even at *nw ~ Ep. The many-particle electronic readjust- ments commonly pursued in high energy spectroscopies are then acces- sible at low energy and high resolution. A variety of results from this emerging valence spectroscopy are described in what follows. Electronic recoil, phonon broadening, Fano interferences, spin-orbit splittings and other "x-ray" threshold effects are all observed at -ttoo < 12 eV. The absolute absorption per atom is given in Figs. 1 and 2 for rare gas and halogen impurities in K films ~ 4000 %. thick. Samples of this type are made [3] by coevaporation of the constituents onto a LiF crystal held at He temperatures. The "persistence" of the spectra is established by threshold energies and profiles that are mainly host-independent, as for Xe in K, Rb and Cs hosts (see Fig. 1) [3]. An unusually broad scale of persistence is shown in Fig. 2 by data [4] for 1% Br in metallic K and for the "interband" absorption in the salt KBr (broken line) . Halogens do_ enter alkali metals as ions, and the structure of their excitations in metals does resemble that of excitons in salts (see below) ; the persistence of spectral features from salt to metal therefore is not accidental. A chemical understanding of metallic screening allows the excita- tion energies to be calculated accurately. The conduction band responds mainly to the core charge. Sketches showing the electron density near C&~, Ar° , id" and Ca"*" 1 " 2p 6 cores in K are given in Fig. 3 (the 2p orbitals bind below the band bottom [5]). But a core excita- tion that promotes one core electron into the conduction band also changes the core charge by +|e| . A halogen excitation therefore causes a transition 2(a) ■> 2(b) in the electron gas distribution; 2(b) ■> 2(c) and 2(c) ■* 2(d) describe rare gas and alkali metal core excitations. Calculations based on this insight, and atomic levels, 26 estimate the threshold to - 0.1 eV for suitable rare gases (arrow for Cs in Fig. 1). For halogens the predictions (some years before the experiments ! [6 ]) agree with the data and a Stokes shift of 1.5 + 0.1 eV for each halogen [4], A similar accuracy appears feasible for deep levels predictions. The halogen spectra in Fig. 2 show much structural detail. Fano interferences [7] with conduction band continua, visible below thresh- old, are most pronounced for F. Spin-orbit splittings similar to those in the salts break phonon broadened threshold edges. From the known S tokes sh ift E g one predicts [4] a rms phonon broadening of ~ /(2 E S E ) - 110 MeV , with E Q the potassium zero-point energy. A gaussian step of this width (dotted line) agrees well with the observed Br edge profile. The intrinsic Br profile, due to the elec- tron gas, is therefore a sharp step. Analogous results and conclu- sions hold for other halogens in potassium. We thus reach the central topic of x-ray threshold effects in metals. Lacking a quantitatively predictive theory of optical thresh- old profiles, our past efforts have aimed to uncover the physical parameters relevant to the threshold shape. Three results will be mentioned: 1. The profile is determined by chemical properties of the optical center . We find that different halogens have almost identical thresh- old characteristics in K: sharp steps of similar height, when correc- ted for phonon effects. The rare gas profiles for Xe (Fig. 1) and Kr (Fig. 2c) resemble each other and are quite distinct from the halogen edges. They rise smoothly to a maximum - 1 eV above threshold. The Na L 2 3 edge [10] resembles the K M 2 3 edge [11]; both are sharp, with small cusps at threshold. The different characteristic shapes are sketched next to the ground state of the relevant element in Fig. 2. These different shapes characterize elements from successive columns of the periodic table. We deduce that the profile is determined by the chemical structure of the active center. 2 . Some optical excitations are decoupled from quasiparticle-pair creation processes . Sharp lines that emerge [8] with increasing Xe content in Fig. 1 have widths comparable with exciton lines observed in pure Xe , with no sign of broadening by the conduction electron response. The spectra are due to near neighbor Xe 2 pairs, and have been observed also for Kr 2 and XeA pairs in potassium [8] . In a determinantal theory this occurs when the excited (molecular) orbital is a virtual bound state [9] . 3. The MNP formula gives qualitatively incorrect predictions in some cases . The rare gas profiles can be parameterized for ~ 0.5 eV above threshold by an exponent a - -0.9 + 0.1. Realistic estimates of this parameter from the impurity structure gives the contrary prediction of a cusped threshold with a = 0.35 +0.1 [3]. The prediction thus has the wrong magnitude and sign. It is provocative that halogens, also repulsive, have sharp edges (a positive?). Acknowledgement . This research was completed through the efforts of R. Avci , D. J. Phelps and R. A. Tilton, using funds provided by the National Science Foundation under Grant DMR-72-03026 . References . T. Y. Onodera and Y. Toyozawa, J. Phys . Soc. Jap. 24-, 341 (1968). 27 CO T3 U C 4J eg O Cu Ph • CO ,--n T3 4J co a a) CO cd co m a CU fc^ ^ u cfl d co K «H C_> }h CO ^ w >-> c CO * 4-1 o a; -C M « CO •H •H x 'J CO 4J >h >-i CO 4J •H cu 2 4-1 e CO 4-1 CU a CU 3 O CO u a cu ■X3 O CO •H cfl CO TJ a •H rH *H d CO d M H 4J 00 " X 4-j • rO •H rt o w a M M >h 14-1 on iH -a OJ cO CO o •rl CO C (3 rH cu d -C M Jh K -H 03 w d •H a Cu ■w CO en caO 00 00 •H •H •H fc Ph Pn • CN » /-n co ^-^ ^^ a\ rH • CO vO • r»s / ^ N (^ CTi 4J C-N m OA rH 4J rH r^ rH s_^ CU s_x • CT\ ^^- J ^-v H r-^ MD 00 s^ rH OS • LO vO VO o > m CTi O . >cr * x • • • 00 • PL. 4J *■ 4J 4J •H > 4J O 4J 4J Ph cu » CU >> > r^ !>>Ph JC CU r^ X cu CU On 43 CO Ph CT> P-i CtJ pel rH PM • •H iH ■w Ph rH • v_^ • • » #1 X CO "V CO CO r^ CO • 3 t^O" O t^ >,oo •H C_) ax oo s x X CO O Ph Os Ph Cm •H T3 CU tH • . *s c a X * > " ^ s <* -i CT> Pr4 (3 0) cfl ^X 4-3 Q a. ^-^ O, pq " rH CO c • CU H •H J-< fe •H c 4J T3 CU C r-l . CU rH o 4J 43 R . > a • X tyj OJ • Ph CU o P-, 3 ►J H rH O Pi o CX • • Ph o • Pn • • >-3 • CJ> • a 4-1 13 00 C_> Cfl •-) ^-^ d *s •H a ■ c co oo Ph CO O r — \ x) d co o c •H CU 4J . >, Cfl rH Fi o r-l /CU «H o\ rH rH -H rH Q o •H H H •H Ph Pm O H Ph S3 N -— ' o • 3 • • O • > . . 1-3 . ss ^-^_ ^ o E 5 ~ O _ ° C " /? 9 B U- fO O (M r-l CNJ 1 1 1 , , / • _• (UJ0tD/ g UJD) t/ z| QI 3. There are two additional effects that must be considered in x-ray edge measurements. One is the exchange mixing between spin- orbit components [7] and the other is the optical transition density of states (TDOS) [8, 9, 10 ]. These effects have been known to exist for some time, but their possible importance in x-ray edge measurements of simple metals is only now being considered seriously [11,12,13]. A similar statement applies to the hole -phonon broadening mechanism, but its magnitude can be empirically determined rather unambiguously from XPS measurements (exchange mixing and TDOS are absent in XPS experiments) High resolution A^Ka x-ray photoemission has been measured from all the accessible core levels in Na, Mg, and M [ik], and from Li as a function of temperature [15]. The data were analyzed using procedures previously described [lk]. Briefly, a lineshape function after Doniach and Sunjic [l6], containing the singularity index a and the hole-state lifetime width r, is convoluted with the spectro- meter response function of known width. Subsequent convolution with an additional gaussian lineshape of width Fp^ is then performed to take into account the effects of phonon broadening. Detailed analysis of the high binding energy side of the XPS peak determines a while that of the low binding energy side determines T and r , . 29 Transition density of states for the L^ 3 absorption edges in Na, Mg, and A£ and for the K absorption edge in AJK have been cal- culated using a combined pseudopotential-OFW formalism. The pseudo- potential input parameters were extracted from accurate Fermi surface studies. The pseudo-valence wave functions are orthogonal! zed to atomic-like core states and the transition matrix elements are cal- culated directly. TDOS's are obtained by sampling k-space using the Gilat-Raubenheimer scheme. In order to assess the relative importance of the five in- dependent mechanisms which may affect x-ray absorption edges (MED, life- time, phonons, TDOS, and exchange), we have analyzed the L^ 3 edge data from Na, Mg, and M [l7], and the K edge data from Li [12, 1&, 19] and U [20]. Wherever applicable, structure and/or broadening from these mechanisms, along with broadening from the appropriate Fermi function and spectrometer response, were taken into account and compared with the edge data. Lifetimes measured from the XPS data were used in the analyses while phonon contributions were determined from the absorption edge data directly. In all cases phonon broadening from the edge data was consistent with that from the XPS measurements. In all cases MND threshold exponents empirically determined from our edge analyses were consistent with values predicted from the measured XPS singularity indices and Friedel's sum rule [2l]. Results and conclusions of our work are as follows: (l) The K edges in Li, Na, Mg, and Pd are essentially unaffected by the con- sequences of the MND theory [l, 2], in agreement with proposed arguments [5] and with electron energy loss measurements in Li [IT]. However, this result does not imply [5] the MND theory is invalid; quite the contrary, that theory predicts [3,22, 23, 2h] small threshold exponents for Na, Mg, and hi, that are in excellent agreement with our analyses [2l]. (2) In Na, Mg, and Al the K edge rounding is primarily due to lifetime broadening. Structure in the TDOS and broadening from phonons are only weakly important in these metals. (3) In Li, the reverse is true for explaining the K edge rounding. Contrary to previous proposals [25,26], lifetime broadening is negligible. In agreement with the suggestion by Petersen [12], structure in the TDOS [9] is important, but is only partly responsible for the rounding. The primary mechanism is the hole-phonon coupling, suggested [9,21] and rebutted [26,28] by a number of workers. The new XPS temperature dependence studies [15], which are consistent with those reported earlier on edge measurements [19]; provide magnitudes of the broadening which are not in good agree- ment with any published theory [27,29,30]. (k) The peakings of the L2 3 edges in Na, Mg, and M are in quantitative agreement with pre- dictions [ 3, 22, 23, 2^] of the MND theory [l, 2]. While this result strongly confirms the validity of the MND theory in these metals, it is obtained only after including the effects of phonon broadening (small in absolute magnitude but large relative to kT) and exchange coupling [ll]. This latter mechanism appears to be important only for Na. (5) Structure from the TDOS has virtually negligible effect on the peaked edges in Na and Mg. For the case of AZ, inclusion of such effects are moderately important for achieving quantitive agreement comparable to 30 that for Na and Mg. (6) The quality of agreement between the edge data and our fitted lineshapes including all the effects mentioned above deteriorates > 1.5 eV above the edge. It is not clear, however, up to what energy above threshold the MND theory remains valid. (7) Previous neglect or incorrect consideration of phonons, lifetimes, or exchange appears to be responsible for the apparent discrepancies between pre- dictions of the MND theory near threshold and previous analyses of experimental data. 6. p. 7. Y. 8. G. 9. A. 10. L. 11. Y. 12. H. 13. R. Ik. P. 1. G. D. Mahan, Phys. Rev. 163, 612 (1967). 2. P. Nozieres and C. T. DeDominicis, Phys. Rev. 178, 1097 (1969). 3. G. A. Ausman, Jr. and A. J. Glick, Phys. Rev. 1§3, 687 (1969) . k. G. D. Mahan, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 197*0, Vol. 29, p. 75. 5. J. D. Dow, J. E. Robinson, J. H. Slowik, and B. F. Sonntag, Phys. Rev. BIO, 432 (197*0; J- D. Dow, Phys. Rev. BQ, U165 (197*0- W. Anderson, Phys. Rev. Lett. 18, 10*^9 (1967). Onodera and Y. Toyozawa, J. Phys. Soc. Japan 22, 833 (1967). A. Rooke, J. Phys. C: Solid State Phys. 1, 767 (1968). J. McAlister, Phys. Rev. 186, 595 (1969). Smrcka, Czech. J. Phys. B21, 683 (1971). Onodera, J. Phys. Soc. Japan (to be published). Petersen, Phys. Rev. Lett. 35; 1363 (1975). Gupta and A. J. Freeman, Phys. Rev. Lett. 36, H9I+ (1976). P. H. Citrin, G. K. Wertheim, and Y. Baer, Phys. Rev. Lett. 35, 885 (1975). 15. Y. Baer, P. H. Citrin, and G. K. Wertheim, Phys. Rev. Lett, (to be published) . 16. S. Doniach and M. Sunjic, J. Phys. C: Solid State Phys. 3, 285 (1970). 17. C. Kunz, R. Haensel, G. Keitel, P. Schreiber, and B. Sonntag, "Electronic Density of States", edited by L. H. Bennet, NBS Spec. Publ. 323 (U.S. G.P.O. Washington, D.C., 1971), p. 275- 18. J. J. Ritsko, S. E. Schnatterly, and P. C. Gibbons, Phys. Rev. BIO, 5017 (197*0. 19. C. Kunz, H. Petersen, and D. W. Lynch, Phys. Rev. Lett. 33; 1556 (197*0 . 20. H. Keddermeyer, Phys. Rev. B13, 2*H1 (1976). 21. For the case of Li, S. Girvin and J. J. Hopfield, Bull. Am. Phys. Soc. 21, 309 (1976), argue that spin exchange modifies the conven- tional sum rule, thus destroying simple phase shift analyses of XPS singularity indices. Our analyses of the LiK data, however, indi- cate a very small exponent in agreement with Ref. 18. 22. P. Longe, Phys. Rev. B8, 2572 (1973). 23. C 0. AOjribladh and U. von Barth, Phys. Rev. B13, 3307 (1976). 24. P. Minnhagen, Phys. Lett. 56A, 327 (1976). 25. D. R. France schetti and J. D. Dow, J. Phys. F*+, L151 (197*0. 26. G. D. Mahan, Phys. Rev. BILL, *+8l4 (1975). 27. J. D. Dow, J. E. Robinson, and T. R. Carver, Phys. Rev. Lett. 31, 759 (1973). 28. B. Bergersen, P. Jena, and T. McMullen, J. Phys. F*+ L219 (197*0. 29. A. W. Overhauser, footnote 23 in Ref. 9. 30. B. Bergerson, T. McMullen, and J. P. Carbotte, Can. J. Phys. 49, 3155(1971) 31 CATEGORIZATION OF TWO-ELECTRON PROCESSES ACCORDING TO THE MAJOR MANY-ELECTRON INTERACTIONS* i M. 0. Krause Transuranium Research Laboratory Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 One important class of x-ray satellites derives from a single- electron jump in a multi-hole configuration that is created in the ini- tial excitation process of the atom. Hence the study of multiple, es- pecially two-electron, processes is basic to the understanding of x-ray satellites. Two-electron processes are a manifestation of electron correlation (EC), which is prohed readily by photoionization. If all EC effects are included in the description of the atom, the transition matrix elements contain the exact wavefunctions of the initial and final states of the atom and give finite values for all allowed transitions, whether single or multiple. Similarly, the sharp distinction between single and mult- iple transitions fades away, when we visualize the following sequence of events: (i) before the perturbation by the incident photon, the atom is in its ground state; (ii) during the interaction none of the electrons is in a stationary state; and (iii) following the interaction, the re- maining orbital electrons will be in the various stationary states of the resulting ion. However, since exact wavefunctions are available only for the simp- lest systems and since single-electron processes usually dominate, it is a realistic approach to start a calculation with the single, independent particle model and then apply successive EC corrections. The multi-body perturbation theory (MBPT) has proven successful and lucid in its application to two-electron transitions. Chang and Poe's MBPT calculation [l] of the double photoionization probability in the 2p shell of neon is in excellent accord with experiment [2,3]. The following effects, represented in Fig. 1 in the diagrams of MBPT, were shown to be major contributors at photon energies sufficiently far above threshold: (a) Core rearrangement (CR), or core relaxation, or shakeoff (in the restricted sense of the term); (b) Ground-state cor- relation, or initial-state configuration interaction (ISCI); and (c) Virtual Auger process, or final-state configuration interaction (FSCl). In this paper, Chang and Poe's results [l] are used as a framework for the categorization of two-electron (e&, e'&' or n£, e£') processes, *Research sponsored by the U. S. Energy Research and Development Admin- istration under contract with the Union Carbide Corporation. 32 2p€d 2 P ep which are observable in x-ray, Auger, and especially in photo- electron spectra [k] . Although all mechanisms are generally ex- pected to he active, and their CORE GROUND VIRTUAL . -,-,... rearrangement state correlation auger process contributions are non-additive Fig. 1. The major contributing and var y with Photon energy, it effects for the ei, e'£» process wil1 be assumed ad hoc that one in the 2p suhshell of neon [l]. mechanism dominates under a giv- en set of conditions, allowing the process to be classified as either CR, ISCI or FSCI. The CR mechanism is the major contributor when the two-electron pro- cess involves electrons from different principal shells. Examples are given in Fig. 2. for an zi, e'£' and an n£,e£' event. In Ne (ls,2p), about 90% of the intensity comes from CR and the remainder from ISCI. If the same many-electron interactions are considered to improve the K- level energy of Ne, an analogous result is obtained: the CR correction of 20 eV [5] is about 20 times the ISCI correction. [6]. To use the rare gases as examples, CR should be predominant for Ar(ls,n); Ar(L,n); Kr(ls,n); Kr(L,n); Kr(3s,n); Kr(3p,n); Xe(ls,n); Xe(L,n); andXe(M,n), where n denotes the less tightly bound shell of a pair. np,n>6 3d \/,„ \ / \> Ne Is €ft, € JL Fig. 2. The CR term, major contributor in two electron processes in- volving an inner and an outer electron. The ISCI term is of significance when (e&, e'£') and (n£, e&') in- volve electrons of the same subshell. A specific case is depicted in Fig. 3., where the term shakeup is used in a generalized sense. In He, ISCI is dominant at all photon energies; in Ne(2p,2p), and the outer p levels of the other rare gases [l], ISCI is large; and it is important for processes involving inner K and L shells, for example, in double-internal conversion and 2e "*■ hv events [8]. In elements with an ns 2 nominal configura- tion, ISCI plays a significant role [9]. Fig. 3. The ISCI term; for The FSCI mechanism assumes AL = 1, I = or 1. importance when configurations of the same symmetry are closely spaced, as in the presence of partially filled or empty subshells. In Fig. k., evidence is shown for FSCI involving 2 S states in Ar by way of photoelectron [10] and x-ray emission spectra [ll]. FSCI also appears 33 Conjugate Shakeup Is 2p Is €S Shakeup is \ 2s / is \ ep / He Is \ / \ A 24, a' \ / \ /•• in Auger spectra [2] and in the form of interchannel coupling in partial photoionization cross sections [13] • A particularly interesting mani- festation of FSCI occurs in the %> shell of elements near Z = 50 "because of the strong coupling of ^p with Uf 2 - states [lU]. 3s3p 6 ( 2 S) 3s 2 3p 4 3d( 2 S) 3p 3d 3p 200 220 240 PHOTON ENERGY (eV) Fig. h. The FSCI term, depicted for Ar3s as a diagram (center), and as evidenced in a photoelectron spectrum (left, C',C) and an x-ray spect- rum (right); [10 and 11 ]. CR contribution is designated as S in photo- electron (left) and unresolved in x-ray spectrum (right). At this stage of theoretical development and with the still limited number of experiments, the proposed categorization and treatment of two- electron processes is mainly of heuristic value, affording a systemati- zation of data and hopefully an impetus for more extensive and detailed experimental and theoretical studies. (1) T. N. Chang and R. T. Poe, Phys. Rev. A12, l*+32 (1975). (2) V. Schmidt, N. Sandner, H. Kuntzemuller , P. Dhez, F. Wuilleumier, and E. Kallne, Phys. Rev. A13, 17^8 (1976). (3) G. R. Wight and M. J. Van der Wiel, J. Phys. B(l976). (To be publj (k) M. 0. Krause in "Photoionization and Other Probes of Many-Electron Interactions" NATO Advanced Institute Series. F. Wuilleumier editor, Plenum Press (1976), pp. 133 - l63. (5) U. Gelius, Physica Scr. 9, 133 (197*0 • (6) H. P. Kelly, Phys. Rev. A, 11, 556 (1975). (7) V. L. m Jacobs and P. G. Burke, J. Phys. B 5_, (8) W. Wolfi, Ch. Stoller, G. Bonani , M. Suter, Rev. Lett. 35,, 656 (1975). (9) See e.g. S. Siizer and D. A. Shirley, J. Chem. Phys. 6l, 2^8l(l97 1 . (10) D. P. Spears, H. J. Fischbeck and T. A. Carlson, Phys. Rev. A £, 1603 (197*0- (11) J. W. Cooper and R. E. LaVilla, Phys. Rev. Lett. 25, 17*+5 (1972). (12) W. Mehlhorn, W. Schmitz, and D. Stalherm, Z. Phys. 252, 399(1972). (13) For example Ar3s: P. G. Burke and K. T. Taylor, J. Phys. B l6, 2620 (1975) and References therein. [lk) G. Wendin in Proc. of 2nd Conference on Innershell Ionization Phenomena, W. Mehlhorn et al. , eds . , Univ. Freiburg (1976). L67 (1972] . and M. Stockli, Phys 34 EFFECTS OF RELAXATION AND CONTINUUM INTERACTION ON THE NEON KLL AUGER SPECTRUM G . Howa t Department of Chemistry Edinburgh University Edinburgh EH9 3JJ, Scotland T. Aberg Department of Physics Kansas State University Manhattan, Kansas 66506 and 0. Goscinski Department of Quantum Chemistry Uppsala University S-75120 Uppsala 1, Sweden In this report we discuss generalizations of the conventional Auger theory which is based on Wentzel's Ansatz |l|. Previously we have denon- strated that it is not possible to generalize Wentzel's approach to the many-electron case involving non-orthogonal spin orbitals by replacing the perturbing two-electron Coulomb interaction by its many-electron counterpart | 2 | . Hence a systematic investigation of the effect of re- laxation on Auger rates requires a consideration of the full Hamiltonian unless the relaxation can be adequately described by using transition orbitals (TO's) |3|. We indicate, however, that the use of the TO ' s does not significantly improve the frozen-core restricted Hartree-Fock (RHF) KLL Auger rates of Ne. The Hartree-Slater (HS) approach \k\ givesbetter agreement with experiment than the HF method especially when the 2s"2 ^Sq - 2p"2 1 Sq configuration interaction is included. However, the HS rates are expected to approach the frozen core HF rates if the inter- action within each outgoing channel of the Auger electron is included |5|- Hence a consistent theory of the Auger effect requires the consid- eration of other interactions like the interaction between the final ^S continuum states which we shall include in the lowest order by general- izing Fano's variational configuration interaction approach |6|. As indicated by the many-body-perturbation calculation of Kelly |7| this interchannel mixing is very important. Since the inner-shell hole states of the same symmetry are usually well separated, it is sufficient to consider an isolated discrete sta- tionary state interacting with N continuous stationary states ^j£- The corresponding energy submatrix to be diagonal i zed is = V. «j>|H-E| iE H-EU. E „> ' >J = 1 N, iE'.JE" (0 where the bound state wave function tf> is not necessarily orthogonal to the continuum wave functions ty-c |8| . In Fano's work |6| it is assumed that Vj£i jjrn = 6 j j6 (E"-E' ) (E 1 -E) . This assumption is uasually not valid for basis sets which are used in Auger calculations so that a pre- diagonal izat ion 9 of the continuum submatrix must be carried out. 35 If we choose a HF basis, then there is no intrachannel interaction so that Vj[ri | pi i = 6(E"-E' ) (E'-E) . With this assumption it can be shown | 1 [ that'the diagonal izat ion of the matrix (1) leads to the following lowest order result. The total resonance width r(E) of the Lorentzian decay curves is a sum of the partial widths Tj(E) = 2ir| Vj (E, E) | *-, where N V. ._ M.(e,E) V.(E,E) = M.(E,E) + I P / de J £> ' E j (2) jVi E " £ In the sum which represents the continuum interaction, P denotes the "principal part" of the integral and E coincides with the resonance ener- gy which is given by E^ to a high accuracy. The matrix elements M.-(e,E) and V. . F are given by Eq. (l). j e , i l As a first step to explore the orbital dependence and relaxation we consider the calculation of the Ne KLL HF rates. Two sets of one-elec- tron bound state spin orbitals were employed in these calculations. The first set consisted of TO's obtained from the variation of (1/2)x [E(1s"1 )+E(L"2) ] , where E(L~ 2 ) refers to the LS average energy of a particular L~ 2 configuration. Hence there are actually three sets of TO's corresponding to the final 2s~ 2 , 2s _1 2p~ , and 2p~ 2 configurations. The second set consisted of RHF spin orbitals of the initial Is -1 state. In both cases the continuum orbital ei was solved in the field of the residual ion with two L vacancies. The wave functions of each term of the ion were constructed from the TO's or the initial state HF orbitals and coupled to the continuum orbital e£ to yield the 2 S wave function. The corresponding Fock operator was constructed and the orthogonality of the continuum orbital to the bound state orbitals was imposed by the introduction of the appropriate non-diagonal Lagrangian multipliers. The calculation of the continuum orbitals and the rates was performed using a computer program (ALKO) constructed by one of us (GH) . The bound state orbitals were those provided by the Froese-Fi scher program |11|. The energies of the Auger electrons were the experimental energies which practically coincide with the corresponding TO energies |12|. In Table 1 we compare our results with the HS results of Bhalla |4| and with the HF results of Kelly |7|. Bhalla \k\ employs initial bound state orbitals and solves the continuum orbital in the inital state HS potential which approaches 2r~ 1 for large r. Kelly's HF rates |7| are based on final state orbitals except that the 2s orbitals are spin polarized HF orbit- als associated with the initial state configuration. None of the calcu- lations reproduces the experimental results very well. However, the inclusion of relaxation via the TO's improves the KL^ L2 3 ' »3p and KL£ f 3I-2 3 D Auger HF rates somewhat. We compare also our improved Auger rates which are based on initial 1s" 1 2 S bound orbitals with Bhalla's HS rates involving the 2s~ 2 'Sg - 2p" 2 Sq mixing \k\ and with Kelly's many-body-perturbation results |7|. Our HF results modified by the 2s" 2 1 S Q - 2p~ 2 S Q mixing and our results based on Eq. (2) are shown. It is seen that the inclusion of the final state interchannel interaction in the lowest order results in a signifi- cant improvement of the HF results. Note that the mixing of the final 36 2s"2 1$q es ^s and 2p"2 'S^ es ^S configurations is equivalent to the mixing of the corresponding configurations of the residual ion. Our result suggests that the success of the HS approach involving the "2 1s n - 2p"2 ' Sq mixing is partially due to a cancellation of the 2s intra- and interchannel mixing in the final state. An analysis intra- and interchannel effects on HS rates is in progress. 13 of References: *Supported by Imperial Chemical Industries (U.K.) "^Permanent Address: Laboratory of Physics, Helsinki University of Tech- nology, 02150 Espoo 15, Finland, partial support by USERDA Contract. 1 G. Wentzel, Z. Phys. 43, 524 (1927). 2 G. Howat, T. Aberg, and 0. Goscinski, in Abstracts of the 2nd Inter- national Conference on Inner Shell Ionization Phenomena (Freiburg, 1976) p. 126, and to be published. 3 0. Goscinski, G. Howat, and T. Aberg, J. Phys. B 8, 11 (1975). 4 C. P. Bhalla, Phys. Lett. 44A , 103 0973) and private communication 5 See e.g. U. Fano and J. W. Cooper, Rev. Mod. Phys. 4_0, 441 (1968) for a discussion of the intrachannel interaction in the context of photoabsorpt ion . 6 U. Fano, Phys. Rev. 124 , 1866 (1961). 7 H. P. Kelly, Phys. Rev. A JM, 556 (1975). 8 F. H. Mies, Phys. Rev. J_75, 164 (1968). 9 A. Starace, Phys. Rev. B 5, 1773 (1972). 10 G. Howat, T. Aberg, and 0. Goscinski, to be published. 11 C. Froese Fischer, Comp. Phys. Comm. J_, 151 (1969). 12 G. Howat, 0. Goscinski, and T. Aberg, Physica Fennica % Suppl . S1 , 241 (1974). C. P. Bhalla, M. Ahmed, and C. S. Soong, private communication. 13 Table 1. Ne KLL Auger rates. Units are 10 ' a.u ,-3 Transition T0 a RHF 8 HF b HS b C I ( I ) C C I ( I l) c HSC S d C I ( I ) d Expt 6 KL 1 L 1 KL 1 L 2,3 KL 2,3 L 2,3 S 1.09 1.14 0.95 0.83 P 1.82 2.31 2.03 1.83 P 0.75 1.07 0.79 0.61 S 0.41 0.44 0.46 0.39 D 5.18 5.44 5-68 5-14 0.85 0.60 0.62 0.49 0.51 2.31 1.95 1 .83 1 .40 1.48 1.07 1 .01 . 6 1 0.50 0.54 0.71 0.95 0.61 0.86 0.76 5.44 6.06 5.14 5.20 5.15 a b c Our calculation using bound TO orbitals and 1s~^ RHF orbitals. The HF rates are from Ref. 7 and the HS rates from Ref. 4. Our Cl(i) calculation includes the 2s~2 ^ Sq - 2p" z ^Sq configuration mixing and CI (I I) the mixing between the final continuum states in the lowest order according to Eq. (2). The HSC I results are from Ref. 4 and C0RR(l) includes the diagrams described in Fig. 1 of Ref. 7. The absolute total rate measured by U. Gelius et al . (Chem. Phys. Lett. Z8, 1, 1974) has been scaled by the experimental relative rates of M. 0. Krause et al . (Phys. Lett. A3J_, 81, 1970). 37 DOUBLE L- VACANCY STATES IN THE ELECTRON CAPTURE DECAY OF W-181 P. Venugopala Rao Department of Physics Emory University, Atlanta, Ga. , U.S.A. 30322 The double L-vacancy atomic states are produced in the decay of W-181 by the following mechanisms: a) KLL Auger electron emission following K capture decay to the ground and 6.25-keV levels in Ta-181, b) KLL Auger electron emission following K electron conversion of 136- and 153-keV transitions in Ta-181 (K electron capture decay is energetically forbidden to the levels at 136- and 159-keV), and c) Internal ionization in K or L shells following electron capture or internal conversion. The mechanism (a) contributes predominantly resulting in the formation of 0.02 double L-vacancy states per decay approximately. The remaining two mechanisms contribute very little of the order of 10 -lf or 10~ 5 per decay according to the present theories . Konstantinov et al. [1] measured the rate of production of these double vacancy states by measuring L X-ray - L X-ray coincidences with two proportional counters and found three times larger than the expected number. In their opinion these additional states arise because "the change in the total binding energy of all electrons of an atom in electron capture is spent on production of additional vacancies in the electron shells, starting with the L-shell, and is not carried off by the neutrino as has been assumed previously." In the present work two Si (Li) detectors, placed at 180° to each other in a fast coincidence arrangement with a resolving time of 200 nsec, are employed to measure the Ta L x rays, Cl(L) anc * Ta ^ a X rays, C^/^) in coincidence with Ta L x rays. The ratio of these two coincidence rates is related to the number, a(LL), of double L-vacancy states created per decay and the number, b (L) , of single L-vacancy states created in Ka x ray emission per decay through the following relation, C L(L) m 2a (LL) _ m(LL) C Ka(L) b < L > ' w K aL where w(LL) is the average L x ray fluorescence yield of double L vacancy states and ojj^l ^ s tne average L x ray fluorescence yield of single L vacancies created in Ka x ray emission. A value of 0.096 + 0.002 is obtained for this ratio which is corrected for the directional correlation between L x rays and K x rays and the presence of the true L x ray - L x ray coincidences from cascade nuclear transitions. Assuming that all the double L-vacancy states are created in K Auger electron emission, the ratio a(LL)/b(L) is calculated from the knowledge of KLL Auger electron branching ratios, K x ray branching ratios and K fluorescence yield (reviewed by Bambynek et_al. [2]) for Z =73. Using this value of 0.036 in the above relation, w(LL)/a)^ a L 38 ratio is found to be 1.33. The estimated value for this ratio, based upon the knowledge of the relative population of L subshell vacancies and their average L x-ray yields from Bambynek et al. [2], is 0.97, thus showing a substantial discrepancy. One possible explanation is an increase in the fluorescence yield of double L-vacancy states. But in a recent measurement by Campbell et al. [3] in which they measured L x rays in coincidence with KLL Auger electrons no such increase is reported. The angular correlation between the two cascade L x rays emitted during the decay of double L-vacancy states can also be a source of discrepancy. No theoretical studies of such effects are available but a measured value of 18% for the anisotropy in the angular correlation of cascade L x rays in the decay of W-181 is reported [1]. Thus the present result obtained with 180° between the two coincident L x rays needs to be reduced by about 10 or 12% approximately. Such a correction still leaves the experimen- tal value 20% higher than the estimated value, but not three times larger as reported by Kanstantinov et al. [1] . Before searching for other mechanisms for the production of double L-vacancy states, it is important to recognize that the estimated value of a (LL) depends heavily upon the K x ray fluorescence yield through the factor (1-oj^)/coj^. A one percent decrease in the presently accepted value of w^ (0.956) can increase the estimate of a(LL) by about 20%. At Z = 73 neither reliable experimental values nor theoretical estimates are available for K x ray fluorescence yield. A direct measurement of KLL Auger electrons per decay of W-181 would be of considerable value. References: 1. Kanstantinov et al., in Proc. Int. Conf. Inner- Shell Ionization Phenomena and Future Appl., Atlanta , U.S. Atomic Energy Comm. Report No. CONF-720404, edited by R.W. Fink, S.T. Manson, J.M. Palms and P. Venugopala Rao, p. 2035 (1973). 2. Bambynek et al., Rev. Mod. Phys . 44, 716 (1972). 3. Campbell et al., Proc. Second Int. Conf. Inner-Shell Ionization Phenomena , Freiburg (1976). 39 MULTIPOLARITY OF SOME TRANSITIONS IN Th-231, BY APPLICA- TION OF GAMMA-X-RAY COINCIDENCE TECHNIQUE E. VANO AND L. GONZALEZ JUNTA DE ENERGIA NUCLEAR. SECCION DE FISICA NUCLEAR DE BA- JA ENERGIA. MADRID -3-. SPAIN. Research on the nuclear level schemes needs in many cases the multipolarity measurement of some transitions, to es- tablish the level angular momenta. In this field conver- sion electron spectrometry is the most common method, but its convenience for nuclides having a very low specific - activity is questionable, because spectra with sufficient statistics require long measurement times, compromising - the spectrometer stability. A gamma-X-ray coincidence experiment can provide, at times, sufficient information for the determination of multipola- rity mixing in the gamma transitions involved, having the advantage that it can be performed simultaneously with the routine gamma-gamma coincidences, if an adequate low ener- gy detector choice is made. The U-235 decays to Th-231 by alpha emission, with a -- 7.13 x lo" y half-life. Due to its low specific activity, about 2 ju.Ci/U-235 gram, the use of electron spectrometry for multipolarity determination becomes practically impos- sible. The more recent works on the level scheme of Th-231 (l,2,3) have been made without direct measurement of mul- tipolarities . For this reason we have applied to this nu- clide the method described here. This method has been applied for a 42 keV transition deex citing a level of that energy to the ground state. This - level is populated via alpha decay, with an intensity of 4,5$« It is also filled by some gamma transitions. One of them, with an energy of I63 keV, arises from a 205 keV le_ vel, which is also deexcited to the ground state by means of a 205 keV transition, both 163 and 205 keV gammas ha- ving practically equal intensities, about 5 photons per 100 c<-decays . o Bidimensional coincidences have been made using a k'J cm CANBERRA Ge (Li) coaxial detector, covering an energy ran ge between 75 and 220 keV and 0,37 cm3 ORTEC Ge (Li) pla- ne detector, operating from 10 to h^ keV. The electronics was conventional, ORTEC and CANBERRA, for this type of ex periment . The data adquisition system was an INTERTECHNI- QUE TRIDAC-C, which allowed simultaneous recording on mag_ netic tape of the coincident events and their convenient display in a reduced matrix. The employed dynamics were, 40 in this experiment 512 channels for the coaxial detector and 1024 channels for the low energy detector. Stability of the linear electronic chains was assured by means of two digital gain stabilizers, placed in the analogic-to- digital converters, surveying the position of an electro- nic pulse supplied by an ORTEC hk8 pulse generator and - driven into the detector preamplifiers for obtaining a - coincidence peak, which was placed at the most energetic end of the biparametric coincidence map. Computer programs COIN, DENSIS, STEREO and ANYS (k) permit the general treat ment of the results on a 1106 UNIVAC Computer. The first one classifies the coincident events in a matrix, the se- cond and the third are used for the matrix digital plot, either as a contrast map or as an isometric projection - display. ANYS program permits row-or-column superimposi- tion in the matrix. The process that follows the matrix classification cons- ists in selecting one transition arising from a determi- ned level, coincident with that whose multipolarity is - to be investigated, as well as another placed between the same issuing level and the ground state. In the present work, the involved transitions are the 163 keV gamma, in coincidence with the k2 keV line and the 205 keV one. The difference between the 163 keV and 205 keV coinciden- ce spectra (obtained by superimposition of some lines on the coincidence matrix) after adequate detector efficien cy corrections and corresponding normalization to the in tensity unit, becomes a neat coincidence spectrum, due - exclusively to the k2 keV transition, this spectrum con- taining information about the k2 keV photons and also about the XL-Rays following the internal conversion of - the k2 keV transition. From this spectrum, the peak areas can be calculated and by using the low energy detector efficiency values and - the XL-ray emission ratios (5) one can obtain the inten- sities of the XL-rays proceeding from every subshell LI, L2 and L3 • Calculation of the L3 subshell X-ray intensi- ty presents no difficulties and it can be estimated from the referred ratios, using L £ or L c* peak areas. To - separate the L2 and L3 subshell X-ray contributions one can make use of the LTgroup , fundamentally constituted - by the L2-N4 and (L2-04+L1-N3 ) lines. So, if the theore- tical L2-N4/L2-04 ratio is supposed sufficiently precise, it is possible to find the ratio L1-N3/L2-04 (placed in the second doublet peak) calculating the peak gravity- center and establishing a proportionality between its - energy position and the L2-04 and L1-N3 respective con- tributions. In this way, the XL-rays from every subshell are obtained, these values corresponding to the Coster- 41 Kronig modified vacancy distribution* f Cos ter-Kronig fac- tors and the w L-subshell fluorescence yields (6) permit one to obtain the primary vacancy distribution, produced by the k2 keV transition internal conversion. The values are, in this case 17, ^7 and 36$, for LI, L2 and L3 res- pectively. Internal conversion coefficients for Ml and E2 k2 keV transitions (which are the possible multipolarities assumed for the 42 keV transition, taking into account the level angular momenta and parities), lead to the results, 75$ for Ml and 25$ for E2 . The same neat coincidence spectrum due to the k2 keV trans ition permits the measurement of the total internal con- version coefficient for this transition, using the X-rays and h2 keV peak areas, so determining the transition in- tensity (this calculation is normally very difficult by others procedures). The validity of this method must be judged with regard to the high sensibility of the multipolar! ty mixing obtained from the LI, L2 and L3 vacancy percentages. If the L2 and L3 vacancies calculated shift by 10$, this can produce - variations of up to 50$ in the E2 calculated mixing. Con sequently, this point must be taked closely into account when calculating multipolarity mixing. References (l) E. VANO, R. GAETA, L. GONZALEZ and C.F. LIANG, Nucl. Phys. A251 (1975) 225 2) W.TEOH and R.D. CONNOR, Nucl. Phys. A 228 (197^) ^32 3) L.A. KROGER, C.W. REICH and J.E. CLINE, ANCR-1016 (1971) J.M. LOS ARCOS. No published J.H. SCOFIELD, Phys. Rev. 179 (1969) 9 E.J. McGUIRE, Phys. Rev. A 3 (l97l) 587 42 SIMPLIFIED CALCULATION OF AUTOIONIZATION RATES IN TWO AND THREE-ELECTRON ATOMS* Donald R. Franceschetti Department of Physics and Astronomy University of North Carolina Chapel Hill, North Carolina 27514 and Donald L. Miller* Department of Physics and Materials Research Laboratory University of Illinois at Urbana - Champaign Urbana, Illinois 61801 The Auger decay, or autoionization, of atomic inner shell vacancy states has been the subject of numerous theoretical calculations [1,2]. Most of this work falls into one of two categories; high accuracy studies of autoionization of two-electron systems - He and H~ [1] , and broad sur- veys of autoionization in many-electron systems [2] . The calculation of energies, widths, and lineshape asymmetries for two-electron atoms has served as a testing ground for many-electron and scattering-theoretic methods. The existence of such high-accuracy results also permits the testing of simpler, physically motivated, methods more readily applica- ble to complex systems, and the development of a qualitative understand- ing of the role of electron-electron correlation in the autoionization process. We present here some simple calculations of energy widths for KLL Auger transitions in He, Li and Be . Comparison of our results for He with those of high accuracy calculations and with available experimental data permits a rough estimate of the reliability of our approach. The results for He, Li and Be + together provide an indication of qualitative trends in going from one system to another. Our method is motivated by the realization that the best single- (or few-) determinant approximations to the wavefunctions of two different atomic states would employ two different sets of atomic orbitals. By de- termining atomic orbitals for the initial and final states of each auto- ionization process in independent calculations, we are able to take into account, in an approximate way, the difference in electron-electron re- pulsion of the two states. This difference should be particularly sig- nificant for atoms of only a few electrons. Autoionizing states were taken to be Slater determinants or linear combinations thereof as re- quired in LS coupling. The atomic orbitals employed were of simple form and were determined by a variational procedure described in detail else- where [3] . Continuum wavefunctions were determined by self-consistent solution of a one electron Schrodinger equation including Coulomb and ex- change interactions with the atomic core. 43 Table I. Autoionization widths (eV.) for He 2s 2 -""S 2s2p 3 P 2s2p 1 P 2p 2 1 S 2p 2 """D Source 0.091 0.018 0.032 0.049 0.105 1 configuration calc. 0.149 - - 0.00095 - 2 term C.I. 0.138 0.0094 0.038 0.0067 0.072 Expt. (see Ref.[3]) or Calc. [1] The lifetime half-widths obtained for He autoionizing states are shown in Table I, together with accurate values. In addition to single configuration calculations, a two-term configuration-interaction calcu- lation was performed for the 2s and 2p , S states. Our results agree with the accurate values to within a factor of 2, except for the 2p^ -J-S state, for which the Auger matrix element involves small differ- ences between large terms. We feel that the agreement is quite good con- sidering the approximate nature of the method. It has been realized for some time that the major contribution to the Auger matrix element in He comes from the region of configuration space with both electrons near the atomic core [4]. A qualitative examination of energy terms suggests that our variational determination of atomic orbitals for the autoioniz- ing state provides a fair description of the outer shell orbitals in the core region, and that the effects of instantaneous electron-electron cor- relation in this region are, in most cases, smaller than in the atom as a whole [3] . Within the atomic orbital approximation employed, the Auger transi- tion matrix element for He involves only conventional Coulomb terms of the form Cls,. k£Jr7i|2£! 2&") , (1) f f ' 12 ' i l where the subscripts i and f designate initial and final state orbitals, respectively. For the three-electron atoms Li and Be , the use of dif- ferent sets of atomic orbitals leads to a transition matrix element which is the sum of (i) conventional matrix elements (Eq. 1), multiplied by near unity overlap factors, (ii) other Coulomb matrix elements be- tween initial and final state orbitals, multiplied by small overlap fac- tors, and (iii) matrix elements of the electron kinetic energy and electron-nuclear attraction operators between initial and final states orbitals, multiplied by products of orbital overlaps. Lifetime widths obtained from the full Auger matrix element and from the conventional Coulomb terms alone are given in Table II. 44 The conventional Auger matrix elements (Eq. 1) for He, Li and Be were found to correlate well with the amplitudes of the wavef unctions in the core region. For given £, V, I" the matrix elements were found to be proportional to a\ s (aH k)l (aH 2£f (a^^.U) (2) (a is the final state Is radius), to within about 25%. In Table II, the conventional Coulomb matrix elements are seen to account for most of the energy width of the ls2s and ls2p 2 states but not for the Is2s2p states. In the latter case the dominant contribution to the Auger matrix element is . (3) f i r f ' 2 r ' r i Although results obtained using more accurate wavef unctions will differ somewhat from those presented here, this result does indicate the pos- sible importance of one-electron operator contributions to autoioniza- tion in few electron atoms. Table II. Autoionization widths (eV.) for Li and Be . Values in parentheses are widths computed from conventional Coulomb terms (eq. 1) alone. 2 2 ls2s S Is2s2p 2 P Is2s2p 2 P 2 2 ls2p D 2 2 ls2p ^S Li 0.026 (0.017) Be + 0.038 (0.028) 0.037 (lO" 6 ) 0.073 (0.002) 0.098 (0.003) 0.258 (0.011) 0.013 (0.013) 0.030 (0.030) 0.011 (0.009) 0.009 (0.007) *Research supported by the National Science Foundation under Grants DMR-72-03026 and GH-39132 tNational Science Foundation Energy-Related Postdoctoral Fellow 1975-76, ^National Science Foundation Predoctoral Fellow. 1. A. K. Bhatia and A. Temkin, Phys. Rev. A 11, 2018 (1975) and references cited therein. 2. W. Bambynek, B. Craseman, R. W. Fink, H.-V. Freund, H. Mark, C. D. Swift, R. E. Price, and P. V. Rao, Rev. Mod. Phys. 44, 716 (1972). 3. D. L. Miller and D. R. Franceschetti, J. Phys. B (to be published). 4. J. W, Cooper, in M,R.C. McDowell, Atomic Collision Processes (North Holland, Amsterdam, 1964), p. 595. 45 THEORETICAL X-RAY AND AUTOIONIZATION RATES FOR FOUR-ELECTRON IONS WITH 2s n 2p m CONFIGURATIONS* M. Ahmed, S. C. Soong and C. P. Bhalla Kansas State University, Department of Physics Manhattan, Kansas 66506 USA The theoretical investigations of few-electron ions are impor- tant for the diagnostic applications to plasmas and for the analysis of x-ray relative intensities as observed in solar flares. These calcula- tions are also relevant to the recent high-resolution spectral measure- ments in heavy ion-atom collisions. Bhalla, Gabriel and Presynakov [1], and Bhalla and Gabriel [2] have recently published theoretical results for the Is 2p 2 , Is 2s 2 and Is 2s 2p configurations. A detailed discussion and the analyses of the experimental data from laser-produced plasmas and from solar flares were presented [1]. Using the formalism developed by Fano [3], the autoionization rates were calculated for all the spectroscopic terms [4,5]. Similarly, the theoretical expressions relevant to the radiative decay for the four-electron configurations were derived. Configuration mixing between all the various terms of the following electron configurations 2p A , 2s 1 2p 3 , 2s 2 2p 2 , Is 1 2p 3 , Is 2s 2p 2 , Is 2s 2 2p were calculated. The spin-orbit parameter for the 2p shell was computed with the Hartree-Fock [6] program. The Hamiltonian was then diagonaliz- ed for each value of J^ to obtain the eigenvectors. The autoionization and x-ray rates were then calculated using the generalized Slater integrals and the transition matrix elements. Table 1 contains the numerical results for Fe + 22 > The dominant electronic configuration and the spectroscopic term are identified in the first two columns for each value of the total angular momentum. The individual transition rates to the various final states are not listed, since the total number of x-ray transitions are very large. The sum of the autoionization rates and x-ray rates gives the total transition probability in a.u. (1 a.u. = 2.419 10~17 S ec). 46 TABLE 1 Total autoionization (R^) and x-ray (Rx) rates in a.u. for Fe ^ , calcu- lated with the inclusion of configuration mixings and in the intermedi- ate coupling scheme. Initial State R xlO 4 A R xlO 4 2 2 2s 2p 105.8 163.0 113.1 138.2 2p 130.7 137.0 195.6 232.7 2 2 2s 2p 2p 107.1 130.9 110.8 196.7 2 2 2s 2p "D 185.7 106.9 126.2 107.8 2p "D 207.6 130.5 201.3 278.9 2s2p' 115.4 186.4 D 1 1 1 1 92.41 68.73 92.58 47.50 183.6 186.2 188.4 185.3 D D 97.66 115.2 39.41 7.284 203.1 184.3 174.7 187.8 D 146.1 183.4 47 REFERENCES Supported by the U. S. Energy Research and Development Administration under Contract No. E(ll-l)-2753 [1] C. P. Bhalla, A. H. Gabriel, and L. P. Presynakov, Mon. Not. R. Astr. Soc. 172 , 359 (1975). [2] C. P. Bhalla and A. H. Gabriel, in Beam-Foil Spectroscopy , ed. Sellin and Pegg (Plenum Press 1976) p. 121. [3] U. Fano, Phys . Rev. 140, A67 (1965). [4] C. P. Bhalla, Phys. Rev. A 12, 122 (1975). [5] C. P. Bhalla, J. Phys. B 8, 2787 (1975). [6] C. Froese Fischer, Comp. Phys. Commun. <4, 107 (1972). 48 INTERPRETATION SCHEMES FOR CORE ELECTRON EXCITATION SPECTRA OF SMALL MOLECULES W.H. Eugen Schwarz, Institute of Theoretical Chemistry, University of Bonn and Gesamthochschule Siegen, Wegeler Str. 12, D 5300 Bonn, Germany 1. Introduction In order to obtain chemical information on a molecule from an experimental X-ray absorption spectrum, one has usually at first to assign it within the one-electron-orbital re- presentation. This can be achieved on the basis of more or less sophisticated ab initio calculations. However, often it is sufficient to have recourse to simple rules of thumb and to other experimental data. Several model concepts of this kind will be discussed below. Examples are presented, for which these models work, and also other ones, which ex- hibit specific deviations from the simple schemes. Explain- ing such "irregularities" will help to get a deeper under- standing of the physics of core electron excitation pheno- mena in molecules. 2. The Equivalent Core or Z+l Core Analogy Model The basic premise of this model (1-4) is that the energy levels and valence shell properties of a system with an ex- cited core electron (Z ) should be very similar to those of a species with one more proton in the nucleus and a fully occupied core shell (Z+l). This model is applied in two di- rections: l) If the valence electron spectrum of the Z+l molecule is known, this helps to assign the Z spectrum. 2) If the Z+l species is a radical difficult to investigate, its properties may be deduced from the Z spectrum (3-10). 2^1 Geometric Corrections 2.1.1 caused by different valence configurations of the in- itial states of the Z and the Z+l molecules 2.1.1.1 Bond length effects: Since in their ground states the Z+l molecule has one more valence electron (of antibon- ding character in most cases), the equilibrium bond lengths 49 of the ground state of Z, of its core excited Rydberg and ionized states, and of the Rydberg states of Z+l are very similar, but are different from that of the ground state of Z+l. Therefore the vibrational structure of the excitations l) core to valence of Z; 2) core to Rydberg or free elec- tron of Z; 3) valence to Rydberg of Z+l; exhibit specific differences. They explain some of the discrepancies already showing up in diatomics (il). Neglecting them means to id- entify vertical and adiabatic ionization potentials and e- lectron affinities. 2.1.1.2 Bond angle effects: Since bond angles are more sen- sitive than bond lengths, bond angle effects may be quite drastic in polyatomic molecules (12,13). Not only valence but also Rydberg orbitals may undergo significant changes. 2.1.2 Geometric corrections caused by different core sizes. The closed shell core of Z+l is slightly more compact than the core shell of core excited Z . This effect will be of significance for very light atoms only. It then results in Franck-Condon shifts not only of valence but also of Ryd- berg transitions (9). Whereas core to Rydberg excitations usually show very short vibrational progressions, the con- trary holds for compounds of light atoms like Li. 2.2 Exchangeand CoulombCorrections 2.2.1 Exchange effects The exchange interactions of the valence electrons with the closed shell core of Z+l and with the open shell core of Z is not negligible in many cases (4,6,9,13). A rough rule states that the doublet to doublet term values of Z+l cor- respond to the singlet to triplet term values of core exci- ted Z , whereas the singlet to singlet term values of Z are smaller by twice the exchange integral. / 2.2.2 Corrections due to different Coulomb interactions. So far we have accepted the frozen orbital approximation which, however, will result in significant errors for pene- 50 trating orbitals of light atoms, since they perceive diffe- rent effective nuclear charges in the Z+l and Z systems (9 ,14). 3. The 'Constancy of Rydberg Term Values' Model Whereas in section 2 we have compared the core spectrum of Z with the UV spectrum of Z+l, we will now compare with the UV spectrum of Z. At least the Rydberg term values are transferable from valence to core excitations in many cases (15-17), but sometimes this model fully breakes down. 5^i_ Tn £_l5-Type_Rydberg^_Diff iculty The lowest Rydberg MO's, especially those of s-type, are very sensitive to perturbations by virtual valence orbitals. The most dramatic example is represented by the core spec- tra of second row hydrides (8,18). 3 JL 2_Exchange and_Coulomb_Corrections Even within the frozen orbital approximation two correcti- ons have to be applied to the model (ll): The difference in exchange energies of the core and valence excited states will usually increase the term values of the core excitati- ons. The difference in Coulomb energies is difficult to predict generally. It is symmetry-dependent, but will often decrease the term values. 3 1 3_Comment_on Selection_Rules The atomic symmetry symbols of core excitations do not re- present the molecular symmetry. E.g. Cls to 3s is electro- nically forbidden in CH. but not in other hydrocarbons. The short and long range behavior of MO's may be very different. h. SCF Models ^ii-59!iiY a i^5i_I oni 2 2 o I e _YlE*:Ual_0rbi.tal Model The term values of core excitations are approximately given by the virtual orbital energies of the Z+l species. Al- though this model neglects the exchange and coulomb cor- rections, it is usually of much help (8-lo,13). 4.2 Correlation_Corrections 51 Usually the model underestimates the term values, because orbital reorganization has been neglected and because the the correlation energy will often increase with the number of electrons. The contrary happens, if the excited electron strongly disturbes the correlation of the other valence electrons as in the case of C0 2 (13). Specific correlation effects occur in molecules with two equivalent nuclei (14). 4.3 Koopmans ' _Theorem Koopmans' Theorem is useful to estimate the magnitude of extra structure due to core orbital splittings. Failure of Koopmans' theorem (14,19) may sometimes be explained by a rule based on Green's Function method (11, 2o). 4.4 Intensities Although intensities predicted within the framework of the independent particle model are often qualitatively correct (8,9,21), initial and final state correlations have an en- ormous effect in other cases (ll). i M.Nakaiuura et al. Phys.Rev. 178(1969)80 2 W.L. Jolly, D.N.Hendrickson JACS 92(1970)1863 3 G. R. Wight, C.E.Brion, M.J. Van der Wiel J.El.Spect. l(l9?3) 457 4 W.H.E.Schwarz Ang.Chem. Intern. Ed. 13(1974)454 5 W.H.E.Schwarz Ber.Bunsenges. 78(1974)1206 6 G.R.Wight, C.E.Brion J.El.Spect. 4(1974)313 7 G.R.Wight, C.E.Brion Chem. Phys. Let . 26(1974)607 8 W.H.E.Schwarz Chem. Phys. 11(1975)217 9 K.Radler et al . Chem. Phys. 13(1976)363 10 M.E.Schwartz Chem. Phys. Let . 40(1976)1 11 W.H.E.Schwarz et al . to be published 12 G.R.Wight, C.E.Brion J.El.Spect. 3(1974)191 13 W.H.E.Schwarz,R.J.Buenker Chem. Phys. 13(1976)153 14 W.H.E.Schwarz, T.C.Chang Int. J. Quant .Chem. 10S(l976)ooo 15 F.J. Comes, U.Nielsen, W.H.E.Schwarz J. Chem. Phys. 58(1973) 2230 16 M.B.Robin Chem. Phys. Let . 3l(l975)l4o 17 U.Nielsen, W.H.E.Schwarz Chem. Phys. 13(1976)195 18 W.H.E.Schwarz Chem. Phys. 9(1975)157 19 F.J. Comes et al. J. Chem. Phys. 58(1973)516 20 L.S.Cederbaum Chem. Phys. Let . 25(1974)562 21 U. Nielsen, R.Haensel, W.H.E.Schwarz J. Chem. Phys. 6l(l974) 3581 52 AN AB INITIO CALCULATION OF A VIBRATIONAL STRUCTURE IN X-RAY SPECTRA OF MOLECULES L.N. Mazalov, F.K. Gel 'mukhanov, A.V. Kondratenko, and V.I. Avdeev Institute of Inorganic Chemistry Novosibirsk, USSR We suggested a theory of a vibrational structure in X-ray spectra of molecules in a one-particle approximation in [1]. An X-ray fluorescence arises as a result of an inelastic scattering of an X-ray photon with a frequency w by a molecule (h=m=e=l) do „ i M in I? „ r / i , , ~vk~ , » vk\ dfi ivk ' vi ki ' ^ v £ v k vk ' i vk+ vi i A - i vi+ in < n u v y n ,• > ly vK 1 ' Vi Vi ' | |2 \i [ w - (£ k ■ E i + w n vi + Ae " w n vk - Ae )] + n 2 = G(u') + IG(co'). (1) (1) Here G(w')- the main member, IG(u)') describes an interference between vibrational sublevels of intermediate states. An absorption cross section of a photon with a frequency u> has a form r I I vl + In 12 2 C-Vi Vl G-, ^ Z. I W , i a Vl ' Vl ' r / . A "VI , . Vlx-,2 . r U) vl v 1 vl 4 vi+ i a i? j i A i ^k+ vi |0 > I vi In Eqs. (1) and (2) ! < n . y v 1 6 >| 2 and < n , i i 1 vl vk vl -Franck-Condon factors, U - the unitary shift operator. A vibrational structure in X-ray and ESCA- spectra of molecules N 2 , CO, BF, HF, HC1 are calculated from Eqs. (1), (2). A good agreement with experiment is obtained, when experimental data are available [2], References 1. F.K. Gel 'mukhanov, L.N. Mazalov, A.V. Nikolaev, A.V. Kondratenko, P.I. Wadash, V.G. Smyrny, A. P. Sadovskii, Dokl . Acad. Nauk SSSR 225, N3 (1975). o 2. L.O. Werme, J. Nordgren, H. Agren, C. Nordling and K. Siegbahn, UUIP-876 (1974). 53 SOFT X-RAY ABSORPTION OF MOLECULAR ALKALI -HAL IDES K. Radler, B. Sonntag, and H.W. Wolff II. Institut fur Experimentalphysik, Universitat Hamburg, D-2000 Hamburg, Germany The absorption spectra of molecular LiF, LiCl, NaCl, CsF, CsCl, and CsBr have been determined in the energy region of the Li + ls, Na + 2p,2s and Cs + 4d transitions. The alkali-halide vapours were contained in a tubular furnace mounted in front of a 2 m grazing incidence spectrograph. The synchrotron radiation of the 7.5 GeV electron synchrotron DESY, trans- mitted through the vapour column, was registered on photographic plates bent along the Rowland circle. The absorption bands dominating the spectrum of molecular LiF at the on- set of the Li + ls transition are presented in Fig. 1. Due to the high concentration of dimers present in the vapour there is a considerable overlap of the spectra of LiF and LioF2. By analyzing the vibrational structure superimposed on the broad bands the contributions of monomers and dimers can be separated. The assignment of the bands (lj, based on SCF calculations, is indicated in Fig. 1. a. a ' LiF molecule J 1 I l I L J I I I I I L 55 60 65 PHOTON ENERGY (eV) 70 Fig. 1 Li + ls absorption of molecular and crystalline LiF 54 -5 1 — l — i — r T — I — | — l — I — i — l — f / \ i — i — r NaCi molecule PHOTON ENERGY (eV) Fig. 2 Na + 2p,2s absorption of molecular and crystalline NaCl A doublet shows up at the threshold of the Na + 2p excitations in molecu- lar NaCl (Fig. 2). Towards higher energies this doublet is followed by absorption bands, which show a rich vibrational fine structure. The low energy doublet and the maximum at 50 eV are only given by a dashed line because of the uncertainties involved in the determination of the rela- tive heights. Transistions from the Na + 2s level give rise to the maxima at 64.5 eV, 67.5 eV and 70.2 eV. In the framework of a simple ionic model the absorption bands at the onset of the Na + 2p,2s transitions can be ascribed to transitions to final states mainly originating from the 3s, 3p and 3d states of the free Na + ion. The same final states have been invoked by Aberg and Dehmer for the interpretation of the exciton lines A to E detected in the spectra of crystalline NaCl [2} . Above 45 eV there is a striking similarity of the spectra of molecular and crystal- line NaCl. Close correspondence has also been found between the Cs + 4d spectra in molecular and crystalline CsCl (3j . The absorption spectra of molecular 55 and crystalline CsF, CsCl and CsBr at the Cs + 4d threshold are presented in Fig. 3. In all molecular spectra there is a weak peak A at the onset followed by four prominent bands B,B' , C,C'D. The separation of B,B' and C,C' is determined by the spin orbit splitting of the 4d hole. These bands are due to transitions of the Cs + 4d electrons to final states with dominant Cs + 6s,6p parentage. Going from the molecular Cs halides to the crystalline Cs-halides the small peak A persists where- as the maxima B,C and B',C' coalesce. The strong band E showes up at almost the same energy in all spectra. In contrast to this the other maxima shift considerably. The insensitivity of the peak position to the environment supports the assignment of E to transitions to highly localized f-symmetric final states. This is in agreement with Hartree- Fock calculations for the Cs + 4d 9 4f states. 1. K. Radler, B. Sonntag, T.C. Chang, and W.H.E. Schwarz, Chem.Phys . \3 t 363 (1976) 2. T. ftberg and J.L. Dehmer, J.Phys. C6, 1450 (1973) 3. K. Radler and B. Sonntag, Chem.Phys .Lett . 39, 371 (1976) CsF o CD < CsCl CsBr solid _ Fig. 3 Cs 4d absorption of mole- cular and crystalline CsF, CsCl and CsBr. 76 80 84 PHOTON ENERGY(eV) 56 INTERPRETATION OF THE X-RAY EMISSION AND PHOTO- ELECTRON SPECTRA OF SIMPLE SOLID COMPOUNDS G-.Leonh.ardt, A.Kosalzow, H.Sommer, M.Petke Sektion Cheuie der Karl-Marx-Universitat , DDR-701 Leipzig, Linnestr. 2 We have investigated the electronic structure of the va- lence bands of some A B - and ApB^-componnds using X-ray emission and photoelectron spectroscopy. The Ge KB emission and K absorption spectra of GeS and the As KB band of AspOo were measured with a double crystal spectrometer (secondary excitation, experimental resolution about 1 ♦ 5 eV) [1,2]. The photoelectron spectra excited by UV- and Al fry-radiati- on (VG instrument, resolution 0.2 and 1.2 eV,resp.) were got from evaporated samples of GeS, GeSe, GeTe, ASpO^AspS^, SbpOo, and BipO^ (base pressure 10" torr, substrate tempe- rature 20 C) . The results are shown in fig. 1-3 and tab.1 . Having in mind the interpretation of the valence bands of the A B and A B crystals [3,4,5j one can conclude: 1 .) The valence band is built up from two lower bands with mainly s-character and several p-bands on the top. The sym- metry character of the states can be derived from the X-ray emission (see fig.1 and 2). For an exact calculation of the shape of the X-ray spectra, a computation of the transition probability involved is needed T6J. In the calculation of the photoelectron spectra, there are important cross pro- ducts ill and final hole state effects [8] . 2.) The energy distnace between the s-bands and the width of the antisymmetric gap can be described by a chemical bond parameter with an accuracy of several 0.1 eV. A model including covalent and ionic partsjgives better agreement with the experiment than a pure ionic model including Made- lung and polarisation corrections. The ionic part can be described via a Madelung energy. Conclusions concerning the absolute energy scale of the spectra can also be made. 57 GeS XES Ge XES S Ef«VJ Getp S3p Ge4$ S3$ Fig. 2 Photoelectron spectra and the As KB emission band Fig.1 Photoelectron spectra excited by X- and UV-radia- tion and Ge KB- and S KB- eraission bands of GeS (in the lower part are given the atomic ionization ener- gies) if? Fig. 3 X-ray photoelectron spectra of AspCU, SbpCU, BipOo, and ASpS^ iWl 58 3.)^he p-bands on the top of the valence band can be descri- bed by an LCAO-model. For the IV-V1 compounds we have got. a good agreement between experiment and such a calculation L"9J Table 1 . Energies of characteristic structures of the spec- tra (all values in eV relative to the top of the valence band) Label of the Bi 2 0o Sb 2 3 As^O^ As 2 S 3 GeS GeSe GeTe structure 1 2.9 1 .8 3.6 2.0 2.2 1.9 1.5 1 ' 3.3 4.5 2 4.5 3.7 5.55 4.2 3.^ 3.0 3.0 2' 6.8 4.4 6.45 6.9 4.0 3 5.5 7.65 11 .2 4.9 4.15 4.5 3' 8.6 10.5 6.6 6.5 6.4 4 9.9 13.35 15.0 8.1 8.2 8.2 4' 11 .0 15.3 11 .5 11 .5 9.8 5 22.0 23.2 13.6 13.9 12.5 5' 19.0 20.6 Width of p-states 6.8 8.6 10.5 6.9 6.6 6.5 6.4 Width of the valen- 24.7 25.5 18 15.8 15.8 14.7 ce band References 1 A.Kosakow, G.Graeffe a.o., to be published 2 I. Topol, J. Tilgner, G.Leonhardt ,A.Meisel,J.Phys.Chem.Sol. 35(1 97 4), 1657 3 S.P.Kowalczyk,L.Ley a.o., J.chem.Phys. 61 (1 974) ,2850 4 G.Leonhardt, J.Electr .Spectr. 5(1974), 603 5 G.Leonhardt,A.Kosakow,H.Sommer,Proc.Int.Symp.ESCA, Kiew 1975, in press 6 I.Topol, K.Unger a.o., phys. stat. sol.(b) 61(1974), 485 7 A.Kosakow, K.Unger , G.Leonhardt, phys. stat . sol. , in press 8 A.Kosakow, E.Kurma jew, G.Leonhardt, to be published 9 A.Kosakow, H.Neumann, G.Leonhardt, to be published 59 TI- THE OXYGEN X-RAY EMISSION SPECTRUM OF SOME OXYANIONS N. Kosuch, E. Tegeler, G. Wiech and A. Faessler Sektion Physik der Universitat Munchen, 8 Munich 40, Germany The K-emission spectrum of ions of the type X0„ , X0_ , and XO " were excited in fluorescence using the synchrotron radiation of the storage ring DORIS in Hamburg and recorded in a 2m concave grating spectrometer with an open multiplier. The main intensity of the spectra with pronounced structures appears between 520 and 530 eV, a structure of very low intensity is observed at 500-510 eV. Positions and relative intensities of the structural features differ considerably depending upon the nature of the central atom and the symmetry of the anion. The nature of the cation is without noticeable influence . 2- 3- For many of the anions studied, as for CO and PO. , photoelec- tron spectra (XPS) of the valence states are available. In some cases where the binding energy of the Is level with respect to the vacuum level was determined, an unambiguous correlation of photoelectron and X-ray spectra is possible. In the examples mentioned above the X-ray spectra of the central atoms are also known. They provide additional information on the sequence and position of the orbitals and the symme- try character of the valence electrons. 2- 2- Fig. 1 shows the K- spectrum of CO . The C K-spectrum of CO was also measured and is shown below. The photoelectron spectrum and results of a MO-calculation (1) fitted to the main maximum of the K- spectrum are shown above. There is good correspondence between the ex- perimental observations. The calculated orbitals can be satisfactorily 60 [■rvB] X)|suajui W C o -H P as <-* u id o i S c. «' <0 u 4J u 0) a, en C o ■P o H a> o -P .c ft ro o c (d S H ■P O 0) ft W c o ^ -p u 0) a> p o ft I a. P •H 97 5 R. Prins and T. Novakov, Chem. Phys. Letters 16 (1972) 86 f E. Diemann and A. Miiller, Chem. Phys. Letters 12 (1973) 538 8 S.Foster, S. Felps et al. ; J. Amer. Chem. Soc. 21 (1973)5521 9 D. W. Fischer, J. Phys. Chem. Solids ^2 (197D 2455 10 A. P. Sadowski, Izv. Sib. Otd.Akad.Nauk SSSR, Ser. Chim. 2. (1975), 62 11 S. Foster, S. Felps et al., J. Amer. Chem. Soc. 21 (1973)6578 12 A. Miiller and E. Diemann, Chem. Phys. Letters 2 (1971) 369 63 ON TEE 1S-ABS0RPTI0N LINE SPECTRA. OP LI IN LITHIUM HALIDES AND OP B IN BCL^ AND BF^ T. Hayasi lijima-cho Nagano -ken Japan 399-37. and Y. Hayasi Department of Applied Physics , Faculty of Engi- neering, Tohoku University, Sendai Japan 930. 1. An attempt was made for interpretation of the chemical shift of absorption threshold and the line absorption spectra appearing near the threshold.- For this purpose we calculated the x-ray terms of free atom and ions. We considered also the bond dissociation energies, which are necessary to define the initial states of the atoms and ions. The resul- ts are compared with the measured absorption peaks of Li ls-absorption spectra in Li-halides and of B ls-absorption spectra in BCl* and BF^.In the following the method is illustrated by application to Li ls-absorp- tion spectra. 2, The Is-excited states of Li atom as a whole are approximately calculated by the following procedure. The Li Is 2 ion has two terms ls2s US as the lowest Is-excited states of the ion.Adding a 2s electron to these states results in two Li ls2s* a S, which are the low energy ls-ex- cited states of a neutral Li atom. For simplicity we assume that these two 2 S terms have the same energy separation as that of the parent terms, this assumption is approximately valid in the optical energy levels (l). The error is estimated about 10 per cent or less of the parent term separation. The method to obtain the term values of the two 2 S terms is as follo- ws. Adding a 2s electron to Be Is 2 2s and Li Is 2 2s leads to Be Is 2 2s 2 , Li Is 2 2s 2 respectively, where the spin of core Is 2 is d. If the spin of the Is electron in Li ls2s is ignored, which we denote by Is', then Li Is '2s becomes iso-electronic with Be Is 2 2s, Li Is 2 2s. Upon them we app- ly the procedure of iso-electronic sequence. The effective core charges Z^are defined by term values T of Lils2s 2 S, Be ls 2 2s 2 S and Li ls^s^S respectively, expressed as T= RhcZe/n a for n = 2, taking the core states Li ls z ,Be Is 2 ,Li Is' as T=0. Optically known term values of Li ls 2 2s 2 S, Bs ls 1 2s 2 S determine Z* of Li Is 2 and Be Irrespectively. For the term value of Li Is '2s, we assume Li Is 1 - Li Is '2s is equal to the mean value of Li Is - Li ls2s' 3 S, then we ob- tain the Z e for Li Is 5 . The term Be Is 2 2s 1 is optically known, referred to T=0 mentioned above, and the term Li Is 2 2s g is the sum of electron affinity 0.82 eV and Is 2 - ls 2 -2s. If we assume, as a modified Moseley's law, that the x-ray term value T is proportional to the effective core charge square Z\ , then the term Li Is'^s^ is obtained by linear interpolation. Subsequently the term Li ls2s a a S is obtained from Li ls'2s 2f S; sin- ce the separation ^S -^S in the parent terms approximately remains, the former lies lower than the latter by half "the separation of Li ls2s ^S terms. Another term Li ls2s( 3 S)2s 2 S lies lower than this by the separa- tion of the parent terms. So we find Li ls2s( 3 S)2s X S - Li Is 2 2s ^S =-54. 97 eV, This corresponds to the ls-excitation threshold of a free Li at- om, to which the transition from Is- 2 2s ^S is allowed by the selection 64 Aj=0,il for jj -coupling. This method is applied also to obtain the term of the ls-excited state ls2p(^ 3 P)2s 2 P or other states by repeating the procedure from the beginning. The energies of ls-excited states of Li atom of small quantum number, referring to the ground state, are shown in Table 1, Table 1. The ls-excitation energies from the ground state for Li atom in eV. Is2s( 3 S)2s 2-S 54.97 ls2s(3s)5s 2 S 62.37 ls2s( 198.3 199.51 197.74 199.17 c 200.7 200.41 d 202.3(202-203) 201.85 201.93 205.03 e 205.8 204.85 205.95 2 04 4-7 (20^.5-209) 207.59 207.47 208.57 f 212(210-212)210.01 5. In conclusion the ls-absorption line spectra near the threshold of the bonded atom are interpreted as the ls-excitation spectra of free atom shifted by the energy of bond changes, or the superposition of tho- se spectra. (1) C.E. Moore, Atomic" Energy Levels I, NBS-Circular 46j_ 1949, Cf. e.g. II 3s «*, 3s f 2 D, 3s" 26. (2) B.deB. Darwent, Bond Dissociation Energies in Simple Molecules, NSRD S-N3S 31. 1970. V.I. Vedeneyev et al, Bond Energies, Ionization Pot- entials and Electron Affinities, Acad T Sci. USSR Moscow I962. (3) R. Haensel, C. Kunz and B. Sonntag, Phys. Rev. Letters 20 262, I968. (4) B.A. Fomichev and R.P. Barinski, J. Str. Chimi, 11 875, 1970. (5) B.A. Fomichev, Ph.T.T. , £ 5167, I967. 66 RESONANT X-RAY RAMAN SCATTERING FROM SOLIDS P. M. Platzman Bell Laboratories Murray Hill, New Jersey 0797^- Historically x-ray scattering has been one of the oldest and most useful tools for the investigation of the microscopic properties of solid state systems. [1] Until about ten years ago most of the applications utilizing x-rays were confined almost exclusively to elastic or Bragg scattering. Recently there has been a renewal of interest in the phenomenon of inelastic x-ray scattering. [2] This rebirth owes its origins to the availability of new and more powerful sources of x-ray radiation including synchrotron radiation In a typical inelastic scattering process for a photon of frequency o)]_ most of the information is contained in the angle of scattering (momentum transfer k = 2k]_sin0/2) and frequency shift od = o^-coi • In some cases the relevant cross sections can depend on the frequency of the incoming or outgoing photon if this frequency is near a resonant absorption frequency for the system. In this talk we will focus on several aspects of the frequency dependent inelastic scattering of x-rays from simple metals. Qualitatively the general properties of such scattering arises from the nature of the one electron excitation spectrum of such materials. (See Fig. 1) Electrons occupy levels starting with K shell which are bound for materials like Cu by thousands of electron volts . The electrons in the L shell are typically bound by hundred's of electron volts while those electrons in the conduction band have energies in the several electron volt range . X-rays which scatter from such a system leave it in varying states of excitation which are well separated in energy. The excitation of conduction electrons leads to so called plasmon and Compton scattering The excitation of the L and K shell electrons has been called x-ray Raman scattering. Since x-rays which have 67 a* _i_ Fig. 1 the appropriate wavelength to probe the microscopic spatial behavior of the outer electrons are in the 10 KeV range, the resonant process which is involved in all such scattering experiments involves the virtual excitation of a K electron. No scattering experiments to date have investigated the real excitation of such a K shell electron In this talk we will consider two kinds of resonant processes. In the first a real hole is left in the L shell leading to Raman scattering while in the second, a hole is left in the conduction band leading to Compton scattering. Schematically the basic coupling of nonrelativistic x-rays is given by, c = /^[skp^+r^p* 2 ! • ^ Here A is the vector p the density and P the momentum density of the electronic system. In general the P «A term taken to second order is small unless a resonance exists. To lowest approximation the second order matrix element for L shell Raman scattering is _ .^ 1 |s> M ti - m(cD 1 -e k -O k +ir K ) ( 2) Here |S)>, |p^> are the one electron K and L shell wave functions and r^; is the K hole lifetime. The resonance is immediately put into evidence . The matrix element given in Eq. 2 is strictly one electron in character and is obtained by evaluating dipole matrix elements of the momentum operator p* between various filled and empty levels . In reality the excited electrons and holes may interact with one another and with the sea of electrons which remain by means of coulomb interaction. Since the Raman scattering experiments of Sparks, [3] Eisenberger, Platzman and Winick[4] are extremely new and in many ways rather crude we will discuss these experiments within the framework of the one electron approach. This approach gives an accurate description of all such experi- ments to date. The inclusion of both the K and L shell lifetime in a detailed analysis of line shapes and posi- tions predicts a variety of interesting resonance phenome- non which have been observed. These phenomenon are analogous to, but not precisely equivalent to, similar phenomenon in the visible. One of these effects, the narrowing of the inelastic spectrum as one approaches resonance is shown in Fig. 2. We will discuss this effect in some detail. 68 For Compton or conduction electron scattering the nonresonant situation has developed rapidly over the last few years and much information regarding elec- tronic wave functions and collective modes in simple metals has been obtained .[ 5] f However, at this writing no experiments on resonant Compton scattering exist. A theoretical investigation of this phenomenon indicates that a variety of v -7 -5 -5 -4 -3 -2 -i interesting physical AE R anc * the differ- ential cross section can be denoted by d 2 °~ _ / e z x 2 . k s 2 l+cos 2 e _ , . d^TdT" ( "^ 1r) ( T7 } 2 S(^tf), S(q,u)= 2 I \\*Sl?io)-(E F -E o )] Assuming a rigid lattice and in the one-electron approxima- tion, the dynamical structure factor S{q 3 id) can be express- ed using one-electron wave functions: s(«^)= 2 E|| 2 £[*„-(?,-£,)] _ (a) Compton scattering: S Comp^»>lk)*! Si * W -^ ik + f)2 ~ Hl } Ik. (b) Raman scattering: In the dipole approximation S{q 3 u)) can bewritten as: S Ram (q 3 u))=N K q 2 e-T{id)-e 3 where T(*0= L** $[ floi - ( £ f - E *)]< f^T \ f K >. T(ti>) is known as the K-absorption tensor. The dipole ap- proximation is satisfied when qa K ^l, where a^ is the mean radius of the K-electron orbital. (c) Plasmon scattering is a collective excitation, in con- trast with the above two cases. However, since q is small, it is a modulation of the ground state. Therefore, it can also be expressed by an individual excitation formula simi- lar to that for Compton scattering. Using the random 72 phase approximation, Sicg^u) for plasraon scattering is s 7 / ,,\- o % (fia-fiu ), where w^ depends upon the plasmon frequency and the Fermi velocity. From the above described dynamical structure factors, the profile of each spectrum and dispersion relation can be seen. The Compton profile is parabolic, corresponding to the area of a section of the Fermi sphere for the ideal electron-gas model. However, a small modification due to the anisotropy in the electron momentum distribution or the many-body effect can be seen. The Raman profile corresponds to that of K-absorption depending upon the unoccupied state density above the Fermi level. The plasmon profile is of the ^-function type due to the definite energy of the plas- mon oscillation. The dispersion relations for Compton and plasmon scat- tering are well-known and are given by -fi z j /., 3 q 2 V F x (J= o — q and w=w ( 1 + -r-r- — ) , 2m H p v 10 u ' ' respectively, where q is the plasmon frequency and V F is the Fermi velocity. ^ Raman is scarecely dispersive. Usually it is thought that Compton scattering is as- sociated with nearly free valence electrons and Raman scat- tering is associated with bound electrons, and that Raman scattering should appear as spectral lines. However, gen- eraly speaking, this is not valid. The difference between the conditions for the two types of scattering is decided only by the value of qa 3 where a is the mean radius of the orbit of the target electron, in general. For Raman scatt- ering, qa < 1 and for Compton scattering, qayl. Details of the features of each type of scattering will also be discussed. Literatures can be seen in the references of the fol- lowing articles: B. I.Lundquist and C.Lyden, Phys.Rev.B. 4(1971)3360 G. G. Cohen, N.G.Alexandropoulos and M.Kuriyama, Phys.Rev.B. 8(1973)5427 P.Eisenberger ,P.M.Platzman and K.C.Pandy, Phys. Rev. Lett. 31(1973)311 T.Suzuki and H.Nagasawa, J. Phys . Soc. Japan 39(1975)1579 73 in c .2? I— • c o <_> 100 Energy Loss 200 (eV) Spectra observed at different scattering angles. Symbols E,R,C and P indicate respectively the TDS , Raman, Compton and plasmon scattering peak. Although not presented in this figure, the plasmon peak can be observed at the scattering angles, G =10*~50°. The peak of the Raman band does not shift appreciably with scattering angle. T.Suzuki and A.Tanokura, J.Phys.Soc. Japan 29(1970)972 T.Suzuki and H.Nagasawa, J .Phys. Soc. Japan 39(1975)1579 74 SHAPE RESONANCE EFFECTS IN X-RAY ABSORPTION SPECTRA OF MOLECULES* J. L. Dehmer Argonne National Laboratory, Argonne, Illinois 60439 and Dan Dill Department of Chemistry, Boston University Boston, Massachusetts 02 215 Following the key measurements of x-ray absorption spectra of SFg [1/2] ten years ago, a burgeoning body of data (see, e.g., [3-7]) demonstrate that spectra of deep molecular core levels depart markedly from the corresponding atomic spectra, especially within a few tens of volts of the inner-shell threshold. Although inner-shell photoabsorption takes place ia essentially an "atomic" local environment, the subsequent escape of the photoelectron through the molecular field causes a major redistribution of oscillator strength over tens of volts. In particular, molecular inner-shell spectra commonly exhibit strong concentrations of oscillator strength in narrow bands both below and above threshold, in contrast to the monotonic decrease characteristic of the corresponding spectra in the free atom. Based on this very suggestive empirical evi- dence, early interpretations [8—12] postulated an effective potential barrier on the perimeter of the molecule which blocked the classical escape of the photoelectron and led to shape resonances and related quantum mechanical effects in the molecular spectrum. A more concrete under- standing of these new phenomena required a realistic and practical means for computing molecular photoionization cross sections which was not then available. Fortunately, the multiple -scattering method, adapted to molecular photoionization two years ago [13], has succeeded in several cases [14- 17] to reproduce and reveal the cause of resonance features in molecular inner-shell spectra. In our work on the K-spectra of N2 [14,17] , we have reproduced nearly all prominent features in the discrete end con- tinuum parts of the experimental spectrum and have predicted the cor- responding photoelectron angular distributions [14,17,18]. This de- tailed prototype system demonstrated conclusively that the resonance features in the N2 K-shell spectrum are caused by centrifugal barriers acting on high-i components of the final state wavef unction. Specifical- ly, &= 2 and £=3 shape resonances are observed below and above the K-shell edge, respectively. 75 At the conference we will present new results which emphasize developments in two areas: (1) Energy dependence of photoelectron angular distributions from oriented molecules. [18,19] These calcula- tions bear on future experiments on molecules adsorbed on surfaces and oriented by molecular beam techniques. Moreover, they have great pedagogic value as they express the complete spectral and spatial aspects of the photoionization process. A highlight of this study is the distribution for the case of K-shell photoionization of N£ and CO. If the electric vector is parallel to the molecular axis, the I = 3 shape reso- nance described earlier is reflected as a narrow band (in energy) of en- hanced photocurrent with f-type symmetry. (2) Examination of inner- shell photoionization in other simple molecules, e.g. , acid halides and halogens [20] . FOOTNOTES AND REFERENCES * Work performed in part under the auspices of the U.S. Energy Research and Development Administration. Alfred P. Sloan Foundation Fellow. 1. R. E. LaVilla and R. D. Deslattes, J. Chem. Phys. 44, 4399 (1966). 2. T. M. Zimkina and V. A. Fomichev, Dokl. Akad. Nauk USSR 169 , 1304 (1966) [Sov. Phys. Dokl. U, 726 (1966)]. 3. T. M. Zimkina and A. C. Vinogradov, J. Phys. Paris 32 , Colloque C4, 3 (1971). 4. V. A. Fomichev, Fiz. Tverd. Tela. 9., 3167 (1971) [Sov. Phys. Solid State 9., 2496 (1968)] . 5. G. R. Wight, C. E. Brion, and M. J. van der Wiel, J. Electron Spectrosc. 1_, 457 (1973). 6. See also reference 12 for a discussion of numerous other data. 7. G. R. Wight and C. E. Brion, J. Electron Spectrosc. 4, 313 (1974). 8. R. L. Barinskii, Proceedings of the International Symposium on X- Ray Spectra and the Structure of Matter , Kiev, USSR, September 1968, p. 222. 9. V. I. Nefedov, Zh. Strukt. Khim 11., 299 (1970) [J. Struct. Chem. H, 277 (1970)]. 10. V. A. Fomichev and R. L. Barinskii, Zh. Strukt. Khim. \\_, 875 (1970) [J. Struct. Chem. \\_, 810 (1970)]. 11. R. L. Barinskii and I. M. Kulikova, Zh. Strukt. Khim. 14, 372 (1973) [J. Struct. Chem. 14, 335 (1973)]. 12. J. L. Dehmer, J. Chem. Phys. 56., 4496 (1972). 13. D. Dill and J. L. Dehmer, J. Chem. Phys. 61, 692 (1974). 14. J. L. Dehmer and Dan Dill, Phys. Rev. Letters 35., 213 (1975); also J. Chem. Phys. , to be published. 76 15. V. P. Sachenko, E. V. Polozhentsev, A. P. Kovtun, Yu. F. Migal/ R. V. Vedrinski, and V. V. Kolesnikov, Phys. Letters 48A , 169 (1974). 16. L. N. Mazalov, F. Kh. Gel'muskhanov, and V. M. Chermoshentsev, Zh. Strukt. Khlm. 15., 1099 (1974) [J. Struct. Chem. 15., 975 (1974)]. 17. J. L. Dehmer and D. Dill, Proceedings of the 2nd International Con - ference on Inner-Shell Ionization Phenomena , March 29— April 2, 1976, Freiburg, West Germany, to be published. 18. D. Dill, J. Siegel, and J. L. Dehmer, J. Chem. Phys., to be published. 19. D. Dill, J. Chem. Phys. , to be published. 20. J. Siegel, D. Dill, and J. L. Dehmer, to be published. 77 PARTIAL PHOTO IONIZATION CROSS -SECT IONS IN THE SOFT X-RAY REGION* t>y I. Lindau, P. Pianetta , and W. E. Spicer Stanford Synchrotron Radiation Project and Stanford Electronics Laboratories Stanford University Stanford, California 94305 In this paper, we report on the experimental determination of the partial photo ionization cross-section [1] for a few subshells (3d, 4d , 4f) from the ionization threshold and a few hundred eV up by using the photoemission technique. The measurements were done at the Stanford Synchrotron Radiation Project utilizing the synchrotron radiation from the SPEAR storage ring [2]. Synchrotron radiation from this source pro- vides an intense, continuous spectral distribution from the infrared into the hard X-ray region [2]. A grazing incidence monochromator [3] was used to monochromatize the radiation in photon energy region 32-400 eV. The average distributions of the photoemitted electrons from the different subshells were determined by a double-pass cylindrical mirror analyzer. The experiments were performed on solid surfaces under ultra high vacuum conditions, 10~H Torr [4]. In Fig. 1, we present experimental data for the energy dependence of the cross-section of the 3d levels for Ga and As. The Ga and As 3d levels are, located 19 and 41 eV, respectively, below the Fermi level [5] and the energy dependence can thus be followed continuously from thresh- old to about 3 50 eV above threshold. The experimental points in Fig. 1 are obtained from the photoemission experiment where the energy distri- bution of the photoemitted electron is measured and can be plotted as a function of the electron binding energy. The energy dependence of the photoionization cross section is then quite simply obtained by measuring the area under the photoelectron peak as a function of the excitation energy making proper normalizations for the incoming photon flux and the transmission of the energy analyzer. Thus, the energy dependence of the partial cross-section can be mapped out in detail from the threshold and up. As seen from Fig . 1, the 3d photoionization cross-section for Ga (and As) has a weak energy dependence with a broad maximum 70-80 eV above threshold and a mono tonic decrease towards higher energies « The experimental results are in good agreement with Kennedy and Hanson's calculation [5] for the 3d levels of gaseous krypton. The 4d partial cross section for In and Sb is plotted in Fig. 2 as a function of electron energy above threshold. The experiin ital data are shown as crosses. The cross-section goes through a maximum at45eV above threshold and then decreases rapidly before passing through a broad minimum around 130 eV. A flat and extended minimum is observed about 220 eV above threshold before the cross section starts to decrease 78 -a po z- O b Ss n2 x * " " * » „ oH SljJ Oc/i X 1- 1 X Oco X X ICO X Q-O cr o 1 1 l 1 1 -.1 .__ 50 100 150 200 250 ENERGY ABOVE THRESHOLD (eV) 300 Fig. 1 Partial photo ionization cross section (relative units) for 3d levels as a function of electron energy above threshold (x = exper- imental points). monotonically towards higher energies. Overall, the 4d partial cross section has a very dramatic energy depen- dence for the first 200 eV above threshold . The minima observed at 130 eV is termed the Cooper minima [7,8] and arises from the fact that the 4d wave functions have nodes . In comparison, the 3d wave functions do not have any nodes, and the cross-section shows a weak energy dependence as pointed out in connection to Fig . 1 . The solid line in Fig. 2 is the theoretical calculation of the atomic 4d levels in Xe by Kennedy and Manson [6] , again using Hartree-Fock wave- functions and in the length approximation. The relative amplitudes of the theoretical curve and the experimental data have been fitted at the peak 45 eV above threshold. In overall, there is thus a remarkable agreement between theory and experiment with the energy positions of two maxima and the Cooper minimum reproduced. The cross-sections for the 3d and 4d levels for elements (solids) in the 3rd and 4th rows of the pe- riodic table are thus in good agreement with Kennedy and Manson 's atomic one-electron Hartree-Fock calculations for the corresponding noble gases [6]. However, care should be taken to generalize these results indis- criminatorily to other subshells where shake-up [9] , shake-off [9] , col- lective resonances [10,11], and other effects may considerably compli- cate the picture. The photo ionization cross -sect ions of the 4f levels (e.g., in Au, Pt , W) show a very slow onset at the threshold and a photon energy about twice the threshold value is required before they gain considerably in strength [12]. Again, this energy dependence can be understood from a one-electron picture , where electrons from any energy level with high angular momentum have a large repulse barrier to overcome. The effec- tive potential contains a centrifugal term, which becomes important for f -> g transitions. In conclusion, we want to emphasize that the availability of syn- chrotron radiation makes it possible to map out in detail experimentally the energy dependence of the partial photoionization cross-section from threshold and up in the soft X-ray region. In the case of the 3d and 4d subshells for elements in the 3rd and 4th rows of the periodic table, good agreement is obtained for the general energy dependence with one electron Hartree-Fock calculations by Kennedy and Manson [6] for the corresponding subshells of the noble gases. 79 REFERENCES < Work supported by ARPA, NSF, and ONR. 1. I. Lindau , P. Pianetta , and W. E. Spicer, Phys . Letters A (in press). 2. S. Doniach, I. Lindau, W. E. Spicer, and H. Winick, J. Vac. Sci . Technol. 12, 1123 (1975). 3. F. C. Brown, R. Z. Bach- rach, S. B. M. Hagstrom, N. Lien, and C. H. Pru- ett , in "Vacuum Ultravi- olet Physics," ed . by E . E. Koch, R, Haensel , and C. Kunz (Pergamon, New York, 1975), pp. 795-798. >o. / X X \ O b / <£' / \ mO XI \ 1 ZH 1 \ o<-> / \ — UJ \ Oin / \ h- 1 \ O / \ Q.O / \ q: / \ u 1 \ J "\ X x X X X X X 1/ 1 1 x -x — — H 1 . 1 — =*• 1 50 100 150 200 250 300 350 ENERGY ABOVE THRESHOLD (eV) Fig. 2. Partial photoionization cross section (relative units) for 4d lev- els as a function of electron energy above threshold (x = experimental points, solid line = theoretical curve from Kennedy and Manson [6]). 4. I. Lindau, P. Pianetta, K. Y. Yu , and W. E. Spicer, J. Vac. Sci. Technol. 13, 269 (1976). 5. P. Pianetta, I. Lindau, C. M. Garner, and W. E. Spicer, Phys. Rev. Letters 35, 1356 (1975). 6. D. J. Kennedy and S. T. Manson, Phys. Rev. A 5, 227 (1972). 7. J. W. Cooper, Phys. Rev. 128, 681 (1962). 8. U. Fano and J. W. Cooper, Rev. Mod. Physics 40, 441 (1968). 9. M. Mehta , C. S. Fadley, and P. S. Bagus , Chem. Phys. Letters 37, 454 (1976). 10. M. Y. Amusia and N. A. Cherephov , Case Studies in Atomic Physics 5, 47 (1975). 11. G. Wend in, in "Vacuum Ultraviolet Physics," ed . by E. E. Koch, R. Haensel, and C. Kunz (Pergamon, New York, 1974), pp. 225-240. 12. I. Lindau, P. Pianetta, K. Y. Yu, and W. E. Spicer, Phys. Rev. B 13, 492 (1976). 80 X-RAY RESONANCE SCATTERING BY ATOMS WITH A PARTIALLY EMPTY LOCALIZED SUB-SHELL. C. BONNELLE and R. BARCHEWITZ Laboratoire de Chimie Physique, 11, rue Pierre et Marie Curie - 75231 Paris Cedex 05 - France. The theoretical treatment of the scattering of light by atomic electrons had shown that the scattering cross section is very large if the incident radiation frequency, *9 , becomes equal to one of the characteristic atom frequencies, ^ . Then, the variation of the cross section must present a very sharp maximum in the neighbour- hood of >> = >£ (1). This process is called resonance scatte- ring of light or resonance fluorescence. It is possible to suppose that the resonant ampli- tude is much larger than the sum of the non-resonant amplitudes. In this approximation, the expression of the amplitude scattered by a sample in the vicinity of V = ^c is proportionnal to the probability of finding a strongly resonant state R which may be formed by the absorption of a photon. Indeed, such a resonant state is surely present if a resonant line is observed in the X-ray emission spec- trum of the sample at the frequency >> c (2) (3) .Thus, we thought it would be interesting to study the amplitude scattered by various solid samples whether they contained atoms with a partially filled localized sub-shell or not. We have attempted to analyze the intensity scatte- red elastically in the forward direction under specular reflection conditions. The distribution of X-rays reflected by films deposited on mirrors has been recorded under glancing angles between 10 and 80 mradians in the neigh- bourhood of a characteristic absorption. A large number of different substances have been used (4) . From our results we class these in two groups : in the first, the distribu- tion of X-ray radiation after reflection by the mirror is analogous to an absorption spectrum whatever the glancing angle ; in the second, a large variation in the spectrum is observed with a changing glancing angle and, for a value of the angle which is function of the wavelength, we observed an intense asymmetrical line situated towards the higher energies of the absorption line (figures 1 and 2) . Its intensity is about 15 % at 70 mradians after reflec- tion by La~0_ in the neighbourhood of the My absorption. The observed phenomena are complex because it is necessary to take into account the variation of the refrac- 81 tive index in the anomalous region. However, it seems at present that intense lines can be observed only in the I^L and M spectrum of the reflected intensity by samples containing a rare earth element. Thus during the interaction with the photon, the rare earth atom can be excited to a strongly localized virtual state and the process of de-exci- tation to the fundamental state is the most probable one be- cause the speed of this transition is very large with res- pect to that of other interactions of the excited state in the solid. Before a complete interpretation can be given many other experiments must be made in particular for samples containing transition elements. These results are of interest both from a fundamental and an experimental point of view m In fact this is a method for selecting a narrow energy band-pass (2 to 3 eV at 1 200 eV) with an intensity of up to 50 % of the incident radiation. REFERENCES (1) W. HEITLER- The quantum theory of radiation, Oxford University Press, 3 r( ^ edition 1970. (2) C. BONNELLE, R.C. KARNATAK, J. de Phys . 32^, C4-23 1971. (3) C. BONNELLE, Structure and Bonding Vol. 31 to be published. (4) R. BARCHEWITZ - These de Doctorat d'Etat, Paris, 1976. 82 La 2 3 Emission --~ — Absorption La 2 3 ' 30m rod) Yb 2 3 ( 20 m rod Energie - 83 WHITE LINES AND EXAFS : COMPLEMENTARY EFFECTS+ D. E. Sayers and E, A, Stern, Department of Physics, University of Washington, Seattle, Washington 98195 and F, W. Lytle, The Boeing Company, Seattle, Washington 98124 In this paper we discuss the extension of our studies of K edge absorption spectra to the L edges. Using the EXAFS on the L3 edge for structural studies would greatly expand the number of elements which can be studied by the EXAFS technique including Sm through the rest of the periodic table. A natural extension of these measurements has been a systematic study of the "white lines" (the large peak in the absorp- tion coefficient within ^ lOeV) of some L2 and L3 edges. We have found variation in these white lines with changes in the chemical environment of the element being studied thus providing information about the local electronic environment which complements the structural information from the EXAFS. To understand the origins of the "white lines" more completely we have studied the L2 and L3 edges of the elements W, Ta, Ir, Pt and Au as well as compounds of Ta, Pt and Au and catalysts containing Pt and Au. Qualitatively it has long been known that "white lines" arise from the high density of unfilled d states near the Fermi energy (1) , Recently, Brown, et al. (2) have made a quantitative study of Pt in- cluding band effects and have shown that the calculated strength of the white line at the L3 edge using band-calculation values for the number of d-holes of 0.3 is in agreement with the measured value. This quan- titative agreement does not extend to Ta and W which have a large number of holes. Our studies find that the measured strength of the white line is less than one would expect theoretically if all of the d holes contribute. We interpret this to mean that only a fraction of the d-holes closest to the Fermi energy contribute to the white line. The reason for this result is not fully understood. We have also found a considerable variation in the Ta L3 white line intensity for Ta, TaH, Ta205 and TaB2 whose changes, although in qualitative agreement with the number of holes expected on valence considerations, again do not agree quantitatively. Despite the lack of quantitative understanding for transition metals with large numbers of d-holes, it appears that for atoms with a small number of d-holes, such as Pt, there is a quan- titative correlation between the strength of the white line and the number of d-holes. Lytle (3) has carried out such a study with Pt catalysts and Pt compounds in order to understand the d character of these catalysts, demonstrating the usefulness of the white lines in understanding the electronic arrangement about a particular kind of atom in a complex system. To determine structure information from the L edge EXAFS we have applied the fourier transform techniques which have been successful in analyzing the K edge data. The additional complications of the L edge are that the initial p state can couple to both s and d symmetric final states so that the expression for EXAFS can be written as 84 X L - I A (k){y s (k)sin(2kr + 26 (k)) + y d (k)sin(2kr + 26,)} where Aj (k) is the amplitude of the EXAFS as described elsewhere (4), y s and y^ are tne relative probabilities of making transitions to final s and d states, respectively, and 6 S and 6^ are the total s and d phase shifts, respectively. As we have shown (5), the s and d phase shifts are significantly different so that for each shell there are two peaks in the Fourier transform, one for the p -*- s transitions and one for the p ->■ d transitions. The relative height of these two peaks are related to the appropriately weighted average of y s and y^ over the range of data which is transformed. By taking transforms of kN)(, (N=0,l,2,3) we have been able to determine y^/ys as a function of k which shows that p -*- s contributions dominate or are equal to p -*■ d up to k ^ 8&~1 after which p -*• d transitions then dominate. These measurements represent the first experimental measurements of these relative transition prob- abilities and are contrary to the usual arguments of complete domina- tion by p ■*■ d transitions. These studies do show, moreover, that once the doublet structure for each shell is understood then useful struc- tural information (particularly for the first neighbor) can be obtained as directly from L edge EXAFS as from K edge. To illustrate the use- fulness of L edge EXAFS we will show results from a study of a hetero- geneous catalysts (i.e. 1% Pt on SiG*2) which was examined in situ in a specially designed cell both after reduction by H2 at 400°C and after chemisorption by 0. The data show a clear rearrangement of the Pt atoms on the lattice after exposure to oxygen. In conclusion, studies of L edge absorption spectra from elements in complex environments can give information on both the electronic structure about the absorbing atoms by studying the white lines and the atomic structure by studying the EXAFS. t Supported by National Science Foundation Grant No. DMR73-02521, in cooperation with the Stanford Linear Accelerator and the U.S. Energy Research and Development Administration. * Present address - Department of Physics, North Carolina State Univer- sity, Raleigh, N.C. 27607. (1) N. F. Mott, Proc. Roy. Soc. 6_2, 416(1949). (2) M. Brown, R. E. Peierls, E. A. Stern, to be published. (3) F. Lytle, J. Catalysis (accepted for publication). (4) E. A. Stern, D. E. Sayers, F. W. Lytle, Phys . Rev. Bll, 4835(1975). (5) E. A. Stern, D. E. Sayers, F. W. Lytle, to be published. 85 EXTENDED STRUCTURE IN X-RAY PHOTOABSORPTION PRINCIPALS AND APPLICATIONS by P. Eisenberger, W. E. Blumberg, G. S. Brown, P. H. Citrin, B. M. Kincaid, J. Reed, and R. G. Shulman Bell Laboratories Murray Hill, New Jersey 0797^ The first portion of this paper will describe the underlying phenomena responsible for the extensive structure observed above the x-ray absorption edge extending in some cases to 1-2 Kev above threshold. Schematic and simplistic mathematical formulations of the electron backscattering model will be presented. The presentation will stress the techniques ability to provide important interatomic distance determinations between atoms of ones choice if one can de- termine the energy dependence of the phase shift which the recoiling electron experiences. Experiments on simple gaseous molecular systems will be described [1] and comparison with ab-initio calcu- lations [1] will be made. Initial Hartree-Fock calculation of the energy dependent phase shift provided only 5-10% accuracy in interatomic distance determination [1]. More recent Kohn-Shan type calculations yield phase shifts which allow 1 to 2% accurate interatomic distance determinations [2]. To attempt to improve the accuracy of interatomic distance determinations an attempt has been made to empheri- cally determine the energy dependence of the phase shifts [3]. The cornerstone of this empherical approach is the concept of the chemical transferability of the electron phase shifts; the phase for a pair of atoms (absorber and scatterer) is the same for all chemical environments for energies greater approximately 50 eV above the edge. The successful vali- dation of this concept will be presented. Examples will then be given of the ability to determine interatomic distances of importance to a wide range of scientific problems. Examples that will be discussed in detail will include the following: Biology 1. Rubredoxin 2. Hemoglobin 3. Ions in Membranes 86 Chemistry 1. Ions in Solutions 2. Catalysis - Solid, Liquid, and polymer bound Solid State 1. Single crystal anisotropy studies of zinc Following this presentation a summary of the current theoret- ical and experimental status will be given as well as a discussion of possible future studies. [1] Kincaid, B. M. and Eisenberger, P., Phys. Rev. Lett. 3^j_, 1361 (1975). [2] Lee, P. A. - Private Communication [3] Citrin, P. H., Eisenberger, P., and Kincaid, B. M., Phys Rev. Lett. 36, 13^6 (1976). 87 X-RAY PHOTOABSORPTION STUDIES OF SUPERCONDUCTING A15 COMPOUNDS 1 * 1 " G.S. Brown and L. Testardi Bell Laboratories Murray Hill, New Jersey 07974 High superconducting transition temperatures have been obtained for thin films of NbsGe prepared by sputtering at deposition temperatures in the neighborhood of 900°K. X-ray diffraction studies show that the material condenses principally in the A15 beta-tungsten phase. For lower deposi- tion temperatures the transition temperature is much lower, despite the fact that the crystal symmetry remains body-centered cubic. We have performed EXAFS measurements on the germanium and niobium K-edges of 4000 A sputtered Nb 3 Ge films. The samples were prepared at a variety of deposition temperatures, on both sapphire and silica substrates. The measurements were performed with the fluorescence technique, using a Ge semiconductor detector as well as a Nal scintillation counter, The EXAFS spectra were dramatically different among the samples, reflecting a large change in the interatomic distances. A preliminary analysis of the data indicates that the Ge-Nb distance contracts by about 0.2 & for the loc T c material, despite a slight expansion (0.02 K) of the lattice parameter. The data cannot be accounted for by reasonable vacancy concentrations or by anti-site disorder. Several models will be presented which are con- sistent with the X-ray diffraction data but which involve distortion of the atomic distribution within the unit cell. ft The experimental work was performed at the Stanford Synchrotron Radiation Project (SSRP) which is supported by the National Science Foundation Grant No. DMR73-07692, with the cooperation of the Stanford Linear Accelerator Center and the U.S. Energy Research and Development Administration. 88 EXAFS IN PHOTOELECTRON YIELD SPECTRA: COMPARISON WITH PHOTOABSORPTION AND DETERMINATION OF ELECTRON ESCAPE DEPTHS R. Haensel , G. Martens, P. Rabe, N. Schwentner, M. Skibowski, A. Werner Institut Fur Experimental physik Der Universitat Kiel Kiel , Germany K-shell photoelectron yield spectra of metal and insulator films prepared in situ under UHV conditions have been investigated above 3 keV photon energy. The spectra show a structure comparable to EXAFS in photoabsorp- tion spectra. From the increase of the electron yield with the angle of incidence of the X-ray beam electron escape depths are deduced. Due to the short escape depth the electron yield at grazing incidence of the light is sensitive to the surface properties of the sample. The possibi- lity to determine surface and overlayer structures will be discussed. 89 EXAFS OF A SINGLE CRYSTAL OF GALLIUM W.M. Weber Laboratorium voor Algemene Natuurkunde der Rijksuniversiteit Groningen. Westersingel 34, The Netherlands. In the last several years in Groningen the extended X-ray K absorp- tion fine structure (EXAFS) of single crystals of gallium and cadmium was investigated for different orientations of the wave vector k and the polarization vector P of the X rays with respect to the crystallographic axes of the absorber; the degree of polarization could also be varied. The results obtained for an effectively unpolarized beam, for nearly 100 % linearly polarized X rays and for 37 % polarization of the beam can be summarized as follows: the more dominant the K photoejection per- pendicular to the q axis of the gallium and the cadmium absorber, the more pronounced axe the gallium and cadmium K fine structures. No signi- ficant change in the positions of absorption maxima and minima was found D»2]. Interpretation of single-crystal Z-absorption data for polarized and unpolarized X rays were given by Kostarev [3 J and Izraileva [4j . In these interpretations the maxima and minima of the extended X-ray ab- sorption fine structure (EXAFS) are conceived as variations of transi- tion probability of the photoelectron due to elastic scattering of that electron from separate atoms in the nearest neighbourhood of the absorb- ing atom. In Kostarev' s theory, the relative absorption coefficient can be calculated for all orientations of the wave vector k and the electric vector £", encountered in the experiments, by giving the vectors k and E fixed but arbitrary orientations with respect to the crystal axes of the absorber. Kostarev' s theory gives good agreement with the experimental data for cadmium and especially for gallium in the energy region up to 300 eV from the main absorption edge. For gallium, the positions of EXAFS maxima and minima, the orientation effects, the general shape of the curves and some features of the hyperfine structure could be veri- fied [5-8] . If the electric vector E of a linearly polarized X-ray beam is pa- rallel to the c axis of a gallium single-crystal absorber, Kostarev' s theory predicts a very weak fine structure, and the appearance of two extra pairs of absorption maxima and minima in the energy region between 100 and 300 eV (see Fig. 1). To investigate this, measurements at liquid helium temperature were carried out on the gallium single crystal. An EXAFS pattern in satisfactory agreement with the calculated one was found. 90 100 150 200 250 300 ENERGY IN ELECTRON VOLTS ' Fig. 1. Four theoretical curves of the gallium K fine structure, calculated from Kostarev's theory for 28 scattering atoms. Curve 1 : Electric vector E of the X rays almost parallel to the a axis of the absorber. Curve 2: Angle between electric vector E and c axis 38 ; the vector E, the wave vector k of the X rays and the c axis lie in one plane per- pendicular to the plane of the absorber. Curve 3: Electric vector E almost parallel to the b axis of the ab- sorber. Curve 4: Electric vector E parallel to the c axis of the absorber. REFERENCES 1. W.M. Weber, Physica 28 (1962) 689; 30 (1964) 2219. 2. W.M. Weber, Phys. Letters 25A (1967) 590. 3. A.I. Kostarev, Fiz. Metal, i Metalloved. j_9 (1965) 801. 4. L.K. Izraileva, Doklady Akad. Nauk (USSR) K>8 (1966) 777; translation: Soviet Phys. Doklady jj_ (1966) 506; Doklady Akad. Nauk (USSR) \b9_ (1966) 1048; translation: Soviet Phys. Doklady JJ_ (1967) 709. 5. A.I. Kostarev, Fiz. Metal, i Metalloved. 20 (1965) 26. 6. A.I. Kostarev and W.M. Weber, Phys. Rev. B3 (1971) 4124. 7. W.M. Weber, Thesis, Groningen, 1972. 8. W.M. Weber, in X-ray Spectra and Electronic Structure of Matter 3 Pro- ceedings of the International, Symposium 3 Munchen, 1972, edited by A. Faessler, G. Wiech (Sektion Physik der Universitat Miinchen, 1973). 91 ON NEWER DEVELOPMENTS IN ISOCHROMAT SPECTROSCOPY K. Ulmer Physikalisches Institut, Universitat, 7500 Karlsruhe (FRG) Isochromat spectroscopy is fitted in the classical spec- troscopies and its peculiarities are given. It is emphasi- zed that isochromat spectroscopy makes disposable a new free parameter: The quantum energy hw of the radiative transition (Fig. 1). Contrary to the essentially fixed quantum energies of absorption edges for example , spec- troscopy at optimal quantum energies can be performed with continuum isochromats. An example utilizing this new degree of freedom is given. It concerns a simple absolute determination of the 2d- value of a spectrometer crystal. Result: 2d = (6.3390 ± 0.0005) nm for OHM (Octadecyl Hydrogen Maleate) [l] . As a second example illustrating successful cooperation of different spectroscopies a comparison is given of the lanthanum M-series emission-spectrum for nearly threshold excitation [2] to the structure of isochromats (superposi- tion of continuum and characteristic isochromats) [2] . The rich energy dependent structures of the spectra and of the isochromats can consistently be interpreted applying a theoretical electron-density-of-states (EDOS) of Glotzel (Fig. 2 and [4]) and a special two-electron-transition model. As a result of this consideration the essential features of the La-EDOS of Glotzel can be verified. The binding energy of the 3d 5/2-electrons in lanthanum for example turns out to be (831.0 ± 0.2) eV bringing this value nearer to expectations from XPS-energies [5] than from SXS-values given in the literature [6 J . Likely due to angular momentum conservation in connection with the 4f-electron states in lanthanum, both spectra and isochro- mats cannot be interpreted in a simple one electron pic- ture (Fig. 3) . q? brems- isochro- sp*ctrum mat Q5 cons*— E' -w war war -— hui -*■ const ,. S br*msspectrum isochromat Fig. 1 Skeleton sketch of continuum- isochromat and bremsspectrum with Rh-example. 20 10 states (atom- eV) ■1 0.1 eV 2.75 eV eV Fig. 2 f-e lee tron-density-of -state; of lanthanum after Glotzel (1976). Simplified version. 820 b) 5.AeV hw ,' t ' , eU* » 830 840 "eV 830 840 eV Fig. 3 a) La-spectrum (eV+$=836 , 5eV) measured by LBC 1974 b) La-isochromat (tiaj=831 ,OeV) measured by Riehle 1976 93 References : [l] Foil H.and Ulmer K. : Verhandl . DPG (VI) Y\_, 612 (1976). j2] Liefeld R.J. , Burr A.F., and Chamberlain M.B. : Phys. Rev. A9, 316 (1974). [3] Noll H., Riehle F. , and Ulmer K.: Verhandl. DPG (VI) 11 , 614 (1976) . Riehle F.: to be published. [4] Fritsche L. , and Glotzel D.: Verhandl. DPG (VI) 10, 541 (1975) . Glotzel D.: Diss. Clausthal FRG 1976 unpublished. [S] Bearden J. A. and Burr A.F.: Rev. Mod. Phys. 39, 125 (1967) . [6] Bearden J. A.: Rev. Mod. Phys. 39.' 78 (t967) . 94 X-RAY CONTINUA NEAR THE HIGH FREQUENCY LIMIT ELECTRON SOURCE Ef INITIAL STATE PHOTON ENERGY R.J. Lief eld and A.F. Burr - New Mexico State University Las Cruces, New Mexico, 88003 The x-ray continuum near the high frequency limit may be regarded simply as the result of inelastic scattering of incident energetic elec- trons into available states above the Fermi level of the sample with emission of a photon as diagrammed in Fig. 1. A more complete view must acknowledge the role of the matrix element of the transition and its energy dependence. It will be shown that this can be very important. The continuum in- tensity is then proportional to the density of available final states above the Fermi level times the matrix element for the transition from the par- ticular initial state to the particular final state. Hence elucidation of densities of states in solids from studies of continuum limit spectra is frustrated by the need to know part of the "answer", (final state wave functions) , to analyze the data to get another part of the "answer", (densi- ties of states). Other com- plications are the presence of secondary processes such as the excitation of surface or zszgszxssg SAMPLE 2: FIG.l. Simplified energy diagram of the continuum limit process bulk plasmons, (characteristic losses), of phonons, and of valence elec- trons, resulting in an "incident" electron spectrum in the sample which is not single valued. Also, the presence of the scattered electron may distort the electronic structure in the solid. Thus a complete view of the continuum near the high frequency limit regards the intensity as the convolution of the "incident" electron spectrum in the sample with the (possibly modified) density of final states above the Fermi level times the matrix element for the transition. At the N.M.S.U. x-ray physics laboratory continuous spectrum iso- chromats are recorded at a photon energy of 530 eV with a two crystal monochromator because a reflectivity peak of KAP crystals there yields high signal to background data, because the "incident" electron spectrum in the sample is more nearly single valued for the lower electron ener- gies, and because isochromats do not require corrections for spectral sensitivity. Their equivalence to continuous spectra for single energy incident electrons depends on the shape of the continuum near the high frequency limit being independent of incident electron energy over the range of interest. Such isochromat spectra have been corrected for spectral smearing by unfolding the spectral window of the monochromator and have been corrected for the non-single valued nature of the "inci- qc dent" electron spectrum by unfolding x-ray photo electron spectra of nearly the same energy as an approximation to the actual incident electron spectra in the samples. The results of studies of some of the first transition group and neighboring elements [1] and of Mg, A£, and Si [2], and comparisons with recent one electron densities of states calculations are convincing evidence that continuum limit spectra can yield useful information about the electronic band structures of solids. However, for some elements, if the incident electron energy is close to the ionization energy of an inner shell which couples strongly with available orbitals lying close to the Fermi level, the intensity and shape of the continuum limit spectrum depends markedly on the ener- gy of the incident electrons. An example of this effect is x-ray emission spectra from lanthanum for a succession of incident electron energies in the neighborhood of the M5 and M^ shell ionization ener- gies. A time sequenced film of 35 spectra for incident electron ener- gies in increments of 1 volt in this region shows the dramatic intensity resonance of a portion of the continuous spectrum as the incident elec- tron energy is varied. Figure 2 shows a continuum limit spectrum from the lanthanum sample for an energy far from the M5, M4 shell ionization ._ energies. In it we recognize the abrupt onset at the Fermi level and a broad peak representing transi- tions to empty 4f levels on a con- tinuum background. The broad peak is the feature which resonates so dramatically as the incident elec- tron energy is varied through the M5, M^ region. Data from cerium [3] show a similar behavior. In this case the area corresponding to the cross hatched area of Fig. 2 has been obtained from each graph of a series of more than 60. to LJ > - 2 t- < ot CONTINUUM LIMIT 660 eV FIG. 2. A continuous spectrum from lanthanum for in- cident electrons of 660 eV. These areas are plotted in Fig. 3 as the relative cross section for scattering to 4f levels as a function of incident electron energy. Note that the cross section for production of this part of the continuum varies significantly before the M5 and M4 energies are reached. A slow decrease is observed as the M5 energy is approached. As the M5 energy is closely approached the cross section increases by over two orders of magnitude. Between the Mr and M/ energies it is reduced to a very small value before increasing greatly again as the M4 energy is closely ap- proached. For incident electron energies greater than the M4 energy the cross section decreases again, but slowly, with increasing electron energy. This distinct energy dependent resonance behavior of the matrix element of the continuum transition shows how important it can be for certain elements in particular energy regions. Other lanthanides also 96 150 - 100 - 50 - exhibit this phenomena as do elements of the first transition group and the actinides. It can be seen that some "satellite lines" in x-ray emission spectra are ac- tually due to this resonant continuum effect, that it dominates some appearance potential spectra, and thor- oughly frustrates determinations of relative densities of states from continuum limit spectra. It has been speculated [3] that negative ion bound states with single channel decay modes are responsible for the con- tinuum resonance, however, such speculations merely emphasize the need for an adequate theoretical exposition of the phenomenon. 840 880 PHOTON ENERGY FIG. 3. Crosshatched area illustrated in Fig. 2. plotted vs the energy of the continuum peak. The graph shows the variation with energy of the cross section for produc- tion of continuum photons. [1] R.R. Turtle and R.J. Liefeld, Phys. Rev. B, 3411 (1973). [2] D. Bruce, Ph.D. Dissertation, New Mexico State University, 1975. [3] M.B. Chamberlain, A.F. Burr, and R.J. Liefeld, Phys. Rev. A. 663 (1974). 97 BREMSSTRAHLUNG ISOCHROMAT FROM ALUMINUM. t P. E. Best and C. C. Chu Department of Physics and Institute of Materials Science University of Connecticut, Storrs, Conn. 06268 We report a measurement of the bremsstrahlung isochromat (BI) from aluminum, and describe how the characteristic electron energy loss spectrum is unfolded from the raw data to simulate the BI from a thin target. This corrected data is discussed. The raw BI data for an aluminum film evaporated within the experi- mental chamber in a pressure of <10- 10 Torr is shown as dots in Fig. 1. The data was recorded with the apparatus described elsewhere (1), using a monochromator set to pass 2.290 A photons. The angular divergence of the incident electron beam and of the monochromator entrance aperture are less than 30 mR and 15 mR, respectively, the x-ray take-off direc- tion being 87±1° from the incident electron-beam direction. From the step of the Duane-Hunt limit at eV the BI intensity decreases slightly out to a second step which occurs at about 15 eV. The intensity then decreases slightly out to a third step centered at about 30 eV. The fine-structure peaks evident in the raw data curve, having widths of about 2 eV and intensities of about 10% of the step height, are believed to be due to density-of-states variations and will not be considered in this talk. The three steps in the raw data of Fig. 1 can be understood as follows: The threshold and subsequent slow fall of intensity is the thin target BI appropriate to the incident monochromatic electron 10 15 20 25 30 35 40 45 ENERGY (eV) Fig. 1 Bremsstrahlung isochromat from aluminum: raw data, corrected, ----- calculated density-of-states (9). 98 beam. At about 15 eV this thin target spectrum is augmented by a rep- lica or echo of the threshold (2), which replica is the thin target BI from electrons which have excited a plasmon (fiu)=15.3eV) (3). From 15 to about 30 eV above threshold the spectrum is the sum of the BI from the above two classes of electrons. Above about 30 eV a new thin tar- get BI component, due to electrons that have excited two plasmons in separate events, is added to the spectral intensity. To deduce the approximate thin target BI we must remove the plas- mon echoes from the raw data. Before an unfolding technique can be considered we should know the relative number of electrons that have energies Eq, E] and E£ in the target, where Eq is the energy of the in- cident beam, Ei=Eq-Tiu), and E2=EQ-2fiw. Also, we should ask whether electrons of energy Eq, E] and E2, respectively, have similar cross- sections for bremsstrahlung production, and similar mean free paths (MFP's). An electron entering the solid has a MFP of about 90A for inelas- tic scattering (4), and a similar MFP between elastic scattering events (5). The angular distribution of elastically scattered electrons is peaked in the forward direction, as the Bragg angles for these 0.16A electrons are yery small for the intensely scattering low index planes. About 0.9 of the total cross section for inelastic scattering is due to plasmon excitation (4). A rough description of the path of "ty- pical" electron, therefore, can be given as follows: After entering the solid it travels 1 MFP with energy Eq, another MFP with E-| , a third MFP with E2> etc., all with little deflection. The relatively few electrons that contribute to the thin target BI of interest do so rel- atively close to the surface. Electrons that excite K or L-shell electrons, or bremsstrahlung, are removed from the flux that can contribute bremsstrahlung intensity to the energy region of interest. These losses account for 0.1 of the total cross section (4), so the fluxes available for bremsstrahlung pro- duction are in the approximate ratios of 1:0. 9: (0.9)2 f or the Eg, E-| and E2 components, respectively. For electrons whose energies are well removed from atomic excitation thresholds (6), bremsstrahlung cross- sections vary slowly with energy and angle. For our purposes it can be concluded that the bremsstrahlung production rates are in the ratios of 1:0.9:(0.9)2 for the Eq, E-, and E 2 components of the electron flux. It can be shown that there is virtually no loss of intensity due to x-ray absorption in the aluminum for the conditions of this experiment. We describe a simple procedure to "unfold" the electron energy spectrum to reveal the gross behavior of the thin target BI. From the discussion above it can be concluded that the fully developed heights of the three steps in the data of Fig. 1 are in the ratios of 1:0.9:0.8. From threshold to about 12 eV the spectrum represents the thin target BI from the Eq part of the electron flux. When the brems- strahlung component due to the E-j part of the electron flux has reached its full height, at about 17 eV, the experimental curve is made up of 99 a thin target BI due to E-| , which is 0.9 of the intensity due to Eg at 15.3 eV lower energy, plus the unknown component due to Eg. By dis- placing 0.9 of the thin target BI due to E by 15.3 eV to the right, and subtracting it from the data, we are left with the thin target BI from the Eg flux out to about 25 eV. This is shown in Fig. 1 by the solid line. The process was extended to the third step, revealing the Eg thin target data out to 40 eV. This "unfolding" procedure gives no direct information about the regions of the spectrum in the immediate vicinities of the steps in in- tensity. These regions are shown dashed in Fig. 1. While unresolved structure due to density-of-states effects can occur in these regions, there seems little doubt that the solid curve of Fig. 1 represents the gross nature of the aluminum BI out to 40 eV. In particular, there are no abrupt changes of levels or slopes in the corrected curve, features which would indicate an error in the model used. The BI corrected in the above manner decreases from threshold out to a broad minimum at about 25 eV. The rise of intensity after 25 eV, and therefore the minimum itself, are probably artifacts caused by the neglect of structure in the energy loss spectrum due to both single Particle excitations (7) and two-plasmon excitations (8). The calcu- lated density-of-states curve for aluminum is shown by the dashed line in Fig. 1 (9). Over small energy regions it has been shown that the structure in the BI reflects structure in the density-of-states (1,10). It is clear from Fig. 1 that over an extended energy range the BI is not directly proportional to the density-of-states. The BI from a free electron metal and a free atom, respectively, will have the same form. Inasmuch as aluminum is free-electron like, the corrected curve of Fig. 1 is a representation of the BI from free aluminum atoms. Helpful discussions with Drs. L. V. Azaroff, D. Pease, and F. Szmulowicz are gratefully acknowledged. Footnotes tSupported in part by a grant from the National Science Foundation. 1. C. C. Chu and P. E. Best, Phys. Rev. Bl_2, 4575 (1975). 2. G. Bohm and K. Ulmer, Z. Physik 228, 473 (1969). 3. C. J. Powell and J. B. Swan, Phys. Rev. JM5, 869 (1959). 4. C. J. Powell, Surf. Sci . 44, 29 (1974). 5. V. W. Cosslett and R. N. Thomas, Brit. Journ. App. Phys. J5, 883 (1964). 6. M. B. Chamberlain, A. F. Burr and R. J. Liefeld, Phys. Rev. A9 663 (1974). 7. A. J. Glick and R. A. Ferrell, Ann. of Phys. 11, 359 (1960). 8. J, C. Ashley and R. H. Ritchie, Phys. Stat. SoT. 38, 425 (1970). 9. J. W. D. Connolly, Int. J. Quantum Chem. 3, 807 (1970) and F. Szmulowicz, private communication. 10. K. Ulmer, in "X-ray Spectra and Electronic Structure of Matter," Proc. Int. Symp. Kiev, 2, 79 (1968). 100 BREMSSTRAHLUNG ISOCHROMAT OF TUNGSTEN AT 16 EV H. Humberg and H, Merz Universitaet Muenster Physikalisches Institut D 4400 Muenster, Schlossplatz 7 Germany In the case of transition metals photoelectron spectra of the valence bands and bremmstrahlung isochromats are complementary (e.g., Ulmer, Strathclyde, 1971); they give information about the distribution of filled resp. unfilled states in the valence and conduction bands. Photoelectron spectra have been measured over an extended region of photon energies: there are significant differences in the spectra between the UV-region (UPS) and the X-ray region (SPS). When transferring this classification to the analogous isochromat spectroscopy all known isochromats (hw > 150 eV) are due to the X-ray region. With a grating (normal incidence) it was possible to get a tungsten isochromat at hw Q = 16 eV (electron energy: 10-30 eV). The tungsten curve shows the known "d-peak", but the ratio I /I mi - n = 1,5 is significantly smaller than near ho) * 1000 eV. A comparison with tungsten isochromats of other authors, taken at some higher photon energies, shows a strong dependence of the ratio I max /I m ,- n from the photon energy. This dependence will be discussed. 101 STUDIES OF THE 4f STATES IN Ba AND La BY ELECTRON AND PHOTON EXCITED APS* J.Kanski, E-'.O.Nilsson and I.Curelaru, Physics Dept., Chalmers University of Technology, Fack, S-402 20 Gb'teborg, Sweden In the present paper the 1VL and N5 4 excitations in Ba and La are studied by means of electron and photon excited APS (EXAPS and XEAPS resp.) /1/. Both methods are probes of elect- ron states above the excitation threshold. The final state in EXAPS contains two excited electrons and a core hole. In an independent particle picture an EXAPS spectrum is there- fore to be interpreted as a self-convolution of the density of unoccupied electron states. This model has been applied successfully to various kinds of materials /2,3»4/> in which the final electron states are delocalized. XEAPS is in principle a photoelectron yield experiment and the results are expected to be similar to photoabsorption data for the same core level excitation /5/» Ba and La are the elements immediately preceding the rare- earth series in the periodic table. They contain therefore empty 4f states, which are localized in the region near the ion cores. This leads to a breakdown on the one-electron excitation description of the spectra. Our experimental arrangement has been described earlier /l/. The measurements were performed on films evaporated from W- coils. During evaporations the pressure in the experimental chamber was around 5 X "10""° torr. Within a few minutes of eva- poration the base pressure of ^^0 torr was restored and was maintained during the measurements. In the EXAPS experi- ment the primary electrons were produced from a hot W-fila- ment. For XEAPS we used the bremsstrahlung from a Ni-anode. This radiation was "monochromatized" by potential modula- tion /6/. All relevant experimental parameters are speci- fied in the figure captions. The energy values quoted here include a 5»0 eV correction for the filament work function and for the thermal energy of the primary electrons. Core level binding energies were determined by separate XPS experiments, using a HP-5950A ESCA instrument. These data were also obtained on evaporated films and were recorded within £ min of evaporation as the base pressure in the ESCA chamber was in the high 10~" torr region. Only faint oxygen signals could be observed in these spectra. A few minutes after evaporation these peaks became more pronounced, and simultaneously "chemically" shifted metal structures appear- ed. Since the Ba data have been published earlier /l/ ? we restrict ourselves to show only the La spectra here, fig.1. The EXAPS N5 4 spectrum is quite complex, and we cannot at present give any detailed interpretation of all the struc- tures. It does however have some features in common with the photoexcited spectra (XEAPS,SXA), which are better under- stood. We see for example that all N^^ spectra extend over 102 XPS LaN 5.4 XPS EXAPS XEAPS SXA 100 j — u/y\A- 120 140 830 Excitation energy (eV) 840 Figure 1 . Nc 4 and Mr spectra for La. The data were obtained using the following parameters for primary current , modu- lation amplitude (peak- to-peak) and time con- stant: N 5,4 EXAPS : 1.0 mA, 0.5 V, 3 1 N 5) 4 XEAPS: 4.0 mA, 1.4 V, 3 1 M5 EXAPS: 1 .0 mA, 0.5 V, 1 < M5 XEAPS: 6.0 mA, 1.1 Y, 3 e The resulting noise levels are indicated with bars. The SXA data are taken from refs. 9 and 10. a wide energy range due to strong multiplet splitting. Further, the general structure of the spectra is similar, they are all dominated by one strong peak at about 115 eY, which is assigned as a collective dipole resonance of the (4d?4f) 1 P state /7/. As the processes in EXAPS and XEAPS are not subject to the same selection rules, one may however expect different re- sults. In particular, the EXAPS spectrum should be richer in structure when multiplet splitting is a dominant effect. The Mc spectra in fig. 1 are clearly less complicated. The EXAPS curve is qualitatively similar to the corresponding Ba curve /1/. In both cases the spectra are dominated by one peak, which on its low-energy side has a shoulder-like struc- ture. The analysis of these data is greatly facilitated by comparison with the XEAPS spectra. Thus both for Ba and La the position of the shoulder corresponds to the position of the dominant peak in the XEAPS spectrum. Considering dipole selection rules and the narrow width of this peak, one can interpret it as the 3d— >4f excitation. This is also our assignment of the shoulder-like feature in EXAPS. In this excitation the second electron in the EXAPS process is thought to enter an itinerant state, not affecting the local configuration at the excited atom. The main EXAPS peak is then interpreted as approximately the process 3^4f + e** — *• 3d5>4f2. It is now interesting to note that both EXAPS peaks appear 103 at excitation energies lower than 835*8 eV (dashed line in -fig. 1 ) . of the 4f level is determined by c spectroscopy to be 5*5 e V above th bining the XPS and the CI results, 3d->> 4f excitation to occur at 841 particle model. The present result 10.7 3.8 Ba WW###0* (N+1)" La - WW&MR. Here Z is the nuclear charge (18 for Ar) and C, D, and R are the adjus- table parameters. Note that Z(R) = 1 and Z'(R) = 0. The potential is employed to compute phase shifts 6^(E) and the matrix-element ratios 00 00 A s f P r P D dr/ P P r P_, dr, (3) J 3p op Es ' J 3p op Ed which come into the Cooper-Zare model [2]: 2-4 A cos(6 - 6 9 ) p(E) = ? (4) 2 + A Here Po_ is the radial 3p wavefunction of Ar [3], Pg s and P E( j are con- tinuum s- and d-waves, and r op is an average of the length and velocity forms of the dipole operator. f The parameters of the potential (C, D, and R) are adjusted to achieve optimal agreement between the computed p(E) and experimental data at selected energies E^. Here we have in employed the data of Dehraer et al . [4], at only three energies Ej[=5.37, 11.01, and 24.96 eV. Using this pseudopotential we have computed the cross section o(E) in Fig. 1, and £(E) at energies as large as 70 eV. Our results agree well with the data, including Houlgate's et al . ' s [5] measurements which show considerable structure of (3(E) for 25 < E < 70eV (well outside the range of input data). For example, in Fig. 1, our results (solid line) are in better agreement with the data [6] (dotted), than Hartree-Fock length [1] (dot-dashed), Hartree-Fock velocity [1] (dot-dot-dashed), or RPAE [1] (dashed) calculations. The resulting empirical charge distribution Z(r) is reassuringly similar to the Har- tree distribution calculated using wavefunctions of Bagus et al . [3] Moreover, preliminary analyses of Ne 2p data indicate that the success for Ar is not accidental. 50 - -^ \ \ 40 #r " s s:-> \ 30 7/ Xn \ 20 7' ^--0\ \ \\ \ 10 n i 10 20 30 PH0T0ELECTR0N ENERGY (eV) FIG. 1. Photoionization cross-section for the 3p subshell of Ar. (dotted) - experimental data [6], (solid) - present work, (dashed) - RPAE [1], (dot-dashed) - Hartree-Fock Length [1], (dot-dot-dashed) - Hartree-Fock Velocity [1], It should be emphasized that semi-empirical phase-shifts, continuum wavefunctions, and bound charge distributions are all byproducts of the pseudopotential determination. We are optimistic that the method can be extended to a wide class of atoms, and expect that it will prove useful, not only for the description of soft x-ray excitations of atoms, but also for theories of photoemission and of low energy electron diffrac- tion from surfaces and adsorbates. (1-26, J r ^ L j We use op r + h 2m CD [4 28 i.2> 112 where h Ni(3d)e charge transfer and to the different relaxa- tion or the Ni3d orbitals in the two ionic states involved. 2 2. A weak satellite at about 12-15 eV comes from a (0(2p)e ) -> (Ni(3d)e ) charge transfer. 3. The satellite structure in the Is- and 2s-spectrum are essential- ly similar. The larger multiplet splitting in the 2s together with the broad lines makes the analysis difficult. k. It is essential for the model not only to allow for the 0(2p) -> Ni(3d) charge transfer, but also to allow for the different re- laxation of the Ni(3d) orbitals in the ionic ground state and in the "shake-up" states. *) Present address: Laboratory of Physics Helsinki University of Technology SF-02150 Espoo 15, Finland 114 An example of our results is given in table I. Table I. Computed A^ ls-hole states of NiCy ". 2g 6 Both 0(2p) -> Ni(3d) charge transfer and Ni(3d) relaxation included, Configuration^*. E 1. (Ni(3d)e ) 2 (0(2p)e ) k g g 2. (Ni(3d)e ) 3 (0(2p)e ) 3 g g 3. (Ni(3d)e ) (0(2p)e f Relative Intensity V 1 ! State 1 State 2 State 3 0.0 6.6 eV 12.9 eV 0.9 1 * 0.32 0.06 0.28 0.92 0.05 -0.10 -0.08 -0.91 0.51 0.26 0.01 0.51 0.02 1. R.A. Pollack, Ph.D. Thesis (University of California at Berkeley) unpublished. 2. K.S. Kim, Phys.Rev. 11, 2177 (1975) 3. P.S. Bagus, A.J. Freeman, F. Sasaki, Phys.Rev. Letters 30_, 850 (1973). h. P.S. Bagus, U.I. Wahlgren, Physica Fennica 95., 275 (197*0. 115 MULTIPLET SPLITTING OF CORE 2p AND 3p PHOTOELECTRON LINES OF TRANSITION METAL HALIDES M. Okusawa, T. Ishii, and T. Sagawa Department of Physics, Tohoku University, Sendai 980, Japan In X-ray photoemission spectra of core levels of some compounds, fine structures other than spin-orbit splitting are observed, and this phenomenon is one of the remarkable aspects of photoemission. A lot of arguments have been made concerning the origin of the fine structure, and its qualitative explanation appears to have been established. Recent studies in this problem aim at more quantitative analysis of the spectra. Energies of correlation between an outer- shell electron and an inner-shell electron as well as the energy of charge transfer from a ligand ion to a metal ion may be obtained through the analysis of the fine structure. Spectral resolution attainable with presently available experimental instruments is not high enough, but the observable line-profile may be given as an overlap of essentially-unresolved component- lines. We have carried out an experimental investigation of the 2p, 3s, and 3p lines of transition-metal ions in transition-metal halides. In this report, the results on the chlorides and the bromides are presented. Measurements were performed with an electron-energy-analyzer of the hemispherical type with a mean radius of the electron trajectory of 132mm. Samples were prepared by evaporation and subseauent annealing at 150°C. Pressure during measurements and sample evaporation was in the range of 10~° Torr. Measurements and data accumulation were controlled by a Yokogawa- Hewlett-Packard 2100A computor. All spectra observed here have profiles which are dependent on ligand anions. This feature is quite clearly observed when comparison is made with the spectra of compounds other than halides, for example, the oxides and the sulfides. [lj As the metal ion in the sample changes from chromium to nickel, the profiles of the core level lines change markedly. This dependen6e of the spectrum on the number of 3d-electrons in a metal ion, along with the ligand- dependence, is favorable to the interpretation that the fine structures are due to the charge- transfer transition from the ligand p-orbital to the 3d-orbital of the metal ion. [2, 3] The multiplet- coupling between 3d-electrons and a core-hole is appreciable. In the analysis of the spectra the line distributions theoretically predicted are usually convoluted with a window function giving a broadening about leV and then compared with the experimental data. Recently, Satoko£4Jproposed a method of the analysis where the moment of a spectrum around its center of gravity, defined as pi^= \(u- oj ) N l(u))dw/ J I (w)dw, is used. Figure 1 shows the second and third moments of the 2p and 3p lines of transition metal ions calculated from the observed spectra. 116 15 > •10 -o- ^Vomides o--2p 1/2 j <^2p 3/2 P o— 2pi/ 2 >Chlorides r Cr 3 * Mn 2 * Fe 2 * Co 2 * Ni 2 * 40- n > 30 Chlorides 3p J Cr 3 * Mn 2 * Fe 2 * Co 2 * Ni 2 * _l L_ 1 I I 1 3 U 5 6 7 8 NUMBER OF 3d-ELECTRONS 3 A 5 6 7 8 NUMBER OF 3d-ELECTRONS Fig, 1. The second and third moments of the 2p and 3p lines of transition metal ions in the chlorides and the bromides. The moments are calculated from the overall profiles of the lines including satellites. In the 2p spectra, the spin-orbit energies are sufficiently large as compared with multiplet splitting and charge- transfer energies to make the 2p]/2 and 2p^/2 components be separated completely. The moments were obtained for both component- lines. In the 3p spectra, the spin-orbit energies are not large and the moments were calculated for the whole spectra. Before the moments were calculated, the backgrounds of the spectra caused by inelastically scattered electrons were subtracted under the assumption that the intensity of the overlapping background is proportional to the integrated intensity of the true line. The second moments of both 2p and 3p lines decrease as the atomic number of transition metal decreases. If the line distribu- tion is determined by the multiplet splitting only, the width of the spectrum is expected to become broader as the number of energy levels arising from the 3d-electrons of a metal ion increases. Satoko's calculation(4j suggests that the second moment is largest in Mn-compounds. Monotonic decrease towards Cr-compounds in Fig. 1 is brought about by the contribution of the charge- transfer satellite. The contribution of the satellite is largest in Ni-compounds. The main line of a 2pj spectrum is broad^n*=d by the multiplet splitting. It might be possible to separate the main line and calculate the 117 moments for this line. We actually tried this. However, the overlap between the main line and the satellite was not negligible and the results of calculation included appreciable errors. With the inevitable errors thus introduced, the difference in the second moments among different materials was not large and the systematic change due to the difference of the number of 3d-electrons was not found. In the case of the 3p lines, the situation is slightly com- plicated. According to Satoko's theory [4], that the spin-orbit components are unable to be separated is not serious at all, and the analysis can be made with the inclusion of the spin-orbit interac- tion. As is obvious in Fig. 1 , the dependence of the second moments on the number of 3d-electrons in a metal ion is quite similar to the 2p lines. However, the interpretation may not be unique. According to the calculation by Asada et al.£5J> the 3p spectrum of NiClp is explained in terms of multiplet splitting with appropriately- scaled Slater-Condon parameters. Incorporation of the separate contribu- tion of satellites appeared unnecessary. Thus, the result shown in Fig. 1 may be ascribed to the following two possibilities: (l) In the case of the 3p lines, the charge- transfer excitation of p-elec- trons has appreciable effects, and the multiplet splitting and the satellite effect mix each other completely. (2) As the number of 3d-electrons decreases, the energies of high-energy components of the multiplet increase but their intensities decrease at the same time. Low signal-to-noise ratio makes it too difficult to find them. As regards to this point, it is worth noting that high-energy multiplet components are found in both XES and XPS spectra of MnF 2 . C6, 7] More detailed analyses concerning these points are now under progress. References 1 M. Okusawa, T. Ishii, and T. Sagawa: Physica Fennica 9 suppl. SI, 298 (1974) 2 K. S. Kim: Phys. Rev. Bll (1975) 3 S. Asada and S. Sagano: Tech. Repts. ISSP A. 750 (1976), to be published in J. Phys. Soc . Janan 4. C. Satoko; Private Communication 5 S. Asada, C. Satoko, and S. Sugano: J. Phys. Soc. Japan 3_8 855 (1975) 6 V. M. Pessa: J. Phys. C8 1769 (1975) 7 C. S. Fadley and D. A. Shirley: Phys. Rev. Lett. 30 850 (1970) 118 IMPORTANCE OF RELAXATION EFFECT DURING IONIZATION OF MOLECULES J.J. PIREAUX +§ , S. SVENSSON, E. BASILIER, P-A MALMQVIST, U. GELIUS , R. CAUDANO§ and K. SIEGBAHN. University of Uppsala, Institute of Physics, P.O.Box 530, S-751 21 UPPSALA 1 Sweden § Facultes Universitaires, Laboratoire de Spectroscopie Electronique, Rue de Bruxelles 61, B-5000 NAMUR, Belgium INTRODUCTION One observes generally that core electron binding energies are larger for isolated atoms or molecules than for the corresponding liquids or solids. This is also the case when comparing free atoms and their corres- ponding diatomic molecules. The effect is due to the fact that the lar- ger systems have available more degrees of freedom for electronic reor- ganization of a core orbital, increasing the relaxation energy. The alkanes (C n H2 n+ 2) constitute a suitable series to study the in- fluence of the molecular size on the electronic relaxation energy, since the molecule size can be progressively increased by choosing molecules with different n. ALKANES Cls CHEMICAL SHIFTS High resolution ESCA measurements have been performed on the Cls core levels for the alkanes with 1 ^ n £ 13. Table I reports the experimental Cls chemical shifts, referred to the methane Cls binding energy [1,2]. The alkane chemical shifts, determined to within ± 0.02 eV, are small, ranging over an energy scale of about 0.6 eV only. A very smooth varia- tion of binding energies is observed. We report here a negative chemical shift for the alkanes, the Cls binding energies decreasing with an in- creasing length of the molecules. KOQPMANS' THEORETICAL CORRELATIONS ESCA chemical shifts arise generally [3,4] because of different elec- tronic distribution around the atom to be ionized. In the simple elec- trostatic approximation, a positive chemical shift corresponding to an increasing binding energy is correlated to an increase of the positive charge on the atom. Table I (third column) shows that this trend is not encountered for the alkanes series, since the chemical shifts are pre- dicted to be positive from ab initio charges on the carbon atoms. The electrostatic interaction from the other atoms in the molecules have been accounted for in the ground state potential model [4]. This model, using CND0/2 charges, does not improve the previous correlation since signs and trends of the calculated shifts still are incorrect (Table I, fourth column) . These two models rest on the Koopmans 1 approximation. This does not account for the final state influence, generally included in a relaxation + Aspirant du Fonds National Beige de la Recherche Scientifique 119 energy term [5], The fact that the Koopmans' approach is not succesful in describing the alkanes chemical shifts is evidence that in this case the variation in the relaxation energy is a dominant term compared to the classical electrostatic effect. Table I . Alkanes Cls chemical shifts. Comparison between experimental ESCA data with various theoretical models Molecule Experimental shift(eV) a Ab initio charge'-' Potential Model shift (eV) Transition Potential Model shift d (eV) ASCF shift (eV) b CH, 4 0.0 -0.2511 0.0 0.0 0.0 C 2 H 6 -0. 12 -0. 1627 0.37 -0.40 -0.32 C 3 H 8 -0.26 -0. 1468 0.50 -0.62 -0.60 n " C 4 H 10 -0.35 -0. 1293 0.57 -0.82 -0.68 n-C 5 H l2 -0.41 -0. 1122 0.66 -0.93 n " C 6 H 14 -0.47 -0. 1068 0.68 -1 .00 n-CgH l8 -0.52 -0. 1014 — n-C ]() H 22 -0.56 0.70 -1 .09 n-C ]3 H 2g -0.57 — — — a : shift relative to the Cls line; its centroid was measured at 290.83 eV [1 ,2] b : ab initio minimal basis calculations c : AE = k Q + V + L with k = 22.11 eV/unit charge d : AE = kj QT + vT + L T with kj = 24.3 eV/unit charge RELAXATION EFFECT The relaxation effects are implicitly included in the transition potential model [6,7], where charges are calculated for a fictitious transition state, intermediate between the ground and final states of the molecules. The correlation obtained between the experimental che- mical shifts and data calculated with this model is good as can be seen by comparing columns 2 and 5 of Table I. The correct experimental trend is finally reproduced. This reorganisation process can be discussed in terms of a charge redistribution within the whole molecule, with the effect that the created positive charge is screened. Fig. 1 illustrates this charge flow for a n-hexane molecule. As can be seen, all the atoms effectively participate in the screening of the core hole. With increasing molecu- 120 lar size, the electron flow can be taken from more and more distant atoms, resulting in an increasing total relaxation contribution to the chemical shift. In order to estimate the accuracy of this model, explicit ASCF calculations were performed on both the initial and excited states of the molecules using the equivalent core approximation. It was found that the ab initio ASCF binding energies reproduce the decreasing beha- viour of the experimental shifts (Table I, column 6). These results show that a satisfactory description of the alkane core orbitals energies has to include the relaxation effect. t.012 -014 -020 1 089 j030 j018 -008 -009 j013 p030 -.101 t036 ■016 1.003^004^010 ^030 J.491 ' O24_ 037 -.006 -006 -£09 -.014 -034 -.110 -.012 ^002^001 ^.003^010 Jr029,.499_ 110 N-HEXANE Fig. 1 . : charge flow AQ in n-hexane (difference in charge before and after ionization of the atoms marked by a black dot) . ACKNOWLEDGEMENT One of the authors (J. J. P.) is grateful to the belgian F.N.R.S. for financial support. REFERENCES [1] J.J. Pireaux, Ph.D Thesis, Facultes Universitaires , Namur, 1976. [2] J.J. Pireaux, S. Svensson, E. Basilier, P-A Malmqvist , U. Gelius, R. Caudano and K. Siegbahn. Uppsala Report UUIP 920 (March 1976); subm. for publ. [3] K. Siegbahn et al . ESCA. Atomic, molecular and solid state structure studied by means of electron spectroscopy. (Almqvist and Wiksells, Uppsala 1967). [4] K. Siegbahn et al. ESCA applied to free molecules (North Holland, Amsterdam 1969). [5] U. Gelius and K. Siegbahn. Trans. Far. Soc . 54_ (1972) 2571. [6] G. Howat and 0. Goscinski. Chem. Phys. Lett. 30 (1975) 87. [7] H. Siegbahn, R. Medeiros and 0. Goscinski. J. Electr. Spectr. 8^ (1976) 149. 121 ESCA STUDIES OF THE ALKALI HALIDES, LiF, LiCl AND LiBr , AND OF Li METAL. L.I. Johansson, S.B.M. Hagstrom and S.-E. Karlsson Department of physics and measurement technology, Linkoping University, S-581 83 Linkoping, Sweden. Controversies in the interpretation of soft x-ray absorption spectra of alkali halides have arisen because excitonic enhanced absorption peaks may appear below the band edges. These peaks are difficult to disting- uish accurately from the thresholds for interband transitions. An app- roach has recently been proposed [1,2,33 ^ n wn ich x-ray photoemission (ESCA) is used in conjunction with optical band gap data to determine these thresholds. For insulators the threshold for transitions from a core level to the conduction band Ae . can be represented as the sum of two energy differences [1] ; Ae = As ' + As ' . The first Ae ' is the difference between the top of the valence band and the core level of interest. The second Ae' is the difference between the bottom of the conduction band and the top of the valence band, i.e. the optical band gap. The first energy difference can be obtained by subtracting ESCA measurements for the ionization energies of electrons in the core level from those at the top of the valence band. We have performed such mea- surements on the alkali halides LiF, LiCl and LiBr. The photoelectrons, expelled by MgKa or AlKa, 2 radiation, were ener- gy analysed in an electrostatic instrument which 'operates under high va- cuum conditions, 10 torr. The overall resolution of the instrument was set at 1.3 eV FWHM for the Au^f , peak excited by MgKa radiation. The measurements were performed on single crystals of LiF, on films eva- porated in situ and on pressed powder samples of LiCl and LiBr. It was possible to ignore charging effects because the samples were irradiated for at least one hour before any actual measurement and valence band and core levels were then recorded in the same spectrum. The top of the va- lence band was experimentally determined from the intersection of a line extrapolated from the segment of maximum negative slope with the line de- fining the background level in the recorded spectrum. Our estimated un- certainty in this determination is ± 0.2 eV. Our valence band spectra will be presented and compared with available UPS results. The energy separations, obtained between the top of the valence band and the Li 1s level, in these three halides are summarized in Table 1. Litera- ture values of the optical band gap are also given in Table 1 as are * Present address: Xerox Corporation, Palo Alto Research Center, 3333 Coyote Hill Rd, Palo Alto, California 9^30U, USA 122 ?able 1 Summary of energy differences concerning the Li 1s level. The figure in the parentheses represents the estimated uncertainty in the last digit of our measured values. The symbols introduced are defined in the text and their values are given in sV. Compound 11 Va Z\ LiF LiCl LiBr U9.8(3) 53.2(3) 5^.1(U) 13. 6 a „ i a 7.6 63. h 62.6 61.7 taken from ref . k. the interband transition thresholds represented by the sum of those two terms. The agreement between the present results and previously pub- lished results on LiF and LiCl is quite satisfactory. Our result of 51. U eV for LiBr confirms the estimated value of 5^.2 eV [l ,3l which previous- ly has been used for the interpretation of the soft x-ray absorption spectrum. The observed dominant peaks [5] 5 in the soft x-ray absorp- tion spectrum, lie at 61.9» 60.8 and 60.h eV respectively for LiF, LiCl and LiBr. Thus, these can be identified as purely excitonic since their energies are 1.5» 1.8 and 1.3 eV smaller than the thresholds listed in Table 1 for LiF, LiCl and LiBr respectively. Our results on the energy separation between the Li 1s level and the valence band also agree well with the predictions of the point charge model including corrections for polarization effects. Further experimental results as well as references are to be found in ref. 6. For comparison metallic Li was also studied. In this case the measurements were performed un- der ultrahigh vacuum conditions (^2x10 torr). The resolution was set at 1.6 eV FWHM and films of Li were prepared by electron gun evaporation onto a polished copper backing. During deposi- ts o 1 ' i ' i Li Is •"• 3 2 1 ■ •"Ni'V I i 1 i 1 70 60 50 BINDING ENERGY (tV) Fig ] . ESCA spectrum from Li metal showing the Li 1s line and structure due to plasmon losses. tionthe pressure was kept below 1x10 torr. A weak 01 s line was observed in the photoelectron spectrum a few hours after depo- sition so repeated evaporations were made. A recording of the Li 1s spectrum is shown in Fig. 1. The binding energy is given with respect to the Fermi level and the AuUf , line was used as re- 123 ference level (83.8 eV). The larger peak in Fig. 1 corresponds to the Li 1s level. Its binding energy was found to be 5*+«7 (1) eV in good agree- ment with an earlier investigation £7] • Extra atomic relaxation contri- butes a shift of several eV as estimated from values for free atoms £7] • The broad structure in the spectrum is due to plasmon losses. The maxi- mum of the structure lies at 8.0(3) eV below the Li 1s level which corre- sponds rather well to the bulk plasmon loss. The shoulder on the low binding energy side corresponds to the surface plasmon loss. The Li 1s level could not be related to the valence band because the va- lence band spectrum was too weak probably because of the low photoioni- zatidn cross section. REFERENCES 1. S.T. Pantelides, Phys . Rev. B JJ_, (1975) 2391 2. F.C. Brown, Solid State Phys. 2£, (197*0 1 3. S.T. Pantelides and F.C. Brown, Phys. Rev. Lett. 33, (197*0 298 h. W.H. Strehlow and E.L. Cook, J. Phys. Chem. Ref. Data 2, ( 1973 ) 163 5. R. Haensel, C. Kunz and B. Sonntag, Phys. Rev. Lett. _20, (1968)262 6. L.I. Johansson and S.B.M. Hagstrom, to appear in Physica Scripta 7. S.P. Kowalczyk, L. Ley, F.R. McFeely, R.A. Pollak and D.A. Shirley, Phys. Rev. B 8, (1973) 3583 124 X-RAY SPECTRA OF TRANSITION METAL ALLOYS AND THEIR INTERPRETATION E.Z. Kurmaev Institute of Metal Physics The Ural Scientific Centre Academy of Sciences of the USSR Sverdlovsk GSP-170, USSR The experimental results of MeK$ 5 -emission bands (Me=V,Cr,Fe) investiga- tion in alloys with transition metals of II and III periods are represented. The influence of relative arrangement of alloyed components, atomic and electron concentration, type of crystal structure on the electron energy spectra of alloys is analysed. The question about short- order manifestation in X-ray emission spectra is considered and a new interpretation of MeK3 5 -bands is proposed. These investigations show that the CPA theory gives a good description of the electron structures formed in the alloys of transition metals. The state of order and the crystal structure of the studied alloys hardly affects the global features of electron structures in these alloys. The values of 6-parameter for CPA theory are determined from X-ray emission spectra of alloys under investigation. 125 FORMATION OF BAND STRUCTURES IN QUASI ONE DIMENSIONAL MOLECULES J.J. PIREAUX +§ , S. SVENSSON, E. BASILIER, P-A MALMQVIST, U. GELIUS, R. CAUDANO§ and K. SIEGBAHN. University of Uppsala, Institute of Physics, P.O.Box 530, S— 75 1 21 UPPSALA 1 Sweden § Facultes Univers it aires, Laboratoire de Spectroscopie Electronique Rue de Bruxelles, 61, B-5000 NAMUR, Belgium INTRODUCTION X-Ray and UV photoelectron spectroscopies have emerged over the last ten years as powerful methods for studying experimentally the electronic band structures of solids. In this work [1-3] we propose to follow and study by electron spectroscopy the construction mechanism of an electro- nic energy band during the progressive formation of a solid. The basic idea rests on the following simple model. When two identical atoms approach each other to form a molecule, their electronic clouds start to overlap and this results in a splitting of the electronic levels in the molecule. The splitting will be more pronounced for the outermost shells of the molecule where the overlap between the atomic orbitals is larger. The Pauli principle then prevents the electrons from all going into the orbitals with lowest energy, i.e. we have the aufbau principle. As the number of identical atoms in the molecule increases, the level density will increase correspondingly, and gradually this will become a band structure. Another illustration of a band structure formation was recently re- ported through the ESCA analysis of the 4d band of silver particles with variing radii [4]. As for us we found that the carbon compounds in the series of the alkanes (formula C n H2 n+ 2) are suitable to study step by step the formation of a band structure. The successive molecules with increasing number n are in fact considered as progressive steps in cons- tructing a quasi one dimensional solid. EXPERIMENT The valence electronic levels of the alkanes have been recorded by high resolution photoelectron spectroscopy using monochromatized Al Ka radiation source. Spectra from methane to n-tridecane (n = 1 to 13) were recorded in the gas phase with an ESCA spectrometer previously described [5]. Measurements in the condensed phase were performed for n-pentane to polyethylene (n = 5 to °°) on an HP 5950A ESCA spectrometer. FORMATION OF A BAND STRUCTURE The linear saturated hydrocarbons contain 6n + 2 electrons distribu- ted between 3n + 1 energy levels in their valence electronic region. These levels are divided into two groups : a C2p-Hls band containing carbon-hydrogen bonding orbitals, and a C2s band of essentially carbon- + Aspirant du Fonds National Beige de la Recherche Scientifique . 126 Fig. 1. : Valence electron spectra of the alkanes (1 < n < 9) recorded in the gas phase. ag«v M 25 20 nTRIDECANE 13 28 5BeV POLYETHYLENE A W„ 15 10 5 30 BINDING ENERGY (eV) 20 7.7 eV 10 Fig. 2. : Valence electron spectra of n-tridecane and polyethylene recorded respectively in the gas and solid phases. 127 carbon bonding character. The number of electronic levels in this last region equals the number of carbon atoms in the linear alkane chain [6], As discussed above, the C2s molecular orbital splits with the increa- sing number of carbon atoms in the molecule. The single 2aj (C2s) level in methane is divided into two components in ethane, three components in propane, etc. (Fig. 1). Since the C2s band is spread out over a limited energy range of about 7.5 eV, the spacing between each level decreases with an increasing num- ber of carbon atoms. Progressively, the distinction between the levels vanishes and, for larger n, the peaks overlap and form a band structure. It is interesting to find out for which number n, the ESCA spectrum of an alkane becomes essentially similar to the one of polyethylene [7]. This would in fact give the minimal system length necessary to success- fully simulate the real band structure of an infinite one dimensional solid. Fig. 2 shows that no sub-structure can be resolved already for the n-tridecane (n = 13) spectrum. Moreover, this valence band is evi- dently quite similar to the spectrum of polyethylene recorded in the so- lid phase [7]. We conclude that thirteen atoms in the alkane chain are sufficient to simulate the electronic properties of polyethylene. The magnitude of the C2s level splitting depends on the overlap bet- ween the corresponding electronic wave functions on the neighbouring atoms. Consequently, it is a function of the distance between the atoms in the molecule. The ethane (CoH^) , ethylene (C^H,) and acetylene (C2H ? ) molecules constitute a suitable series to study this effect, their carbon-carbon distances being 1.54, 1.33 and 1.21 A, respectively. Indeed, the splitting AE between the two components of the C2s band increases with the shortening of the C-C distance, being 3.49, 4.41 [8] and 4.74 [9] eV. Finally spectra recorded in the gas and solid phases have been com- pared in search of a phase transition effect, i.e. influence of inter- molecular interactions on the band structure spectra. For n-pentane taken as an example, Fig. 3 shows that the two spectra are essentially similar, presenting the same number of structures in the C2s band. The most significant difference between the two spectra is a slight increase in the peak widths recorded in the solid phase. As the alkane molecules do not contain any polar group or dipole moment, it is in fact unders- tandable that the inter-molecular interactions will not affect the solid state spectra significantly. ACKNOWLEDGEMENTS One of the authors (J. J. P.) wishes to thank the "Fonds National de la Recherche Scientif ique , Belgique" for financial support. REFERENCES [1] J.J. Pireaux. Ph.D. Thesis, Facultes Universitaires Namur 1976. ' o [2] J.J. Pireaux, S. Svensson, E. Basilier, P-A Malmqvist, U. Gelius, R. Caudano and K. Siegbahn. Uppsala UUIP 920; subm. for publ. [3] J.J. Pireaux, R. Caudano, J. Riga and J.J. Verbist, to be publ. [4] S.T. Manson and R.C. Baetzold. J. Chem. Phys . 64 (1976) 271. 123 BINDING ENERGY (eV) Fig. 3. : Valence electron spectra of n-pentane recorded in the gas and solid phases. [5] U. Gelius, E. Basilier, S. Svensson, T. Bergmark and K. Siegbahn. J. Electr. Spectr. 2 (1973) 405. [6] See e.g. R. Hoffman. J. Chem. Phys. 40 (1963) 2047. [7] J. Delhalle, J.M. Andre, S. Delhalle, J.J. Pireaux, R. Caudano and J.J. Verbist. J. Chem. Phys. 60 (1974) 595. [8] A. Berndtsson, E. Basilier, U. Gelius, J. Hedman, M. Klasson, R. Nilsson, C. Nordling and S. Svensson. Phys. Scripta \2_ (1975) 235 [9] P-A Malmqvist, E. Basilier, U. Gelius, J.J. Pireaux, S. Svensson and K. Siegbahn. To be published. 129 BERYLLIUM K SPECTRA OF BERYLLIUM COMPOUNDS Yasuo IGUCHI Institute for Optical Research, Kyoiku University Shinjuku-ku, Tokyo 160, Japan Beryllium K emission spectrum of beryllium metal has been one of the important subjects of the soft x-ray spectroscopy for a long time. The spectra of beryllium compounds, however, have been studied in a few cases. Among them, BeO, which is known as a very important substance for material research and for practical purpose, has been studied exceptionally from many aspects. There are excellent papers, for example, on the soft x-ray spectra of it (1), the fundamental absorption spectrum (2), the XPS spectrum (3), and theoretical study of the electronic structure of the valence band (4)« These previous studies give us many infor- mations on the electronic structure of BeO, though they are still not enough. In the present study, beryllium K emission spectra and rela- tive photoelectric yield spectra near the beryllium K absorption edge of BeO, BeF2 f BeSO^, and activated BeCu have been measured by means of a three meter grazing incidence monochromator and a soft x-ray tube as a light source to add some more informations on the electronic structure of these substances. A glass grating with 1Q80 lines per mm was mounted at an angle of incidence of 8^.73 • The resolution of the monochromator was better than 300 for the present experiments. The soft x-ray tube was operated at 3*5 kilovolts and at 10 mA for the emission spectrum and 200 mA for the yield spectrum. A photomultiplier with twenty dynodes was used as a detector. LiF photocathode was used to take the emission spectrum, and a sample plate or Ni plate, on which sample powder was spread over, was used as a photocathode to take the yield spectrum. Pressure of the appa- ratus was maintained at 2 x 10° Torr. BeO has the wurtzite structure, and on the other hand, BeF~ has 0(-quartz structure. Therefore, long range ordering of the crystals has nothing in common. However, if we see the short range ordering, we can find tetrahedrons. A beryllium atom is situated in the center of each tetrahedron, and the other atoms on the vertexes of it. As for BeSO/,, it is well known that BeCl^O)^ tetrahedron is important ior the crystal growth. These facts as well as the circumstance that the core state strongly localizes, suggest that the molecular orbital picture is useful for interpretation of soft x-ray spectra of the sub- stances. As K shell electrons of beryllium atom have ai symmetry in the tetrahedron ( Td symmetry ), the allowed state for elec- tronic transitions giving rise to beryllium K spectra must have t2 symmetry. Height of the structure of the spectra may reflect 130 amount of p-component in the t^ state. Some of the experimental results are shown in Fig.l and Fig. 2. As for BeO, dominant structures have been observed in the emission spectrum at 89.4 eV, 105.0 eV, and 106.1 eV, and in the yield spectrum at 119-6 eV, 124.6 eV, and 138.6 eV. Corresponding structures of BeF 2 have been observed in the emission spectrum at 89.8 eV, 104.5 eV, and 106.4 eV, and in the yield spectrum at 120.5 eV, 124.8 eV, and 138.4 eV. An extra structure has been observed in the emission spectrum of BeF 2 at about 110 eV. The widths of main bands of the emission spectra are 10 eV and 12 eV for BeO and BeF2 respectively. These values of the band widths agree with the ones determined by XPS (3) and UPS (7). The struc- tures at 118 eV observed in both of the emission spectra of BeO and BeF 2 are considered due to double ionization (5). The yield spectrum of BeSO^ agrees with the one reported by Brohin et al. (6), and it shows corresponding structures to the ones of the yield spectra of BeO and BeF 2 . The yield spectrum of activated BeCu has closely similar structures to the ones of the yield spectrum of BeO. This fact and surface composition of activated BeCu observed by Ruttenberg and Haas (8) may support the molecu- lar orbital picture for the interpretation of BeO spectra. Tentative molecular orbital levels with t 2 symmetry of the tetrahedron are shown in Fig. 3 together with experimentally de- termined energy scale. Atomic energy levels of Be, 0, and F atoms are also shown in the figure. Anyhow, K spectra of the atom centered in the tetrahedron are useful for observing t 2 molecu- lar orbitals selectively. References (1) A.P.Lukirskii and I.A.Brytov: Soviet Phys. Solid State 6 33 (2) D.M.Roessler and W.C.Walker: J. Phys. Chem. Solids ^0 157 (1969) (3) K.Hamrin et al.: Phys.Scripta 1 277 (1970) (4) W.O'Sullivan: J. Chem. Phys. ^0 379 (1959) (5) Y.Hayashi: Sci.Rep.Tohoku Univ. (1) £1 1 (1968) (6) T.A.Brohin et al. : Izv.Akad.Nauk SSSR ^8 652 (1974) (7) R.T.Poole et al. : Phys. Rev. B 12 5872 (1975) (8) F.E. Ruttenberg and T.W.Haas: J.Vac.Sci.Technol. 12 1043 (1975) 131 Fig.l Beryllium K spectra of Fig.2 Beryllium K spectra of BeO. BeF 2 . 1: Emission, 2: Photoelectric yield. Be MOLECULAR ORBITAL t 7 -10 ji 2p(t 2 ) — 2s (a,) 10 - 20 30 ■ Fig, 3 Energy level diagram for (W*) tp molecu lar orbitals of — 2pin_ tne tetrahedron. 2pcr — fO|*t 2 ) 2s (a,*t 2 7 100 110 120- to ' — 1s(a.) a. ac CD U-> co I'JUUL 132 CHARACTERIZATION OF SILICON MONOXIDE BY X-RAY SPECTROSCOPY. M.T. COSTA LIMA - C. SENEMAUD Laboratoire de Chimie Physique 11, rue Pierre et Marie Curie 75231 Paris Cedex 05 - France. Silicon monoxide, which has interesting properties for microelectronic applications, has often been considered as a mixture of pure silicon and quartz SiO ? . However, some recent measurements from optical properties (1), nuclear analysis and infrared spectroscopy (2) are not accounted for by the same hypothesis. We have studied comparatively the K X-ray emission and absorption spectra of silicon in amorphous samples of pure silicon, SiO and SiO ? . The in- fluence of the crystalline state of Si and Si0 2 on their spectra is discussed elsewhere (3,4). Without any adjustment in the energy scale, the absorption spectrum of SiO shows that this oxide is not a mixture Si + Si0 2 (5): no structure appears on the recor- dings, neither at the Si K edge position, nor at the wave- length of the strong Si0 2 absorption line. On the other hand, the SiO K£> emission has two structures, separated by about 4 eV, which appear at the position of Si K(3 and Si0 9 Kfi maxima, in agreement with previous results ( 6 ) (7). The two electronic distributions involved in the X-ray transitions are affected by the chemical state of the element. In fact, the relative energetic position of the silicon valence and conduction bands in the element and in the oxide can be deduced from their K spectra, only if we know the shift of the K level. The Si 2p energy has been measured by ESCA in Si, SiO and Si0 2 (8). From our measure- ments of the energy of the Koc emission (2p-~>ls ) (3), we have deduced the energy of the Is level in Si, SiO and Si0 2 , and, consequently the shift of this level in SiO and Si0 2 compared to the pure element. This shift is relatively high and is different for the twooxides = + 2,9 and 5,0 eV res- pectively. Taking into account these values, we have adjusted the spectra of Si SiO and Si0 2 , relatively to the position of the Fermi level obtained from the photoelectron spectra. (Fig. 1) . This adjustement gives the relative position of the valence band and the limit of the conduction band of Si, SiO and Si0 2 . It appears that the SiO KfZ emission is not a superposition of Si and SiO^ spectra (9). This result is the same than deduced from the X-ray absorption spectra. A comparison with photoelectron spectra is shown on the figure. It will be discussed in details. 133 A tetrahedral model Si-Si O. _ has been proposed by Philipp (1) for the silicon monoxide 7 . Following a statis- tical distribution, the arrangements Si-SiQ , Si - Si 2 and Si - Si->0 are the most likely. Then three types of binding are possible for the silicon atoms. They can be related to the three structures observed on the X-ray absorption curve of SiO, and to the maximums of the K(3> emission, assuming that the broadest one corresponds to non-resolved transitions involving two different kinds of Si binding. So our X-ray spectra are consistent with Philipp' s model. Emission SiO, SiO Si Absorption K J 1 1 I L -1 1 ► •25 -20 -15 -10-5 +5 +10 +15 +20 +25 E F E(eV) Fig. 1. X-ray spectra photoelectron spectra : Si (10) SiO (8) SiO (11) 134 REFERENCES (1) H.R. PHILIPP - J. Phys. Chem. Solids 2/Z, 1935, 1971 (2) A. CACHARD, J. A. ROGER, Phys. Stat. Sol. 5a, 637, 1971. (3) M.T. COSTA LIMA, These de Doctorat d'Etat, Paris 1976. (4) M.T. COSTA LIMA, C. SENEMAUD , to be published. (5) C. SENEMAUD, M.T. COSTA LIMA, J. A. ROGER, A. CACHARD, Chem. Phys. Lett. 2_6, 431, 1974. (6) E.W. WHITE, R. ROY, Solid St. Comm. 2, 151, 1964. (7) W.L. BAUN, J.C. SALOMON, Vacuum, 2^, 165, 1971. (8) G. HOLLINGER, J. TOUSSET, TRAN MINH DUG, Intern. Conf. on Tetrahedrally bounded amorphous Semi Conductors, York town Heights 1974, p. 102. (9) M.T. COSTA LIMA, C. SENEMAUD, Chem. Phys. Lett. £0, 157, 1976. (10) L. LEY, S. KOWALCZYK, R. POLLAK, D.A. SHIRLEY, Phys. Rev. Lett. 29, 1088, 1972. (11) T.H. DI STEPHANO, D.E. EASTMAN, Phys. Rev. Lett. 27, 1560, 1971. 135 THE EFFECT OF TEMPERATURE ON X-RAY EMISSION SPECTRA J.B. Jones, M. Kasrai and D.S. Urch Department of Chemistry, Queen Mary College, Mile End Road, London El 4NS, U.K. (m. Kasrai, on leave from, Tehran University, Institute of Nuclear Science & Technology, Tehran, Iran] A Philips PW1410 X-ray fluorescence spectrometer has been modified so that the temperature of the sample can be controlled during irradia- tion (1) . The sample is placed at the end of the probe of an Oxford Instrument CFlOO cryostat which permits the temperature to be varied in the range 80° - 400°K when liquid nitrogen is used. Preliminary results using vanadium pentoxide and neodynium titanate, (see Table) showed that cooling causes a large reduction in peak intensity and that small changes in peak position can also be observed. Table Sample Peak Intensity (counts sec ) % Decrease 350°K 97°K V 2 5 r V K3i,3 165 128 22 V K£ 2 ', 5 12 10 15 Position (electron volts) 350°K 97°K Shift V 2 5 r V K3j 3 5418.4 5419.0 +0.6 V K3 2 ' 5 5455.1 5454.9 -0.2 NdoTi.O, { T± K3 ^3 4932. 4(8. 2) a 4933. 0(7. 6) a +0.6 227 Ti K0 2/5 4963.8 4963.9 (a) full width at half -height It is also interesting to note that peak widths are somewhat reduced at lower temperatures. The reduction in intensity upon cooling was the most dramatic observation, however, and so this phenomenon was investigated further by measuring the intensity of the vanadium K(3i 3 peak from vanadium pentoxide at a variety of temperatures in the range 90-400°K. The results are shown in fig.l. A linear increase in peak intensity with temperature is observed. This increase in intensity may be due to vibronic coupling effects which would make a greater number of states available at higher temperatures. Such effects might also be expected to cause an increase in peak width as is observed. It has been proposed by many authors (2,3,4) that the structure of the K3', Kg} 3 peak in first row transition metal X-ray emission spectra, is closely related to the magnetic moment of the metal ion in the sample . Some complexes are known in which the magnetic moment is temp- erature dependent. A study of the structure of the K3 ' K$i,3 peak as a function °f temperature of one such compound was therefore made;- iron- bis (diethyl dithio carbamate) nitrosyl, the magnetic susceptibility of 136 which diminishes with temperature (5) . The results at 328, 160 and 93 °K are shown in fig. 2. Whilst the reduction in main peak intensity with temperature is apparent it is most interesting to notice that the relative intensity of Kft * also diminishes. This is of course exactly the behaviour that would be expected if the K3*:K3 1/3 intensity ratio is related to the magnetic moment of the iron. These preliminary experiments show that temperature can profoundly affect the intensity of Xray emission spectra and also that when certain physical properties (e.g. magnetic moment) are temperature dependent, corresponding effects can also be observed in the Xray spectra. References 1. J.B. Jones and D.S. Urch, J. Physics E, Sci.Inst ., 8_, 541 (1975). 2. K.J. Tsutsumi, J. Phys. So C.Japan , 14, 1696 (1959). 3. R.A. Slater and D.S. Urch, J.Chem.Soc.D. Chem.Comm . , 1972 , 564. 4. V.F. Demekhin, G.F. Lemeshku and A.T. Shavaev, I zv . Akad . Nauk . SSR , Ser.Fiz . 38 , 587 (1974) - Eng. trans. p. 136. 5. A.H. Ewald, R.L. Martin, G.I. Ross and A.H. White, Proc.Roy.Soc . , A280, 235 (1964). 160- Coo f&S I** /40- r> 5 A 20J i ioo ,1QO .300 Aoo 137 K> * 1 «3 «r> IB o o O o Y* — o o 138 THE CHEMICAL BONDING IN SPINEL (Mg Alp O^ ) STUDIED BY XRAY EMISSION AND XRAY PHOTQELECTRON SPECTROSCOPIES D. Haycock, C.J. Nicholls and D.S. Urch, Chemistry Department, Queen Mary College, Mile End Road, LONDON El 4NS , U.K. The structure of Xray emission peaks that arise from electronic, valence -band -inner orbital, transitions reflects the participation of specific valence shell atomic orbital (s) in the molecular orbitals which comprise the chemical bond. A study of all possible Xray emission peaks from a particular chemical compound thus enables the structure of the bonding to be investigated in great detail. In order that such a study can be carried out it is also necessary to know the ionisation energies of the inner orbitals so that all spectra may be placed on a common ener- gy scale. This can be done using Xray photoelectron spectroscopy. In this paper Xray emission and Xray photoelectron spectra for spin- el, Mg Al20 t+ are discussed. The former were obtained using a Philips PW 1410 Xray fluorescence spectrometer; the latter with a Vacuum Generat- ors ESCA III instrument. The results which are shown in fig. 1 display considerable unres- olved structure. By the use of a simple computer procedure, it was, however, possible to resolve the spectra into three or in one case, four Gaussian components, details of which are given in the table. Oxygen Ka Magnesium K^ 3 position 521.2 522.7 524.9 1290.1 1293.2 1294.7 1296.9 intensity -arbitrary 312 156 1092 182 1325 383 2268 units full -width half-height 2.13 1.15 1.46 1.75 1.95 1.36 1.82 aluminium K3 1 , 3 1545.7 1549.4 1552.3 306 2916 2370 2.58 2.46 2.25 The positions and relative heights of these resolved peaks are indicated in the figure. It can be seen that two distinct bands of orbitals are present separated by about 2 eV. The positions and relative intensities of these peaks can be ration- alised using a simple molecular orbital model for the bonding in spinel. The structure of spinel (1,2) is such that each magnesium is tetra- hedrally coordinated by oxygen and each aluminium is octahedrally co- ordinated by oxygen and that each oxygen is bound to one magnesium and three aluminium atoms in a trigonally distorted tetrahedron. 139 The bonding between oxygen and aluminium can be discussed in terms of an Al^. 0^ cube in which the sp hybrids from Al and p orbital s from oxygen are orientated towards the centre. This model predicts that two sets of m.o's should be formed, the least tightly bound (A) having an excess of oxygen 2p character compared with the more tightly bound set (B) and also that set A should be skewed, with an excess of more tightly bound orbitals. Al 3p character should be greater in set B than A but not exceeding 3:1. When the bonding between the m.o's of sets A and B and the magnesium atoms is considered it is found that Mg 3p char- acter is concentrated in orbitals A rather than B (limiting ionic case for Mg 3p A:B = /3~:1) . A simple qualitative m.o. discussion thus pro- vides an explanation for the main features and relative intensities of the Xray emission peaks from spinel. References 1. W.H. Bragg, Phil. Mag. 30 , 305 (1915). 2. G.E. Bacon, Acta Cryst. 5, 684 (1952). 140 141 AN XES STUDY OF THE STRUCTURE OF As-S GLASSES M. LMhdeniemi and E. Suoninen Department of Physical Sciences/Materials Sc. University of Turku SF-20500 Turku 50, Finland The mechanism of dissolving As atoms in arsenic glasses was studied in this work by measuring the S K emission spectra of As-S alloys in the region 0-40 at% As. The main question to be decided was whether the dissolving takes place through the formation of clusters of As^S.-., Previ- ous similar studies by Salaneck et al [1] were judged inconclusive. Our measurements were made with a double crystal spectrometer [2] using Si (111) crystals in the (1,1) position and fluorescence exitation. The samples were given a homogenization anneal of several days at a tem- perature depending on the composition. X-ray diffraction runs of each sample indicated an amorphous structure. The S K$ band was measured for each alloy. The result for samples with at%(S) and 40 at%(As 9 S„) arsenic are shown in Fig. 1. The energy scale refers to the position of the 3 peak of pure S. The Fermi energy is defined as the half-maximum intensity at the high-energy shoulder (c,f. (Fig, 2). The measured energy shifts and half width of the S Kg bands are shown in Table 1 (indicated by A) . The band shape is seen to change gradually with increasing As content. The low-energy part of the band getting relatively weaker. There is also a negative energy shift of the high-energy part of the band. i it . — I-, i -10 -5 Relative energy (eV) Fig. 1. S Kg band of S and As 2 S 3* /y---100% vT P, *-» c D >» ^v V"5 0?c i- *-• XI *- f\ (0 ■*m^ S / > 1 *-• w \ EF c \f ■ 4) c As 2 s 3 l t, .. i l_ 142 Table 1 Energy shift (eV) Atfo As A I I - 10 -0.15 -0. 16 20 -0.27 -0. 28 30 -0.53 -0. 60 40 -0.84 -0. 84 Half width (eV) A B 6.14 6.14 5.79 6.00 5.59 5.75 5.35 5.37 4.60 4.60 The measured S K/9 band can be quite well interpreted as a weighted superposition of the band shapes of S and ASpS-. Parameters for the band obtained trough superposition are given in Table 1 (indicated by B). A gradual small negative energy shift with alloy- ing is also found for the S Ko( line. This supports the above super- position interpretation. The results are compa- tible with the assumption that arsenic atoms enter the alloy as ASpS^ mole- cules. The above tenta- tive interpretation agrees with the previous work of Salaneck et al £1 ] , but the measured data upon which they ba- sed their conclusions are found to be very different from ours. -10 -6 Binding energy (eV) Fig. 2. Low energy structure of the band : 1 . S, 2. As 2 S 3 , 3. 30 atfo As. The binding energies were obtained by using Fermi energies obtained as shown in Fig. 1 . 143 According to calculations by Chen [3] , the s-p hybrid molecular orbitals 2> with a substantial amount of p character of ASpS^ have binding energies in the region 9.3- 11.65 eV. They can be expected to give rise to satellite lines at the low energy side of the main band. No estimates for the line intensities to be expected are, however, available. It is seen from Fig. 2 that a broad satellite is indeed present in the samples containing arsenic, which again supports the above interpretation. Acknowledgements The authors are grateful to Ms. E.-K. Viinikka for interesting discussions. This research was financially supported by the Academy of Finland. References 1 . W.R. Salaneck, N.O. Lipari, W. McCain and R. LaForce, Solid State Commun. 1£, 1453(1974). 2. E. Suoninen and M. Pessa, Phys. Scripta 7, 89(1973). 3. I. Chen, Phys. Rev. B 8, 1440(1973). 144 INVESTIGATION OF THE X-RAY EMISSION AND PHOTOELECTRIC YIELD SPECTRA OF BERYLLIUM IN ITS COMPOUNDS M.A. Blokhin, E.G. Orlova, and I.G. Schweizer Department of Solid State Physics, Rostov State University 344006 Rostov-on-the-Don, USSR The Be K-photoelectric yield spectra of BeO, Be(OH) 2 , BeC0 3 , BeSi0 3 , BeS0i + *4H20, Be^POi+^j BeF2 , Na2BeF4 and K^BeF^ are measured with a reso- lution of 0.3 eV by means of the RSM-500 soft X-ray spectrometer. For the last two compounds BeK-emission spectra were also measured. As is generally known [1,2] the photoelectric yield spectra, as well as the X-ray absorption spectra, give information about the free electron states. In this work compounds were investigated in which the Be atom is surrounded with oxygen or fluorine atoms or with hydroxyl groups (OH) - or water molecules. From the comparison of ESCA data [3,4] and photoelectric yield spectra one can see that the whole fine structure of the last one is situated above the ionization potential in the continuous absorption region. The discrete absorption lines correspond to the electron transitions from the Be ls-level into quasi-stationary states. In Fig. 1 the photoelec- tric yield spectra are given for some of the compounds investigated. In the next table energies corresponding to the position of the first peak A are listed. We have revealed a systematic displacement of the peak A in the low energy side by changing ligands in the first coordina- tion sphere of Be accordingly to the known spectrochemical series: - H 2 - OH - F. The influence of the second coordination sphere on the position of the first absorption peak can be observed by examining the photoelectric spectra of Na- and K-f luoberyllates, where the alkali metal atoms are located [5] between the BeF^~ tetrahedra cations. When the Na cation is substituted by K the negative charge on F atoms rises and the Be ls- level energy decreases. As the photoelectron data [4,6] shows, the energy difference between Be ls-levels of Na2BeFi + and K^BeF^ is 0.6 eV (the results in [6] were recalculated relative to the traditional cali- bration C ls-line of the hydrocarbon contamination layer) . Such a sub- stitution shifts the photoelectric yield spectra to the low energy side: the peak A energy for K 2 BeF t+ is 1.1 eV lower than for Na 2 BeF t+ , It fol- lows therefore that a change of a Na+ ion in f luoberyllates causes a rise of the first free level of p-symmetry by 0.5 eV roughly. The smeared structure of the Be photoelectric yield spectra of Be (OH) 2 can be explained by low symmetry surrounding of the Be atom in the crystal lattice of the hydroxide (the space group is D^ the possible point group of symmetry for the Be atom is very low -'C\). There is no information about the metasilicate BeSi0 3 crystal structure. A comparison of BeK-photoelectric spectra for BeO and for BeSi0 3 and also of S1L2 3 -spectra for BeSi0 3 and for silicates with differing coordination of the SiO^-tetrahedras allows us to suggest the following structure for BeSi0 3 : slightly distorted Be0 4 -tetrahedra bonded through oxygen atoms with the SiO^-tetrahedra, which form an infinite chain (SiOs)^. The distortion of Si0i+-tetrahedra is low. 145 Table Energy of Compound Peak A, eV BeO 119.5 BeSi0 3 119.5 Be 3 (PO Lf ) 2 119.8 BeS0i/4H 2 120.0 Be (OH) 2 120.8 Na 2 BeF t+ 121.7 K 2 BeF4 120.6 E.eVi Fig. 1. Photoelectric yield spectra fcrom the Be ls-level for compounds: 1 - BeO, 2 - BeSi0 3 , 3 - Be(0H) 2 , 4 - BeS0 l+ *4H 2 0, 5 - Be 3 (P0 t+ ) 2 , 6 - Na 2 BeF t+ , 7 - K 2 BeF 4 . The scale on the ordinate axis is arbi- trary. The peaks A", B", C'(2) belong to the SiL 2 3 -spectrum and the peaks D', E'(5) - to the PL 2 3 -spectrum. The crystal structure of Be 3 (P0 t+ ) 2 is unknown. Generally one assumes that by normal conditions the Be ortho-phosphate is a hydrate. A comparison was made between BeK-photoelectric spectra in Be 3 (P0t + ) 2 and in BeS0 t+ '4H 2 in which the Be atoms are tetrahedrally surrounded with water molecules. The shape and 146 energy position of the phos- phate spectra peaks confirm the last assumption. A superposition of beryllium and oxygen K-spectra of BeO [7] had shown an ^ 8 eV shift of the Be and absorption K-spectra and it allows us to conclude that the states near the bottom of BeO conductivity band can be described with Be p-f unctions in the main. By using ESCA data we have superimposed BeK-photoelectric spectra and FK-absorption spectra. In this case the K-edges of both spectra are practically coinciding and the spectra fine structures of both components are in good agreement with each other . So the more complica- ted character of the absorp- tion spectra, initial part for f luoberyllates, compared to the same part of BeO-spectra can be a consequence of a strong wave function hybridi- zation of the excited Be- and F-states. The BeK-emission spectra are shown in Fig. 2. According to the molecular orbital scheme for the BeFJ; tetra- hedra [8] the transition from Be ls-state to the lt 2 -state (in which the part of Be 2p- states is low) displayed in the emission spectrum as a References 30 100 110 E,eVi Fig. 2. BeK-emission spectra for fluo- beryllates: 1 - Na 2 BeF 4 , 2 - K^BeF^. The dashed line shows the X-ray photo- electron spectrum for the valence band of the BeF£~ ion in the Li 2 BeF 4 salt [9] very faint band d with a relative intensity ^2%, located ^20 eV to the low energy side from the main peak b (the transition Be Is -> 2t 2 ) . The main emission band has a complicated shape. The low energy shoulder c is apparent- ly a consequence of lower symmetry of the BeF^ - tetrahedron in the fluo- beryllates and of the resulting Be 2s- and 2p-levels mixing. The peaks a" and b' of the X-ray photoelectron spectrum (Fig. 2) with a distance 1.0 eV between them corresponds to 3t 2 - and 2t 2 -levels, the main contribution to which give the F 2p- and Be 2p- levels correspondingly. The same distance 1.0 eV is also seen on the X-ray spectrum between the peak b and the shoulder a. The last one corre- sponds apparently to the Be Is •*■ 3t 2 transition and from its great intensity one can conclude that a considerable hybridization of F and Be 2p-states exists. 147 1. A. P. Lukirski, T.M. Zimkina, Izv. AN SSSR, Ser. Phys. 28, 765 (1964) (in Russ . ) . 2. W. Gudat, C. Kunz, Phys. Rev. Lett. 29, 169 (1972). 3. K. Hamrin, G. Johansson et al, Physica Scripta 1_, 277 (1970). 4. V.I. Nefedov, J.V. Kokunov et al, Journ. Neorganich. Khimii 1_8, 931 (1973) (in Russ . ) . 5. Landolt-Bornstein, B.l Atom und Molekularphysik, T1.4 Kristalle, Springer-Verlag, 1955, S.62, 74. 6. Ch.K. J^rgensen, H. Berthon, Mat.-Fys. Medd . Kgl . Dan. Vid. Selsk. 38, 1 (1972). 7. V.A. Fomichev, Phys. Tverd . Tela 13, 907 (1971) (in Russ. ) . 8. B.F. Shchegolev, E.L. Rosenberg et al, Journ. Strukt. Khimii 1_4, 581 (1973) (in Russ.). 9. V.I. Nefedov, J.V. Kokunov et al, Journ. Neorganich. Khimii 18, 1208 (1973) (in Russ. ) . CHEMICAL SHIFTS OF THE K ABSORPTION DISCONTINUITY OP COBAEP IN INTERMETALIIC SYSTEMS Chintamanl Mande and Vivek Kondawar Department of Physics Nagpur University Nagpur (India) It is well known that X-ray absorption spectra are affected by chemical combination. Several types of effects due to chemical combination on X-ray absorption discontinuities are reported in literature. They include the effects on the position, shape and fine structure - near edge as well as extended - of the discontinuities. Amongst all these rffects, the chemical shifts have attracted the greatest attention and in a very large number of papers the chemical shifts of X-ray absorption discontinuities have been reported. Kunzl(1 ) was the first worker to show that the chemical shifts depend upon valency. Later work has shown that the chemical shifts are influenced not only by valency, but also by other factors, such as coordination number, chemical bonding and structure of the compounds. However, it is not yet clear in what way exactly the different factors contribute to the chemical shifts. It should be borne in mind that the chemical shifts should ideally refer to the completely free absorbing atom, such as that in the case of monoatomic gases. However, in practice the chemical shifts are always measured with respect to the discontinuity in the pure element in the solid state, mostly in metals. Probably because of this, one observes altogether different orders of magnitudes in the case of chemical shifts of different elements. Also, one finds that most often the chemical shifts are positive, i.e. the discontinuities in the compounds shift to the higher energy side with respect to the discontinuity in the pure metal. However, occassionally negative shifts have also been reported. In our laboratory, we have been making systematic efforts to unfold the various causes which determine the positive and negative chemical shifts in X-ray absorption spectra. Our earlier work(2) on gallium, germanium, arsenic and selenium has shown that the chemical shifts are positive whenever the absorbing atom is a cation and are negative when the absorbing atom is an anion. It has also been shown that the magnitudes of the chemical shifts for a given 148 absorbing element mainly depend upon the effective charge on the absorbing atom. In the present paper, our study on the chemical shifts of the K absorption discontinuity of cobalt in some intermetallic compounds, viz. CoO, CoS, CoAs, CoSe, CoTe, CoAsS, C0S2, C0AS2, CoSe2, CoTe2» CoGe2 and C02AS is reported. The spectra were recorded using a 40 cm Cauchois type bent crystal spectrograph. The other experimental details are described elsewhere (2, 3) . We have observed that the main cobalt K absorption discontinuity in the above compounds shifts to the high energy side with respect to that in the pure metal. The observed chemical shifts (AE) have been found to depend upon the effective charge (q) on the cobalt ions in different compounds, which have been calculated on the basis of Suchet's model. The AE vs q curves obtained by us in the present case are somewhat different than those obtained in our earlier work on gallium, germanium, arsenic and selenium. Whereas the AE vs q curves for the latter elements pass through the origin, the AE vs q curves for the cobalt K discontinuity do not show this behaviour. Also, instead of a single AE vs q curve for all the compounds, we have obtained two separate curves for the compounds of MX and MXp types, both of which do not pass through the origin, we have tried to explain our observations by considering the possible differences in the nature of the final levels available for absorption. Our work shows that the final level responsible for absorption in the MX type of compounds is situated at least 1.5 eV higher than the Fermi level in the metal and that it goes on shifting towards the high energy side as the effective charge on the cobalt atom increases in the compounds. Similarly, the final level responsible for absorption in the ternary compounds is situated at least 2.2 eV away from the Fermi level of the metal. The final level for the MX? family of compounds also shifts gradually towards the high energy side as the effective charge on the cobalt atoms increases in the series. The positive chemical shifts obtained confirm that the cobalt atom behaves as a cation in all the compounds studied in the present work. It is interesting to mention here that recently it has been shown(4,5) in our laboratory that the cobalt discontinuity shifts to the low energy side in RC02 and RC05 types of compounds, where R stands for a rare earth atom, indicating that the cobalt ion behaves as an anion in these compounds. Our work shows that the chemical shifts in X-ray absorption spectra can be used to obtain fruitful 149 information regarding chemical bonding prevailing in a compound. References 1) Banal, V. 2) Mande, C. and Sapre, V.B. Coll. Trav. Chim. Techecoslovaquie, 4(S) (1932) 213. Proc. Int. Synm. X-ray Spectra and Electronic Structure of Matter, Miinchen, 1, (1972) 237-248. 3) Kondawar, V.K. and J, Phys. C, 9 (1976) 1351-1359. Mande, C. 4) Chetal, A.R. and J. Hiys. F, 5 (1975) L217. Sarode, I.R. 5) Sarode, P,R. and Physica Stat. Solidi (in Press). Chetal, A.R. 150 K-ABSOBPTION SPECTRA OF SOME POLYNUCLEAR COPPER COMPLEXES Jagdish Prasad, Vijai Krishna and Hira Lai Nigam Chemistry Department, Allahabad University, Allahabad-2, India. The shifts in the K- absorption edges and the principal absorp- tion maxima have been shown to depend primarily on the valence state of the metal in que at i on [1 ,2], An observation has been recorded to show that the edge shift notwithstanding its valence dependence is boosted in case of compounds which involve metal-metal inter act ion [3]. Very little X-ray spectroscopic work has been done on such compounds. In fact, the nature of metal-metal bonds remains an open quest ion[4]. The present communication therefore, is an attempt to apply this technique in case of some especially chosen set of polynuclear copper complexes known to involve metal -metal interaction. The spectra were recorded using a 40-cm curved crystal (mica) spectrograph on Kodak X-ray films. The data on edge shifts and the relative energies of the principal absorption maxima of these complexes are given in Table 1 , a perusal of which would readily show that the edge shift as also the energy of the main peak, E A are significantly larger for compounds involving Cu(H) than those involving Cu(l). Surprisingly, however, the magnitudes of edge shifts for the compounds (Nos. XXX-XXII) are seen to fall in the range of Cu(l) and are too small to be expected for Cu(ll). The possibility of copper ion, being in the 4-1 state in these complexes has been ruled out earlier[5J. The relative energies of the main peak of these compounds however, fall close to the value observed for Cu2+ ion[6j. Hence, the criterion based on B A rather than edge shift seems to be more reliable in regard to correct assignment of the oxidation state of the absorbing atom, The suppression in edge shifts may probably be due to enhanced covalency or band formation in these complexes [7,8 J. Further, these observations do not support the hypo- thesis of boosting in edge shift as a consequence of metal-metal interaction. The extended fine structure spectra of the square planar complexes show a general broadening in case of mixed oxygen and halogen ligands as against sharp peaks for only oxygen ligands. This leads to the conclusion that the fine structure is determined not only by the number of surrounding donor atoms, as hitherto believed[9j , but also by their nature. The difference in energy, AE from the second absorption maximum, B to the next minimum, § in the fine structure spectra may be used to compute[lO] , the radius of the first coordination sphere around the central metal ion through the Bragg relation As evident from Table 2, the estimated bond lengths are close to those obtained from crystallographie data. 151 Table 1. Shifts In the K-absorption edge and the main peak of copper In some complexes (in eV) fir, ° Xd ' No ' State C o n p 1 ex Edge shift ±0.6 Main peak (e a )±o.6 I +1 cuCc^ro^Sj) 1.1 8.0 II Cu(N0 3 )(PPh 3 ) 3 1.4 12.8 III Cu(N0 3 )(PPh 3 ) 2 2.2 12.2 IV Cu 4 (tu) 9(1*03)4 3.0 13.7 V + 2 cu(ci 3 c»coo) 2 5.8 17.0 VI Cu(ClCH 2 .C00) 2 7.7 19.1 VII Cu(H0.C 6 H4.C00) 2 8.6 19.3 VIII Cu(C 6 H5.COO) 2 10.1 21.3 IX Cu(CHyC00) 2 10.2 21.7 X Cu(C 11 H 23 .C00) 2 11.7 22.8 XI Cu(C l7 H 35 .COO) 2 11.0 22.5 XII 0^(00^)2(0^2)2 10.9 22.7 XIII KCuCl 3 4.7 16.3 XIV KCuBr 3 6.0 18.7 XV Cu(C 5 H 5 NO)Cl 2 5.4 17.5 XVI Ci^C^NO)^ 4.3 17.9 XVII cu^t^Cth) 2 .ioh 2 o 6.5 20.6 XVIII Cu(C^H 2 N 2 0S)«2H20 5.8 17.5 XIX Cu(C 2 HN 2 S 3 ) 2 1.6 16.3 XX Cu 2 (C 8 H lf N 2 S 2 )Q 2 1.4 15.8 XXI cu(c 7 R 5 n l s) 2 1.2 16.3 XXII Cu(C 7 H 4 N 4 SBr) 2 1.5 16.0 * tu s thiourea, T = C 4 HN 2 S 3 , : 8 H 5 N 2 S 2 152 42.2 1.88 Cu-0 * 1.97 Cu-OCH-^O) =2.20 39.4 1.95 Cu-0 = 1.91 Cu-0(H 2 0) 3 1.97 40.5 1.92 Cu-0 = 1 . 84 Cu-0(H 2 0) =1.92 28.5 2.30 Cu-Cl = 2.25 Cu-Cl = 2.32 34.2 2.10 Cu-0 = 2.03 Cu-Cl = 2.20 Table 2. Average metal -ligand bond lengths A AE(/5 -B) Computed % diffraction _ - Compound ^ y) jdj, ^ * r (|) Ref . Cu(ChyC00) 2 Cu(C 6 H 5 -C00) 2 Cu(H0.C 6 I^.C00) 2 KCuCl, Cu(C 5 PLNO)Cl 2 a. J.N. Van Niekerk and F.R.L. Schoening, Aota Cryst. 6, 227 (1953). b. H. Koi*umi, K. Osaki and T. Watanabe, J. Phys. Soc. Japan, 18, 117 (1963). 0. F. Hanic and J. Miohalov, Acta Cryst. 13, 299 (i960). d. R.D.Willet, C. Dwigglns (Jr.), R.F. Kruh and R.E. Rundle, J. Chenw Phys. 38, 2429 (1963), «. R. S. Sager, R.J. Williams, and W.H. Watson, Inorg. Cham. 6, 951 (1967). REFStENCBS : 1. G. Boehm, A. Paessler and G. Rittmayer, Z. Naturforsch, B9, 509 (1954). 2. G.L. Glen and C.G. Dodd, J. Appl. Phys. 39, 5372 (1968). 3. B.K. Agamal and L.P. Verma, J. Phys. C. 3, 535 (1970). 4. R.S. Nyholm, Advancement of Science, January, 436 (1967). 5. U. Agarwala and S.K. Dikshit, D.Phil. Thesis (Dikshit), I.I.T. , Kanpur (1968). 6. W. W. Beeman, J. Forss, and J.N. Humphrey, Phys. Rev. 67, 212 (1945). 7. U.C. Srivastava and H.L. Nigam, Coord. Chem.Rev. 9, 275 (1973). 8. V.G. Bhide and N.V. Bhat, J. Chera. Phys. 48, 31 03 (l9^8). 9. D. Coster and S. Kiestra, Physica 14, 75 (1949). 10. R.M. Levy, J. Chem. Phys. 43, 1 846 (1965). 153 THE K-EMISSION AND ABSORPTION OF GALLIUM IN GaP, GaAs AND GaSb J.Drahokoupil , H.Klokocnikova and A.Simunek Institute of Solid State Physics, Czech. Acad. Sci ., Cukrovarnick^ 10, 162 53 Praha 6, Czechoslovakia The K(?2~ emission band and the K-absorption edge of gallium were measured and computed in the isostructural com- pounds GaP, GaAs and GaSb. In emission the shape and the integral intensity of the bands (normalized to K$-. -. ) were studied. The shape of the bands is very similar for all the studied compounds while the intensity increases from GaP to GaSb. This is an evi- dence of the increasing valence electron localization on gallium (notice that A B compounds are of the same structure), in agreement with the ionicity and gap width of these materials. In absorption the shape, position of the K-edge and K- absorption "jump" were studied. For GaP and GaAs the shapes are very similar, only the magnitude of the "jump" for Ga&s is greater; to compare with the theory it was necessary to measure the absorption coefficient in the region of several hundred eV from the edge for normalization (see [l] ). The shape for GaSb was found distinctly different. The K-edges of these materials were formerly measured ([l],[2]) but the results concerning the position of the edge significantly 154 differ. Our analysis of the measured and computed curves shows that the edge position is not a good parameter: its experimental value is very sensitive to the form of the apparatus smearing; moreover it does not describe ad- equately changes of the conduction band bottom. As an example the results for GaP are given in Fig.l. Experimen- 1 1 1 1 1 — III'" Till 1 1 1 - 1 1 1 1 1 1 1 ' I 1 1 1 1 1 1 — GaP THEORY > emission / \ / absorption 1 ' top of the valence band EXPERIMENT emission / \ / absorption i i i i i i i i i i 1»V energy ' 1 1 l—l L Fig.l. Profiles of K-emission intensity- curves on the left; absorption coefficient-curves on the right . 155 tal curves are not corrected and so the mirror-like corre- spondence of the K-absorption structure on the high energy side of emission is visible. The measurements were performed on the double crystal spectrometer; the OPW band structure transition probability and partial densities of states were computed. The details of the methods can be found in our paper [3], in which the system Ge, GaAs and ZnSe was studied in a similar way. [l] Kantelhardt D. and Waidelich W., Z.Angew.Phys. 26, 239 (1969) [2~\ Mande C, Chetal A.R. and Sapre V.B., Curr.Sci. 29, 391 (1970) [3] Drahokoupil J., KlokoSnikova" H. and Simunek A., J.Phys.C: Solid St.Phys. 2, 2667 (1976) 156 EFFECT ON CHEMICAL ENVIRONMENT ON SULFUR K a X-RAY SPECTRA G.Graeffe and H.Juslen Tampere University of Technology, 33101 Tampere 10, Finland and E.K. Viinikka Helsinki Technical University, 02150 Espoo, Finland Chemical effects in x-ray emission spectra was observed as early as for fifty years ago. The chemical shifts for K a ._ lines have been measured for many different chemical compounds for different elements by various authors |l|. The chemical shift for x-ray satellites (from double io- nized states) is even larger but the satellite intensities are weak and only quite few measurements have been performed |2|, There are also other chemical effects, which occur but which have not been so much measured or are not so well understood. One of them is the satellite intensities. The integrated intensities relative to Kq.^ line vary from one compound to another but not too remarkably. The fine structu- re of the satellite lines, however, depend strongly on the chemical en- vironment |2|. In heavy ion bombardments where the multiple L-shell ionization has a large probability, the x-ray satellite spectra are also sensitive to the chemical environment | 3 | • The XPS (x-ray photoemission spectroscopy) method seems to have some limitations in studying the lifetimes for core hole states. It has been found that in some cases a large portion for the XPS linewidths is due to phonon effects J4, 5|. The observation of x-ray emission spectra may provide a useful tool for studying some core hole stated even though in x-ray spectra one has both the effects of the initial and fi- nal states. In the present work we have measured sulfur Ka x-ray spectra from rhom- bic sulfur and some sulfur compounds by a double crystal spectrometer. The Kqj x-ray spectrum from sulfur was measured already by Parrat | 6 | ' using a double crystal spectrometer and by using the electron excitation. We used a chromium x-ray fluorescence tube for excite the sample. Two sets of analyzer crystals were used, quarz [(1010), 2d = 0.849 nm] and calcite [(211), 2d = 0.606 nm] . The rocking curve half width for the former was 0.4 eV and for the latter 0.5 eV. Fig. 1. shows the K a spectra from Sg « , Na2S0i| and ZnS. There are several chemical effects which can be observed as chemical shifts, line widths and intensities for K al and K a 2 lines, line widths for satellite lines and the fine structure of the satellites. Chemical shifts are quite well understood | 1 , 7 , 8 | . The effects on K ai2 lines are not large but a careful examination indi- cates some. The satellite spectra are quite complex. In LS coupling there are five components (a' , a 3 , ins almost constant. The electronic transitions to the rare earth Lju discontinuities and the white lines associated with these discontinuities have been suggested. Thus, this study helps in estimating approximately the extent of hybridization of p and d characters of the bonding orbitals in RCo,- eonroounds. We wish to thank Professor C. Mande for his interest in the present work. 1. P.R. Sarode and A.R. Chetal, J. Phvs. Soc. Janan, Vol. 40, (1976) In Press. 2. A.R. Chetal and P.R. Sarode, J. Fnys . F 5, L21? (1975) and references therein. 3. F.L. Carter, Proc. 9th Rare Earth Research Conf. Blacksburg, Virginia P 617 (1971). 4. P.R. Sarode and A.R. Chetal, Communicated to J. Phys. C (1976). 165 POSITRON ANNIHILATION & X-RAY SPECTROSCOPIC STUDIES OF HEAVY RARE EARTH ELEMENTS S.N. GUPTA & V.P. VIJAYAVARGIYA Madhav Science College, U;j jain, India. Holkar Science College, Indo re, India. In recent years attempts have been made to correlate the X-ray spectroscopic studies in the other fields. Important work in this direction is of Bhide et al (1) who have correlated the results with Mossbauer spectroscopy and Magnetic Susceptibilities in case of second transition series elements. In the present work an attempt has been made to correlate the X-ray spectro- scopic results of the heavy rare earth metals (2) with the positron Annihilation rates (3) and other structural properties (4) of these metals. The results are colle- cted in the following table : Element* Annihilation rate (lC^Sec" 1 ). (3) Width of the white line (ev) . (2) Metallic radius Iff- Gd 4.029 + 0.044 8.0 1.802 Tb 4.043 + 0.043 8.2 1.782 Dy 4.158 + 0.042 9.0 1.773 Ho 4.113 + 0.057 9.3 1.766 Er 4.128 + 0.043 9.8 1.757 Tm 4.071 + 0.042 10.5 1.746 Yb 3.746 + 0.035 12.3 1.940 Lu 4.056+ 0.041 7.6 1.734 From the conclusions drawn by Rodda and Stewart from their experimental studies on the positron life times and Annihilation rates in rare earth metals it is noticed that, the 4f electrons are well shielded 166 and do not participate in the Annihilation process and the core Annihilation takes place only with the 5s and 5p electrons, the annihilation rate depending on the density of conduction electrons. The study of white line associated with L-abso- rption edges provide information about the vacant part of the conduction band (2). Hence, it is natural to look for a correlation between the X-ray spectroscopic and positron annihilation studies in these metals. For this purpose a plot of the annihilation rates in the heavy rare earth metals and the width of the white line asso- ciated with the L3 edges of these metals is made. It is seen that a dip is obtained in the plot of annihilation rates at Yb, while a peak is obtained at the same metal in the plot of the width of the white line. It is also observed that for all other metals, both of these quantities remain nearly the same. Thus, it follows that when the number of conduction electrons remains the same both of these quantities remain nearly the same, but whenever the number decreases, the annihi- lation rate decreases and the width of the while line increases. The former depending on the filled part of the conduction band, while the later on the unfilled part. Thus a combined study of both can give information about the whole of the conduction band. Further, the table shows a close relationship of the width of the white line with the well known Lanth- anide contraction (Metallic radius) and consequently with the structural and other properties of these metals. This variation in the width of the white line can also be connected with the melting points and elastic constants (4) of these metals as they also show similar but reason- ably smooth variations with increasing atomic numbers. However, deviation are observed in the case of Lu and Yb, which may be ascribed to the absence of 4f vacancies in these metals . References : 1. V.G. Bhide & M.K. Bhal, J. Chem. Phys . 52 (1970). 2. B.D. Padalia, S.N. Gupta, V.P. Vijayavargiya and B.C. Tripathi, J. Phys. F (Metal Hiys.), 4 (1974). 3. Rodda J.L. & Steward M.G. Fhys . Rev. 131 (1963). 4. Taylor K.N.R. & Darby M.I. Phys. of rare earth solids (Chapman & Hall) 1972. 167 X-RAY SPECTRA OF TRANSITION METAL DISULFIDES FeS 2 , CoS 2 AND NiS 2 C. Sugiura and S. Nakai Department of Applied Physics, Faculty of Engineering, Utsunomiya University, Utsunomiya, Japan T. Matsukawa and M. Obashi Department of Physics, College of General Education, Osaka University, Toyonaka, Osaka, Japan J. Kashiwakura and Y. Gohshi Toshiba Research and Development Center, Kawasaki, Japan The electronic properties of FeS2, C0S2 and NiS2 with pyrite structure have been the subject of recent experimental as well as theoretical interest because of a wide variety of electric and magnetic properties. The experimental studies of the valence- and conduction-band structure have been made by several different research groups [1-4] investigating the X-ray and ultraviolet photoelectron spectra, the X-ray valence-band spectra and the optical spectra. The molecular levels and energy bands have been calculated by Li et al. [2] using the self-consistent-field Xa cluster method and by Khan [5] using the LCAO method, respectively. The characteristic points obtained from the experimental and theoretical studies are as follows: (1) The narrow 3d- like band of the metals lies at the top of the valence band. (2) Going from FeS2 to NiS2, the narrow 3d-like band is broadened and overlaps by degrees with the broad sulfur 3p- like band. (3) The lowest unoccupied band e g is very strongly mixed with the sulfur 3p band. There is still some uncertainty about the valence and conduction bands. The metal (Fe, Co and Ni) and sulfur K-absorption spectra of these compounds were measured on a two-crystal spectrometer and a 50-cm bent-quartz-crystal vacuum spectrograph, respectively. The sulfur K$ emission spectra were obtained by fluorescent excitation and measured on a vacuum two-crystal spectrometer. In the metal disulfides used here, FeS 2 was natural pyrite and CoS 2 and NiS 2 were synthetic compounds [6] . The absorbing layers were prepared by uniformly rubbing the fine powder on a sheet of thin paper. Their thicknesses were about 7 and 5 mg/cm 2 for the metal and sulfur K- absorption spectra, respectively. The Fe, Co and Ni K-absorption spectra of FeS 2 , C0S2 and NiS2 are shown in Fig.l. The sulfur K absorption spectra and sulfur K3 emission spectra of these disulfides are shown 168 in Figs. 2 and 3, respectively. The metal K absorption spectra are alike and the sulfur K absorption spectra are also alike. However the metal K absorption spectra are quite different from the sulfur K absorption spectra : the former spectra consist of a steplike structure, while the latter spectra are characterized by a prominent absorption maximum at the threshold. Going from FeS2 to NiS2, the presence of the first shoulder in the metal K absorption spectra becomes ambiguous and the first and second bands A and B in the sulfur K ab- sorption spectra move to lower energies and the width of the band A is narrowed. Considering that the lowest empty band eg is strongly mixed with the sulfur 3p band, the first absorp- tion band A or the shoulder is probably due to the transition to the eg band. In the sulfur K3 emission spectra, the main peak K3i occurs at nearly the same en- ergy. The shoulder K$x in FeS 2 is clearly separated from the main peak K3i/ while in C0S2 and NiS2 the presence of the corresponding shoulder is some- what ambiguous. The structure K3i of NiS2 is separated from the main peak K3i, whereas those of FeS2 and C0S2 are - ambiguous. The low-energy hump K3 appears clearly in C0S2. in «* -*jy Fe K ABSORPTION OF FeS 2 /** 7110 7120 7130 7140 PHOTON ENERGY (eV ) / Co K ABSORPTION OF C0S2 sS 7700 7710 7720 7730 PHOTON ENERGY (eV) 7740 -J -i r -i 1 r Ni K ABSORPTION OF NiS 2 ob-fcjsrfL. J I L 8330 8340 8350 8360 PHOTON ENERGY (eV) 8370 2470 2480 2490 PHOTON ENERGY (eV) 2500 Fig.l. Fe, Co and Ni K- absorption spectra. 169 Fig. 2. Sulfur K absorp- tion spectra. Comparisons of the Fe and S K-absorption spectra and S K$ emission spectrum of FeS2 and the molecular levels [2] of an octahedral FeS 6 ° "cluster are shown in Fig. 4, where the lowest empty eg level is tentatively associated with the first absorption bands labelled A and a. As can clearly be seen, the first band A in the S K absorption spectrum is much stronger in the intensity than the first shoulder a in the Fe K absorption spectrum. This indicates that the empty band e g is strongly mixed with the sulfur 3p band. In the Fe K ab- sorption spectrum, the second shoulder b is attributed to the transition to the empty 4s band of the Fe 2+ ion, having p- character and the third intense and broad band is attributed to the transitions to the higher lying p-like bands (arising from the 4p states of iron) . The intensity difference be- tween the two absorption curves is probably due to the dif- ferent transition probabilities. In the S K$ emission spectrum, the main band K3i and its high-energy shoulder K3x correspond well to a group of levels tig, tiu, eg, t2U, tiu, t2g and aig and the highest occupied t2g level, respectively. A good correspondence of the shoul- der K3x and the t2g level suggests that the t2g band has some sulfur 3p character. According to Khan's calculations [5] the mixing of the p state to the t2g band is about 7 °/o. Q|g *2g tiu t^egUjtlgUg *g L, et nl Tllll ( KB, FeS 2 -20 -15 -10 2450 2460 2470 PHOTON ENERGY (eV) Fig. 3. Sulfur K3 emission spectra. 5 10 ENERGY ( eV ) Fig. 4. Comparisons of the Fe and S K-absorption spectra and S K3 emission spectrum of FeS2 and the molecular levels [2] . References 1. A. Ohsawa et al 2. E. K. Li et al. 3. G. Wiech and E. 4. T. A. Bither et 5. M. A. Khan : J. 6. S. Ogawa et al. : J. Phys. Soc. Japan 37, 568 (1974) . : n Phys. Rev. Letters 32, 470 (1974). Zopf : J. Phys. (Paris) 32, C4-200 (1971) al. : Inorg. Chem. 1, 2208 (1968) . Phys. C 9, 81 (1976) . : Int. J. Magnetism 5, 349 (1974). 170 MULTIELECTRON TRANSITIONS IN K X-RAY SPECTRA OF ION-ATOM COLLISIONS T. Aberg 1 " Department of Physics Kansas State University Manhattan, Kansas 66506 Recent experiments by Richard et al . [1] and Wblfli et al . [2] have revealed novel features in characteristic K spectra which are asso- ciated with the strong inner-shell multiple ionization in ion-atom col- lisions. Related to the former experiment [1] Fig. la shows a typical K spectrum [3], where the new features are. the four almost equidistant peaks, denot- ed by KL n RER (radiative electron rear- rangement; n is the number of 2p holes.), 55 below the K a L n structure. The Si K x-ray S4 spectrum was obtained by a curved crystal — -* spectrometer. These peaks have been > found to increase with increasing KL n o 2 ionization in Mg, Al, and Si targets [3]. q; \ The two low-energy peaks corresponding to n=l and 2 have also been observed in pho- ton and electron impact [4] but there they are much weaker than the KLL radia- tive Auger [5] structure which is barely visible below the KL n RER lines in Fig. la. N + Si KqLV II 11 11 x50 1.6 Energy (keV) Fig. la The Ne K spectrum [6] shown in Fig. lb reveals a new peak, K a a (Kaa) , far above the K a structure. The energy of this peak is more than twice the K a energy which suggests that it is associated with double K ionization. Observations of K a ^ have been made in the range 7 = Z = 28 with solid state detectors [2,6,7], Neither the K a nor the K a § structure is resolved in these measurements. Ne + + Ne 200 400 Channel Number Fig. lb Term averaged Hartree-Fock (HF) calculations indicate that the KL n RER peaks are due to one-photon ls2s 2 2p m - ls 2 2s°2p m+1 (mi5) electric dipole (El) transitions [8]. In the case of K a ^ various energy calcula- tions [6,9,10] indicate that the principal initial and final configura- tions of this El transition are ls ( -'2s 2 2p m and ls 2 2s2p m- l, respectively. Hence there is a simultaneous transfer of a 2s and 2p electron in both cases which demonstrates the breakdown [11] of the single-configuration frozen core model of the atom. A schematic energy diagram of the KL n RER and K a ^L n transitions (n=6-m) is shown in Fig. 2. The influence of the M electrons and of the multiplet splitting is neglected. In analogy to theory of the radiative Auger effect [5] the origin of these transitions can be described in terms of configuration 171 s 1 2s 2 2p m ls 2 2s 2 2p< m -'> Is 2s 2 2p m u- h i n K^L n ls l 2s 2 2p( m " 1 ) ls 2 2s l 2p (m - |) , Fig. 2 interaction (CI) and the relaxation of the electronic cloud. It has been suggested [3] that the final state 2s22p x - 2s°2p x+2 (x^4) CI, known to affect the KLL Auger transition rates, is responsible for KL n RER. A detailed analysis [12] indicates that this CI together with the same CI in the initial state for m^3, is the major mechanism. The in- fluence of the relaxation with the leading contribution coming from the monopole-dipole amplitude term D (ls2s)Di(2p2s) , where D (ls2s) is the ls2s monopole radial overlap and Di(2p2s) the 2p2s radial dipole inte- gral, is small. The branching ratio defined as the intensity ratio I(KL n RER)/I(KL n ), is approximately proportional to f (2s2p)=Gl(2s2p) 2 A -2 , where G^(2s2p) is the 2s2p Slater exchange integral and A twice the 2s-2p electron energy difference. As a consequence of the 2s2p near de- generacy f(2s2p) = 0.3 is large and almost independent of Z and m. Hence the relative branching ratios are determined almost solely by the proportionality constants which reflect the electron coupling. Predic- tions of this model will be compared with experimental evidence regard- ing intensities and linewidths. It is also suggested that ls2s^2p m - ls 2 2s 2 2p m ~3 (m=3) El transitions, involving three jumping 2p electrons, may be observable on the high-energy side of K a L n . It has been proposed [10] that the principal mechanism of the ls^2s 2 2p m - ls 2 2s2p m ~-'- El transitions is the 2p-ls dipole transition accompanied by the "shake down" of a 2s electron into the second Is hole, This model predicts a branching ratio (with respect to the Ka hypersat- ellite transitions) which is proportional to the square of the ls2s monopole radial overlap integral D (ls2s) multiplied by an energy factor w(K a g) 3 /oo(K^) 3 . According to HF calculations D (ls2s) 2 ^ 0.035Z -2 for 12 < Z ^ 30. These calculations pertain to atoms with two 2p holes. However, D (ls2s) is fairly independent of the number of the 2p holes [10]. The large ls2s overlap is due to the drastic change of the K shell screening of the 2s electron which does not occur in the case of KL n RER, where the role of the Is and 2s electrons is reversed. The cal- culated branching ratios [10] agree within a factor of two with the measured ones [13]. It is suggested that the inclusion of K shell cor- relation in the final state improves the "shake down" model. The mixing between the final ls2s 2 2p m ~l and ls 2 2s2p m ~l configurations is not 172 important within the framework of the HF approximation [10]. Note also that D (ls2s) may be affected by relativistic effects for Z % 20. In conclusion, a unified model of KL n RER and K a ^L n transitions [12] is presented in terms of configuration interaction and relaxation of the electronic cloud. This model indicates that whereas the KL n RER transitions are governed by the 2s2p exchange interaction, the major mechanism of the K a [jL n transitions -is the "shake down" of a 2s electron. The author would like to thank K. Jamison and P. Richard for fruitful cooperation and P. Bagus and U. Fano for helpful discussions. References: * Supported in part by U.S. ERDA Contract No. E(ll-l)-2753. "^Permanent Address: Laboratory of Physics, Helsinki University of Tech- nology, 02150 Espoo 15, Finland. [1 [2 [3 [4 [5 [6 [7 [8 [9 P. Richard, C. F. Moore and D. G. Olsen, Phys. Lett. A43, 519 (1973). W. Wblfli, Ch. Stoller, G. Bonani, M. Suter, and M. Stockli, Phys. Rev. Lett. 35, 656 (1975). K. A. Jamison, J. M. Hall, J. Oltjen, C. W. Woods, R. L. Kauffman, T. J. Gray, and P. Richard, Phys. Rev. A, to be published. See e.g. T. Aberg and J. Utriainen, J. de Physique _32_, C4, 295 (1971). See e.g. T. Aberg, Atomic Inner Shell Processes , edited by B. Crasemann (N.Y. : Academic Press, p. 353, 1975). Th. P. Hoogkamer, P. Woerlee, F. W. Saris, and M. Gavrila, J. Phys B 9_ t L145 (1976). Ch. Stoller, W. Wolfli, G. Bonani, M. Stockli, and M. Suter, to be published. K. A. Jamison, J. M. Hall, and P. Richard, J. Phys. B 8, L458 (1975). H.-D. Betz, Abstracts of Contributed Papers of Second International Conference on Inner Shell Ionization Phenomena (Freiburg, 1976) p. 155; private communications by J. -P. Briand and B. Hodge. [10] T. Aberg, K. Jamison, and P. Richard, to be published. [11] S. Goudsmit and L. Gropper, Phys. Rev. 3j$, 225 (1931). [12] T. Aberg, K. Jamison, and P. Richard, to be published. [13] See Ref. 7; According to Ref. 7 a many-body perturbation calcula- tion of the K a & rate by H. P. Kelly (to be published) for Z=26 un- derestimates the rate somewhat whereas our calculation overesti- mates the rate by almost the same amount. H. Nussbaumer's (to be published in J. Phys. B) CI results are smaller than ours by a fac- tor of 10~2. The agreement between estimates based on J. P. Vinti's calculations (Phys. Rev. 42, 632, 1932) of oscillator strengths of ls^ ^S - qs2plp (q=l,2) transitions in He and measure- ments seems to be fortuitous since the ls^ 3-S - ls2p lp transition corresponds to K a rather than k|J. Furthermore the transition energy correction should be applied to Vinti's results. 173 MEASUREMENT OF CROSS SECTIONS FOR THE TWO-ELECTRON ONE-PHO- TON TRANSITION IN HEAVY- ION COLLISIONS R. Schuch and G. Nolte Physikalisches Institut der Universitat Heidelberg, 69 Hei- delberg, Germany H. Schmidt- B6cking, R.Schule, W. Lichtenberg , and K.E. Stiebing Institut fur Kernphysik der J.W. Goethe Universitat 6 Frankfurt /Main, Germany I. Tserruya Max-Planck- Institut fur Kernphysik, 69 Heidelberg, Germany Measurements of the two-electron one-photon transitions 1 are interesting for two reasons: they yield information on the production of inner double-hole states, similar to the measurement of hypersatellite lines and they open the field of correlation effects in inner shells which is also inve- stigated by measurements of the radiative Auger effect 2 and the three electron Auger effect 3 , In this paper we are mostly concerned with the production of double-hole states deduced from the absolute and rela- tive intensity of the two-electron one-photon (K ) transi- J * aa tion. However, first some comments on the identification of the K transition are in order. The relative intensity of aa the K transition is independent on the rate of K - and K aa r a 3 x-ray events and thus cannot be due to pile-up. Also the energy of K x-rays is slightly different from the double 174 K energy and is in excellent agreement with Hartree Fock calculations for the K transition. This, however, would not exclude the existence of two correlated photons. The use of different absorbers in front of the x-ray detector proved the existence of a single photon with energy E^ *xxa We measured the intensity of the K transition for near- J act symmetric collision systems in the region of S and CI for different impact energies and solid as well as dilute gas targets . The results are in accordance with the assumption of a MO excitation for the double-hole states similar to the produc- tion of single vacancy states under the same condition. The occurence of the K transition under single-collision con- aa & ditions proves the one-step production of both K-vacan- cies. The reinvestigation of the impact parameter dependent x- ray spectra for 35 MeV CI incident on Cl-targets 4 yiel- ded the differential cross section for the K production. aa v In contrast to the (single vacancy) K emission probability, which was found to be flat within the region of the K-shell radius (3100 fm) 5 , the K emission probability is strong- ly dependent on the impact parameter even for very close collisions. The ratio of the emission probabilities P v /F* JNxa Nx is increased by almost a factor of 5 relative to the ratio -7 of the single spectra yields 8*10 , for this case. The re- sults indicate the existence of a new ionization mechanism, 175 occuring only in close collisions. 1 W. WSlfli et al., Phys .Rev. Lett . 35. ( 1975 > 656 > Th.P. Hoogkamer et al., J. Phys. B 9_ (1976) L 115. 2 T.Aberg and J.Utriainen, Phys .Rev. Lett . 22 (1969) 1346. 3 V.V. Afrosimov et al. , JETP Lett. 21 (1975) 249. 4 I. Tserruya et al., Phys .Rev. Lett . 3S_ (1976) 1451, 5 I. Tserruya, H. Schmidt-Bocking, R. Schuch, R. Schule, to be published. 10 -5 0* 0* 10 6 10 J I ■ I 4 6 8 10' CK, oCoC GK. i iii A 6 8 1Q 3 blfm) The ratio of the two-electron to one-electron-one-pho- ton transition probability as function of the impact parameter measured with 35 MeV CI on NaCl. The dashed line indicates the ratio of the total cross sections. 176 EVIDENCE FOR 2e-ly TRANSITIONS IN C&n+ BOMBARDMENT OF KC£+ W. W. JACOBS, B. L. DOYLE, S. M. SHAFROTH and J. A. TANIsI University of North Carolina, Chapel Hill, N. C. 27514 and Triangle Universities Nuclear Laboratory, Durham, N. C. 27706, and A. W. WALTNER North Carolina State University, Raleigh, N. C. 27607 and TUNL The possibility of two-electron one-photon (2e-ly) transitions, in which two electrons simultaneously fill an empty K-shell resulting in the emission of a single photon at approximately twice the K x-ray energy, was predicted nearly 50 years ago by Heisenberg [l]. Recently, evidence for such transitions was presented by Wolfli et al. [2] following collisions of Fe and Ni ions with Fe and Ni targets. In the present work, we report similar evidence resulting from 30 to 80 MeV C£ n+ beams incident on thin (VL00 ug/cm 2 ) targets of KC£ evaporated onto carbon backing foils (20 ug/cm 2 ) . The x-rays were detected with an 80 mm 2 x 5mm intrinsic Ge detector (170 eV FWHM at 5.9 KeV) located in air at 90° to the beam. In order to eliminate pulse-pileup, pure A£ absorber, typically 20 mg/cm 2 , was used to reduce the characteristic x-ray counting rate. Scattered projectile ions were counted at 60°to the incident beam in a solid-state detector for normalization purposes. Typical raw x-ray spectra for 30, 50, and 70 MeV C£ n+ incident on KC£ are shown in Fig. 1. The C£ characteristic x-rays are completely attenuated by the Ail absorber; the largest peaks near 4 KeV are the potassium Kg* and Kg* (the asterisks denote the shifted x-ray lines due to multiple ionization) whose relative intensities have been reversed due to the large A£ absorption. At higher energies, one sees small peaks riding on a background composed of the non- characteristic x-ray continuum. The peak near 5.6 keV is slightly greater than twice the measured K a * energy (2.7 keV) of CI and the peak near 7.0 keV is slightly greater than twice the potassium K a * energy (3.4 keV) . These peaks do not correspond to any known contaminant radiation. We attri- bute these peaks to 2e-ly transi- tions, denoted by K aa , in CI (due to both projectile and target x-rays) and potassium, respective- ly. At the higher bombarding energies, one sees _,*P er haps, transition 33K evidence for th e Kgg 40 60 X RAY ENERGY (keV) Fig. 1. C£-> KCi X-Ray Spectra. for both C£ and K at slightly higher energies than the K aa peaks. One also notes that as the bombarding energy is reduced, the 177 intensity of the K 2e-lY peak goes down relative to the CI 2e-ly peak. This may reflect a difference in the double K-shell vacancy-production mechanism for the two cases. A summary of the observed energies for potassium x-rays is shown in Fig. 2 plotted as a function of C£ n bombarding energy. The straight lines are least-squares fits to the data. One notes that the K^ a and K^ energies (actually, 2E^ a * is plotted) slowly increase with incident C£ energy indicating an increasing degree of L-shell ioniza- tion. • RUN I • RUN 2 » RUN 3 - POTASSIUM X RAYS ~2 K/KCfc 30 3387+10 6964+20 74 3452 (2p) _ 2 (2 P ) ; C2P)I4 (2 P ) Z (2p)"° — 3260 K/KC£ 50 3389+10 6957+20 76 3445 19 40 3306 3355 K/KC£ 70 3395+10 6977+20 82 3465 63 3409 . 88 3466 114 3528 C£/KC£ 30 2683+10 5545+20 61 2746 (2p) _ 2 (2 P ) "i (2P)I4 (2 P ) Z (2?)° = 2580 C£/KC£ 50 2704+10 5562+20 82 2763 16 34 2619 2662 C£/KC£ 70 2718+10 5575+20 96 2776 54 2709 76 2759 99 2814 a. Other than K-shell vacancies. In addition to the (2p) vacancies shown, outer-shell configurations of (3p)~^ and (3p)""3 (4s)~l were used for C£ and K respectively. curved-crystal spectrometer as shown in Fig. 3, to determine the ratio K a */K*J*. Combining this measurement with the K.h*/K * ratio obtained from the low resolution intrinsic Ge spectra gives the desired branch- ing ratio. Our preliminary results indicate values for Kg^/Kh* of about 2-4 xl0~5 for both C£ and K. This value is nearly an order of magnitude lower than that measured by Wolfli et al. [2] for Fe and Ni and is nearly the same factor smaller than that predicted by Aberg €£ al . [6] . fSupported in part by the U. S. Energy Research and Development Administration ^Supported by the North Carolina Board of Science and Technology References 1. W. Heisenberg, Z. Physik 32, 841 (1925). 2. W. Wolfli et al. , Phys. Rev. Lett. 35, 656 (1975), and W. Wolfli et al . , (to be published) . 3. D. J. Nagel et al. , Phys. Rev. Lett. 36, 164 (1975). 4. F. Herman and S. Skillman, Atomic Structure Calculations , (Prentice- Hall, N. J., 1963). 5. H.-D. Betz, Contributed Papers, 2nd Int. Conf. on Inner Shell Ionization Phenomena, (Freiburg, 1976) ; W. Hodge, (to be published). 6. T. Aberg, K. A. Jamison, and P. Richard, (to be published). 179 EXCITATION OF 2 ELECTRON - 1 PHOTON K X-RAYS IN Ni-Ni COLLISIONSt by J. S. Greenberg and P. Vincent, Wright Nuclear Structure Laboratory, and W. Lichten^ Becton Center Yale University, New Haven, Conn. 06520 According to the electron promotion model [1], the number of K-shell vacancies produced in a collision is proportional to the vacancy factor R, the number of prior vacancies in the L shell orbitals of the colliding atoms [2], Thus, the theoretical calculation of Briggs and Macek [3] gives the cross-section for single K-shell vacancy production as a prod- uct of the vacancy factor R and the cross section for a single L-shell vacancy prior to the excitation process. We report measurements of the energy dependence of the cross-sectiors for both the Ka (1 electron, 1 photon) and Kaa (2 electron, 1 photon) x- ray emissions for Ni-Ni collisions in the energy range 17.9 - 91.5 MeV. The measurement of both cross-sections yields valuable information on the excitation mechanism of both single and double K-shell vacancies. In particular, two experimental cross-sections make it possible for the first time to make independent tests of both the vacancy factor and the theoretical cross-section per L-shell vacancy. * 5s Figure 1 shows data points for a (Ka) , and a (Kaa) (multiplied by 10 ) I0 5 10' CO c a 10' 1 - - — K a 1 IS (n >. 3) transitions are greatly reduced in a solid over that of a thin foil target. Outside the two extremes outlined above we observe that, in general, quenching is responsible for a noticeable decrease in x-ray yield when- ever Noqvt ^ 1. This condition covers a good number of the collision systems studied in ion-solid and ion-gas interactions. More detailed descriptions of the quenching mechanism and its relation- ship to the final charge states observed for ions emerging from foil targets will be discussed. Suggested further measurements on quenching in ion-atom collisions include 1) a determination of why we observe non- equal quenching cross sections for states having widely differing life- times, 2) does oq depend on different configurations or multiplets, 3) is on/ay ratio constant with ion atomic number, and 4) is oq collision energy dependent? References: /l/ H. D. Betz, F. Bell, H. Panke, G. Kalkoffen, M. Welz and D. Evers, Phys. Rev. Lett. 33, 807 (1974); /2/ S. L. Varghese, C. L. Cocke, B. Curnotte and G. Seaman, private communication; /3/ F. Hopkins, Phys. Rev. Lett. 35, 270 (1975); /4/ D. L. Matthews, R. J. Fortner and G. Bissinger, Phys. Rev. Lett. 36, 664 (1976). R. J. Fortner and D. L. Matthews (submitted to Phys. Rev. A.). TWO and THREE -ELECTRON FLUORINE KX-RAYS 2'P, F -r»-Graphite 20MeV F 3+ — C K X-RAY SPECTRA H-LIKE SERIES 1 — m He -LIKE SERIES 1 TTTB REC GRAPHITE SLAB '\i I REC 1 S$ii#g\ IOO>g/cm 2 jjft.. • *~ F01L _L J_ 174 17.2 17.0 168 WAVELENGTH (a) 16.6 13 II 9 WAVLENGTH (A) Fig. 1 Fig. 2 *Work performed under the auspices of the U.S. Energy Research and Development Administration, W7405-Eng-48. 185 K X RAYS AND REC FROM Cl n+ BOMBARDMENT OF TARGETS IN THE REGION 19 < Z < 35* J. A. TANIS + , B. L. DOYLE, W. W. JACOBS, AND S. M. SHAFROTH University of North Carolina, Chapel Hill, N. C. 27514 and Triangle Universities Nuclear Laboratory, Durham, N. C. 27706 We have examined the characteristic K x-rays resulting from 20-80 MeV Cl n+ bombardment of C, KBr, Ti, Mn and Cu and the radiative elec- tron capture (REC) resulting from Ci n incident on C. The purpose of this study is to determine the effects of multiple ionization on the observed x-ray spectra and to compare the measured x-ray cross sections with the predictions of Coulomb excitation-'- and K vacancy^ sharing theories. Further, we examine the REC resulting from bombardment of a thin solid target and determine the REC energies, widths and cross sections as a function of projectile energy. Figs. 1 and 2 show the observed target K& and K© energy shifts and Kg/Ra intensity ratios, respectively. The increase in the x-ray energy shifts with projectile energy implies an increasing degree of L-shell ionization while the increase in the Kd/K,^ ratio implies an increasing degree of L-shell ionization with respect to M-shell ionization. At the highest incident energies, the energy shifts and intensity ratios are seen to level off, probably reflecting the projectile velocity matching with the target L-shell which occurs over the range of energies studied here. E c , (MeV! 40 60 E C | (MeV) Fig. 1 Energy Shifts Fig. 2 K a /Kg Ratios 186 The observed x-ray cross sections are compared with those predicted by the various Coulomb-excitation theories as shown in Fig. 3. Single vacancy fluorescence yields have been used to calculate the theoretical cross sections and this is, of course, a source of error. In general the theory predicts the trend of the data but differs somewhat in absolute magnitude. This is not unexpected since the theories are strictly applicable only for Z^/Z2 « 1 whereas in the present case 0.6 £ ^1^2 ^ °«9. Tne PWBABCP+EC, which includes Coulomb and binding corrections, 3 the Z~* polarization correction^, and target electron capture^ by the projectile, should provide the best descrip- tion of Coulomb excitation in its region of validity and this is, indeed, the case for C£-*-Cu. As Z2 decreases the agreement becomes worse probably reflecting the non-Coulombic nature of the excitation for symmetric collisions. Since the PWBA and BEA overpredict the data in their region of validity, the good agreement for C£-*K and Ti must be regarded as fortuitous. cr— x CI ENERGV (MeV) Fig. 3 Cross Sections 4800 4600- 4400 4200 4000 cr Ld 3800 Ld 3600 >- < cr 3400 X 3200 3000 2800 2600 10 20 30 40 50 60 70 80 E c|n+ (MeV) Fig. 4 R.E.C. and Projectile x-ray Energies The observed CI projectile K a , Kg , and REC energies are shown in Fig. 4 as a function of E^^. For comparison, the single vacancy 1^, Kg and K binding energies are also shown. The line labeled T r + BE C£K is a lower limit to the REC energy and assumes capture of a "free" target atom electron into the K-shell of a CI ion with a single K vacancy-*. The measured REC energy is seen to be somewhat higher than this lower limit. A better approximation to the REC energy is obtained by using the measured C& Kg energy shift to estimate the increase in K-shell binding energy and adding this to the relative K. E. of the captured electron as shown. 187 Fig. 5 shows the effect of Cl n bombarding energy on the widths of the Kot, Kg and REC peaks. It is interesting to note that the minimum REC peak width is 520 eV. This is much wider than would be expected from the model of Sohval et. al.", which describes the REC width for 0° + on a variety of gaseous targets, including C3H3, quite well. Much of the increased width in the present work is thought to be due to multiple ionization of the projectile passing through the foil. Finally, the REC differential cross section vs. E^ at 90° is shown in Fig. 6. The measured cross sections assume that each target atom contains a single electron which can be captured. The agreement with the free electron calculation of Bethe and Salpeter' is seen to be quite good although this agreement must be regarded with caution due to possible corrections for target thickness effects^ and the number of electrons available for capture. E a n* (MeV! b « 1 1 1 1 1 1 1 A\ 100 A A • A • A » A 10 1 1 c 1 1 1 dn 4 5§'7. The resulting eigenergies and eigenfunctions were interpolated by either the "Quad"8 or the Slater-Koster" interpolation schemes and the densities of states decomposed per site and per angular momentum com- ponent were found . The calculated x-ray spectra were broadened using an energy-dependent Lorentzian function. This function included spectrometer window broad- ening, core-level life time width and electron life time broadening with one adjustable parameter. Our results indicate that the main features of the x-ray spectra are reflected by the decomposed densities of states^with the energy depend- ent radial matrix elements playing a secondary role. The inclusion of the matrix elements was more crucial for L and M spectra than for K-spectra. On comparing the calculated and measured spectra we find generally, good agreement for K and L spectra and somewhat worse agreement for M spectra. Although we have calculated both the emission and absorption K, L and M spectra, we will present only those results for which measurements were found in the literature. In particular, the calculated emission spec- 192 tra of V were compared with the measurements of Nemnonov and Finkel- shteyn for the K spectrum, the measurements of Brytov for the L spectra and the experiments of McAlister et al 12 for the M spectra. 13 14 For Ca and Ni we concentrated on the K-absorption edge and found good agreement with the measurements of Sugiura and Pease and Gregory-*-" respectively. 17 For the intermetallic compound TiFe we find excellent agreement with the experiments of Nemnonov and Kolobova for both emission and ab- sorption K spectra of both components. 19 In the case of TiNi in comparing with the work of Cuthill et al and Kallne ^ we find some discrepancies for the L and M spectra. Our calculations on NbC and V^Si are compared with the measured spectra of RamqVlist et al and Nemnonov et al 22 and obtain generally good agreement . In conclusion we note that accurate self-consistent band structure cal- culations produce energies and wavefunctions which can be used to ac- count for most measured X-ray spectra, without invoking any subtle many body effects, beyond the effective one-electron Hamiltonian. Collaborations with D. J. Nagel and J. W. McCaffrey on the X-ray cal- culations and with B. M. Klein and L. L. Boyer on the band calcula- tions are gratefully acknowledged. I am also indebted to L. S. Birks for many useful discussions . REFERENCES [1] D. J. Nagel and W. L. Baun; L. V. Azaroff and D. M. Pease, X-ray Spectroscopy (edited by L . V. Azaroff) McGraw-Hill New York (1974) [2] A. Neckel, K. Schwarz, R. Eibler, P. Rastl and P. Weinberger, Mikrochimica Acta [WienJ , Suppl 6, 257 (1975) [3] R. P. Gupta and A. J. Freeman, Phys . Rev. Lett. 36, 1194 (1976) [4] D. A. Goodings and R. Harris, J. Phys. C, 2, 1808 (1969) [5] J. C. Slater, Phys. Rev. 51, 846 (1937) [6] L. F. Mattheiss, J. H. Wood and A. C. Switendick, Methods in Com- putational Physics Vol. 8, p. 123, Academic Press, New York (1968) [7] D. A. Papaconstantopoulos, J. R. Anderson and J. W. McCaffrey, Phys. Rev. B5, 1214 (1972) [8] F. M. Mueller, J. W. Garland, M. H. Cohen and K. H. Bennemann, Ann. Phys. (New York) 67, 19 (1971) [9] J. C. Slater and G. F. Koster, Phys. Rev. J^ 1498 (1954) [10] S. A. Nemnonov and L. D. Finkelshteyn Ann. Physik 18, 42 (1966) 193 [11] I. A. Brytov, Phys. Metalmetal 24, 174 (1967) [12] A. J. McAlister, J. R. Cuthill, R. C. Dobbyn, M. L. Williams and R. E. Watson, Phys. Rev. B12, 2973 (1975) [13] J. W. McCaffrey and D. A. Papaconstantopoulos , Solid State Commun. 14, 1055 (1974) [14] D. J. Nagel, D, A. Papaconstantopoulos, J. W. McCaffrey and J. W. Criss, Proc. Int. Symp . on X-Ray Spectra and Electronic Structure of Matter (Edited by A. Faessler and G. Wiegh) p. 51 (1973) [15] C. Sugiura, Japan J. Appl . Phys. 11, 598 (1972) [16] D. M. Pease and T. K. Gregory, Solid State Commun. 18, 1133 (1976) [17] D. A. Papaconstantopoulos, Phys. Rev. Lett. 31, 1050 (1973) [18] S. A. Nemnonov and K. M. Kolobova, Phys. Metalmetal 23, 66 (1967) [19] J. R. Cuthill, A. J. McAlister and M. L. Williams, J. Appl. Phys. 39, 2204 (1968) [20] E. Kallne, J. Phys. F^, 167 (1974) [21] L. RamqVist, B. Ekstig, E. Kallne, E. Noreland and R. Manne, J. Phys. Chem. Solids 3_2, 149 (1971) [22] S. A. Nemnonov, E. Z. Kurmaev, and V. P. Belash, Phys. Stat. Sol. 39, 39 (1970) 194 VALENCE BAND STRUCTURE OF DIAMOND, GRAPHITE, AND AMORPHOUS CARBON OBTAINED BY X-RAY AND PHOTOELECTRON SPECTROSCOPY G. Wiech Sektion Physik der Universitat Munchen, 8 Munich 40, FRG The X-ray K-emission bands of diamond, graphite and evap- orated carbon were measured, and are compared with recent X- ray photoelectron (XP) spectra (1) and theoretical calcula- tions. The intensity distribution of these spectra is govern- ed by the dipole selection rules and the photoionization cross-sections 6*£ and 6/o , respectively. Since the core level of carbon has a well defined s orbital symmetry, the C K-emission bands reflect the p states in the valence band. In X-ray photoelectron spectroscopy of light elements the cross-section for valence s-like electrons is considerably larger than for p-like electrons. The XP spectra therefore arise predominantly from s-like electrons. Thus both experi- mental techniques for the light elements and compounds of them yield complementary results. In diamond the electrons at the bottom of the valence band are mainly s-like, those of the top part are mainly p- like, and there is considerable s-p-mixing throughout the va- lence band. As Fig.1 shows, these properties are clearly re- flected by the XP spectrum (1) and the C K-emission band. Since the band structure and the density of states for di- amond and silicon are in qualitative agreement, one expects close similarity between the distribution of s- and p-like electrons in the valence bands of the two elements. Fig. 2 shows that the structural features of the Si KB- and C K-band agree well. There is also good agreement between the XP spec- trum of diamond and the L2 3~band of silicon which arises from s-like valence states. This indicates that GJ" » 281 eV) the 195 Silicon 1 £ 50 a diamond h - XPS X I f / . c , , I . . . , 1 . , , , 1 ,\j , «. 260 265 270 275 280 285 E B (C1s)-E B (valence band) (eV) 270 275 280 285 Photonenergy (eV) 1825 1830 1835 Energy (eV) Fig.1 XP spectrum (1) and x-ray K-emission band of diamond Fig. 2 Si L23- and Si KB- emission band of silicon (2) intensity is extremely low, due to the large value of the cross-section ratio (Tj /^/> • While 6~-*1 radiation, the is strongly an rallel to the emitted radiat of the take-of the region of region of the take-off angle tural features tures E,F, and s transitions yield an isotropic radiation resulting from v"— *■ 1s isotropic, no //'-radiation being crystallographic c axis. By me ion of a graphite single crystal f angle, the width of the <5"* and overlap (Fig. 3) could be determi // bands the x-ray emission band of 1 5° is intense and shows det . For the 80° spectrum the inten G is almost zero. ly distributed transitions emitted pa- asuring the as a function a" bands, and ned (3) . In the obtained at a ailed struc- sity of struc- In Fig. 4 the XP spectrum of glassy carbon (1) and the K- band of evaporated carbon are shown. The gross features of the spectra resemble those of graphite. All structural de- tails, however, are smeared out as it is typical for amorphous materials: the over-all structure of the density of states depends on the short-range order in the material, while long- range order leads to additional fine structure. 196 i 00 > graphite XPS r? b ! 50 A fi , - I , , , v c v e 255 260 265 270 275 280 285 E B (C1s)-E B (valence band) (eV) C 255 260 265 270 275 280 285 Photonenergy (eV) 2755 c h n Fig. 3 XP spectrum (1) and K-emission band of graphite 100 50- glassy carbon/^~N XPS / b \l 1 i . . . . i , . . , L , , , . 1 7>T-r+-f-^, , «. 255 260 265 270 275 280 285 E B (C1s)-E B lvalence band) (eV) A evaporated carbon X-ray C K-band C I \ E 50 ^/ , , i . , , 255 260 265 270 275 280 285 Photonenergy (eV) Fig. 4 XP spectrum of glassy carbon (1) and K-emission band of evaporated carbon References (1) F.R.McFeely, S.P.Kowalczyk, L.Ley, R.G.Cavell, R.A.Pallok, and D.A.Shirley, Phys.Rev. B 9_, 5268 (1974) (2) G.Wiech and E.Zopf, Journal de Physique 3_2, C4-200 (1971) (3) Chr .Beyreuther and G.Wiech, in: VUV Radiation Physics, edit. E.E.Koch, R.Haensel and C.Kunz, Pergamon Vieweg, 1974, p. 517. 197 a) POLARIZATION AND ANISOTROPY OF THE C K-SPECTRUM. J. Kieser Physikalisches Institut, Universitat, 7500 Karlsruhe (FRG) Graphite exhibits a layered structure, where the monolayers consist of hexagonal arrays of carbon atoms. The bonds bet- ween the layers are weak and mainly due to van der Waals interactions . The strong covalent bonds in the monolayers consist of a- and tt -bonds . The a-bonds evolve from the hybri- disation of three electronic wavef unctions , namely the 2s, 2p x and 2p functions, which yields three half filled coplanar a-bonds per atom with bond angles of 120 °. The one half filled ir-bond per atom is generated from the occupied 2p z wave function . In the case of the a-bonds the centers of gravity of the charge distributions are localised bet- ween all pairs of next neighbours Therefore, if 1s-vacancies are produced in the atoms, transi- tions of electrons from the a- bonds into the vacant states give rise to an X-ray emission which can be expected to be pola- rised in the plane of the layer, while its intensity distribution should be isotropic. As concerns the it -bonds, the charge due to one p z -electron per atom is distributed above and below the layer atoms. Since the ir-bond of a carbon atom is uniformly distri- buted over the three next neigh- bours, the center of gravity of the corresponding charge distri- bution should be situated exact- ly above and below the atom*. From this follows that the radia- tion due to transitions of tt- electrons into 1s-vacancies should be polarised perpendicu- lar to the layer plane, i.e., parallel to the c-axis. As a consequence all directions of maximum emission intensity lie in the layer plane. Fig. 1: Geometric arrange- ments of the c-axis (per- pendicular to the layer planes) of the probe rela- tive to the Rowland circ- le R. The direction of the exciting electron beam is indicated, a) a = 87 °; b) a = 3 °; c) a = 87 °. 19S The a- and ir-subbands, which result from the respective radiating transitions overlap strongly in the C K-spectrum. Investigations of monocrystalline carbon employing gratings as monochromators have been performed by Brummer et al /1/ and Beyreuther and Wiech /2/. In both cases the anisotropy of the TT-radiation could be demonstrated by the investiga- tion of C K-spectra measured with different relative orien- tations of the sample. The obtained spectra showed a marked dependence of the relative intensity of the 7T-maximum on this orientation. These results have been used to estimate the shape of the tt- and a-subbands. The presented contribution deals with the experimental veri- fication of the proposed polarisation and anisotropy pro- perties of the C K-spectrum. By making use of these proper- ties the shapes and bandwidths of the tt- and a-subbands of monocrystalline graphite have been measured. The investiga- tion has been performed employing an Octohydrogenmaleate - OHM - crystal as monochromator. This crystal exhibits a lattice constant of 2d = 63.39 A. Due to the investigated energy range of the C K-spectrum of 260 eV < E < 284 eV the Bragg angles vary between 48 ° and 42 °. In this range the OHM-crystal monochromator acts simultaneously as a nearly perfect analyser (> 96 %) for the polarisation of the mono- chromatized radiation, due to the Fresnel equations. First orienting measurements of the C K-spectrum of diffe- rent carbon samples employing an OHM-monochromator have been performed by McFarlane /3/. Fig. 1 shows the investigated positions of the c-axis of the probe relative to the Rowland circle. The arrangement of Fig. 1a should yield the TT-subband only, since the a- component, which is polarised in the Rowland circle plane should be suppressed in the reflected beam. The spectrum measured with this arrangement is shown in Fig. 2. According to the expectations the dominating a-maximum has disappeared 10 0.5 I V 3 1 v max 1 T I V 3 1 max ™ CK Tt- Spectrum : • . . • • i • • * • a • • / ■ «* / • .••" • p .« • ....•• • E-Ef . • " eV ■ ■ 1 1 1_ ••••«. -20 -15 -10 -5 199 Fig. 2: C K TT-spectrum ob- tained with the arrangement of the probe according to Fig. 1a. The Fermi level corresponds to the zero of energy. 1,0 0,5 T 1 1 Iv 3 1 "max ■ i I V 3 . • 'max . • CK o-Spectrum / \ • * m • • . - * • * • t ■ s ..•* * # • « » V.. > eV Fig. 3: C K a-spectrum obtained with the arrangement of the probe according to Figs. 1b and 1c. The Fermi level corresponds to the zero of energy. -20 -10 -5 1,0- 0,5- arb. units ■ T r " 1 " » a:i0 *• t ° / \ Vl + PI TC i . % '. • ° • o * R I .^ ' # • jT \ E-E F . • «*T \ \, eV i ■ i • '" Fig. 4: Corrected it- and a-spectra and an arbitrary linear combination. The Fermi level of all curves corresponds to the zero of energy. -20 -10 -5 Figs 1b and c show two further mountings of the probe which are both useful for maximum supression of the ir-subband. In the first case no iwradiation reaches the monochromator due to its anisotropy. In the second case (Fig. 1c) the ir-radiation is polarised in the Rowland circle plane and should therefore be supressed by the monochromator. The C K a-spectra obtained with the two mountings of Figs. 1b and c are identical within the experimental accuracy. This is a strong confirmation for the proposed anisotropy as well as polarisation properties of the C K-radiation. It further demonstrates the excellent polarising properties of the OHM monochromator. Fig. 3 shows such a C K a-spectrum. The spectra of Figs. 2 and 3 contain a small amount of the suppressed component. This is mainly due to the used probes of natural graphite which were no perfect single crystals. Additionally even at the used pressure < 2 x 10 - 9 Torr car- bon containing contaminations were deposited on the probe which caused a progressive smearing of the investigated 200 structure. Therefore a simple correction procedure has been applied to the measured spectra. The corrected 'pure' ir- and a-components are shown in Fig. 4 together with an arbi- trary linear combination. This linear combination is nearly identical with a C K-spectrum taken from a polycrystalline graphite probe, as is shown in Fig. 5, thus confirming that the shapes of the subbands as shown in Fig. 4 are essen- tially correct. Fig. 5: Comparison of the linear combina- tion of Fig. 4 (dots) with a C K-spectrum from polycrystalline graphite (circles) 1,0 1 1 1 arb units *> • 1 1 i V i" •, •* fc t r m f m 05 » - \jp • « • *> < f • V .8 *\ ©•* fc o» 8# % * 1 8* t „ _ • o • ° v E-E F 1 ° • 1 1 1 ' * ■ -20 -15 '-10 References f\j Brummer, O. et al in: X-Ray Spectra and Electronic Structure of Matter, ed. A. Faessler and G. Wiech, Munchen 1973, Vol. I, p. 78. /2/ Beyreuther, Ch., Wiech, G.j Physica Fennica £, Suppl. S. 1 , 176 (1974) . /3/ McFarlane, A. A. : Carbon 11, 73 (1973). 201 CALCULATION OF THE K-ABSORPTION SPECTRUM OF ALUMINUM t F. Szmulowicz* Case Western Reserve University Cleveland, Ohio 44106 B. Segall Case Western Reserve University Cleveland, Ohio 44106 We have performed a first principles calculation of the K-absorp- tion spectrum of aluminum using band structure and matrix elements of momentum determined by the symmetrized APW method (1). Comparison be- tween theoretical and experimental results for the x-ray spectra pro- vides a sensitive test of the one-electron band theory. Therefore, there has been a great need and interest concerning these calculations. The potential for the calculation was obtained by superposition of free atom charge densities with Slater's free-electron exchange. Eigen- values and wavefunctions were obtained at 89 k-points in the irreducible wedge in 4.2 Ry range above the bottom of the conduction band at r. The Is level and its wavef unction were calculated with the muffin-tin poten- tial and used to obtain transition strengths between the core level and states above the bottom of the conduction band by the W(r) method. An OPW non-linear least-squares fit (2) using 27 plane waves was performed for the purpose of interpolating energies and gradients throughout the wedge (rms deviation of .03 Ry for the first 10 bands). The integrals over the Brillouin zone for the density of states and linear absorption coefficient were done with the Gilat and Raubenheimer method (G-R) (3) while the Fermi energy was obtained by a variant of the G-R scheme for volumes. ENERGY ABOVE E(r,)(eV) 01 23456789 10 E F I ENERGY ABOVE E F (eV) 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 -i 1 1 n 17 16- 13- 2 l3 " P 12 uj KJ- S 9- (A 6- CO 7- I- 5- oL 7- i 1 1 1 1 1 r j i i_ L4.V 2 , 4 « V i \ - LI w, W, 55eV 1 «. I2.8.V ^O- 2 ' 2 ' f- i .} > Ls k 1 A,(l,l,l) A^l.l.D .ii iiii i i_ 0,(2,4.6) I / I, "I A.(l,l,l) _1 I 1_ -.20 -K> .10 .20 .30 .40 .50 .60 .70 .80 90 1.0 UO L20 L30 1.40 1.50 1.60 1.70 L80 190 ENERGY (Ry) 2 00 2.10 2 20 Fig. 1 202 Results for the density of states where n is the unit cell volume, are presented in Fig. 1 with identifi- cations of points leading to the structure in the curve and of their locations in units of (2ir/8a). This plot is in good agreement with the previous density of states calculation of Connolly (4). Results for the absorption coefficient Pls.n Sfeniti-^-ud are shown in Fig. 2. The curve above Ep represents the K-absorption spectrum of aluminum while the curve below Ep is proportional to the K- emission spectrum. The contributions to the plot are separated by bands with band symmetry and ^-character classifications, e.g. irredu- cible representation (band index, Jo-character). The K-emission spectrum is in good agreement with the previous calculation of Smrcka (5). ENERGY ABOVE E(D (eV) 2 3 4 5 6 7 ENERGY ABOVE E F (eV) 8 9 10 II 12 J 45- t 40- JO- 25- - i * «-* *"'* T 'If ff *i T * p- 90 100 110 ENERGY (Ry) 1 90 2 00 2 10 Fig. 2 The Lorentzian broadened (half-width at half-maximum of .02 Ry) absorption curve is shown in Fig. 3 together with the experimental result (6) normalized to 5.5 eV peak. We find that peak A, which can arise due to level Wi is suppressed in going from D(o)) to y(w) while there is no evidence for peak B. Peak C is at 5.5 eV in excellent agreement with the experiment and the structure around 12.8 eV peak D is flanked by other peaks not seen in the experiment. It should be ENERGY ABOVE E F (eV) 9 10 II 12 13 14 15 16 17 18 19 20 21 22 70 80 90 LOO MO L20 130 140 ISO 160 170 180 190 200 210 220 ENERGY ABOVE E(n) (RYOBERGS) Fig. 3 203 noted that Shaw (7) reports a peak on the low side of the 12.8 eV peak. The appearance-potential spectrum also shows a peak of 21 eV which is reflected in the theoretical curve in Fig. 3. + Work supported by AEC and grants from NSF. Present address Institute of Materials Science, University of Connect- icut, Storrs, Conn. 06268. 1. L. F. Mattheiss, J. H. Wood, A. C. Swidendeck (1968), in "Methods in Computational Physics" Vol. 8, (B. Alder, S. Fernbach, M. Roten- berg, editors), p. 63. Academic Press, New York. 2. J. W. D. Connolly (1971), in "Electronic Density of States" (L. H. Bennett, editor), p. 27. NBS Special Publication 323. 3. G. Gilat, L. J. Raubenheimer, Phys. Rev. ]44, 144 (1966). 4. J. W. D. Connolly, Intern. J. Quant. Chem. 3, 807 (1970). 5. L. Smrcka, Czech. J. Phys. B21_, 683 (1971). 6. C. Senemaud, M. T. Costa Lima, J. Phys. Chem. Solids 37_, 88 (1975). 7. C. H. Shaw, in "Theory of Alloy Phases", (1956) pg. 13, American Society for Metals. 8. P. 0. Nilsson, J. Kanski, Phys. Letters 41A, 217 (1972). 204 VALENCE BAND SPECTRA OF ALUMINIUM-NOBLE METAL ALLOYS + L.M. Watson, D.J. Fabian, J.C. Fuggle*, E. Kallne , and P.R. Norris Metallurgy Department, University of Strathclyde, Colville Building, 48 North Portland Street, Glasgow Gl 1XN, Scotland. *Physik Departmente 20, Technische Universitat MUnchen, D-8046 Garching b, Miinchen, W. Germany. Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico, USA. The valence band x-ray photoemission (XPS) , the Al L2 3 and the Al KB spectra for a number of aluminium-noble metal alloys have been superimposed on the same energy scale for comparison. Those for AI2CU, AlAg2 and Al2Au are shown in figure 1. Although the emission process from solids is extremely complex, we assume to a first approximation that the XPS spectra reflect the overall density of states in the alloys, the Al L2,3 the partial density of valence band s and d states in the spatial region of the aluminium 2p core wavefunctions, and the K3 spec- tra the partial density of valence band p-states in the spatial region of the aluminium Is wavefunction. That this approximation is justified has been demonstrated by the excellent agreement between calculation and experiment for the Al L2 3 emission from Al 2 Au [2,3]. The Fermi level is clearly defined in all spectra and is taken as the zero of binding energy. The high intensity regions of the XPS spectra are attributed to the 3d, 4d and 5d states of Cu, Ag and Au respectively. Splitting of these levels is resolved in the silver and gold alloys but not in the copper alloys (resolution ^leV) . The L2 3 spectra show sharp peaks at high binding energies and coincide with the high binding energy onset of the d-bands. These are interpreted as be- ing due to the mixing of the Al 3s states with the high binding energy d-band causing a flattening of the E(k) curves and a consequent increase in the density of states. This occurs over a small energy region and the peaks are accentuated by a depletion of the s-state density at the aluminium sites in the region of the noble metal d-bands. This behav- iour has been predicted by Kudrnovsky et al [4] using CPA theory for disordered alloys and has been given experimental support by Norris et al [5]. Al2Au is probably the most thoroughly investigated alloy and the Al s-state density predicted by Switendick is in general agreement with the overall shape of the L2 3 spectrum. However, the calculation fails to predict the pronounced peak at 6.3eV binding energy. Since the d- bands of gold are more spatially diffuse this peak plus a contribution to the main peak is attributed to the overlap of the gold d-bands with the Al L2.3 core levels thus contributing to the emission, A similar effect has been observed in the L2 3 emission from Mg-Au alloys [6] . Another remarkable feature of this alloy is the extremely sharp rise in the L2 9 3 absorption spectrum 1.4eV above the absorption edge mea- sured by Gudat et al [7] . 205 AlAg 2 > H I/) Z L±J z XPS AIL23 i] AIK/3 — BE(eV) E f 2 i 6 8 10 12 BE(eV) 1) BAUN & FISCHER AI2AU t 1 f >- i h- z XPS_^ .^•* J J \ \ LU h- r" \ z AIL23 y ' "••••. I —S 1 1 \ 1 V AIK/3 / *"*•"»-■ > 1 .——.t. . 1 - , 1 * 1 E, 2 A 6 10 12 BE(eV) Figure 1 Valence band spectra of some aluminium-noble metal alloys. 206 In all cases the Al KB spectra show a second peak at high binding energies for the alloys. The d band widths decrease with increasing aluminium concentration. The high binding energy onset remains con- stant in energy within experimental error whereas the low binding ener- gy onset recedes from the Fermi level. The peak in the KB spectra fol- lows this recession and suggests that it is caused by the mixing of the Al 3p states with the low binding energy d-bands. Many intermetallic compounds are strongly bonded and some indica- tion of the types of bond could be expected from XPS core level shift measurements. However, in most of these alloys core levels from both species shift to a greater or lesser extent to higher binding energies. A striking example is again Al2Au where the Au N6 and N7 levels shift by 2eV whereas the Al Li peak shifts in the same direction by O.leV. All these shifts being measured from the Fermi level. References [1] D.W. Fischer and W.L. Baun, 1967, J. Appl. Phys . , 38_, 229, 2092. [2] A.C. Switendick, 1971, N.B.S. Spec. Publ. No. 323, p297. [3] M.L. Williams, R.C. Dobbyn, J.R. Cuthill and A.J. McAlister, 1971, N.B.S. Spec. Publ. No. 323, p303. [4] J. Kudrnovsk?, L. Smrc'ka and B. Velick?, 1973, "X-ray Spectra and Electronic Structure of Matter" ed. A. Faessler and G. Wiech, Vol. II, p94. [5] P.R. Norris, D.J. Fabian, L.M. Watson, J.C. Fuggle and W. Lang, 1974, J. de Physique, 35_, C4-65. [6] J.C. Fuggle, L.M. Watson, P.R. Norris and D.J. Fabian, 1975, J. Phys. F, 590. [7] W. Gudat, J. Karlau and C. Kunz, 1973, "X-ray Spectra and Elec- tronic Structure of Matter" ed. A. Faessler and G. Wiech, Vol. I, p205. 207 SXS AND XPS IN THE INVESTIGATION OF ORDER IN ALLOYS AND LIQUID METALS. + C. F. Hague, J.-M. Mariot, G. Dufour and R. C. Karnatak Laboratoire de Chimie Physique (L. A. n° 176) Universite Pierre et Marie Curie 11, rue P. et M. Curie 75231 Paris Cedex 05 France 1. Introduction : the invariance of the lattice under translation is a fundamental aspect of band theory. So the study of the modifications to the band model when long- range order breaks down is most interesting. Two types of disorder can be met with : i) a composition disorder, which exists in disordered crystallized alloys, ii) a topological disorder, which is found in liquids and amorphous solids. We report here two examples of work undertaken to stu- dy the alterations in the density of states upon disorde- ring : the well known NigFe alloy, whose long-range orde- ring can be eliminated by quenching from a high temperature (1), and Fe in the liquid phase. NigFe alloy was studied by soft X-ray spectroscopy (SXS) and X-ray pho toelec tron spectroscopy (XPS). These techniques are usefully comolement ar y especially where alloys are concerned : on the one hand SXS gives an indica- tion of the partial densities of states, depending on which type of atom is ionized in an inner shell ; on the other hand, XPS gives an overall picture of the combined densi- ties of s tates . Fe was studied in the liquid phase by SXS only. 2. Experimental : the Ni and Fe L~ spectra were studied in the pure metals and in the NioFe alloys by electron bom- bardment (2 kV) with a 25 cm radius bent crystal spectro- meter equipped with gypsum and KAP crystals respectively. The photoelec tron spectra were induced by Mg K$( radiation and run in UHV conditions. The details of the alloy expe- riments can be found elsewhere (2). The Lg spectrum of liquid Fe was obtained in a newly designed 50 cm radius bent crystal spectrometer (3). It is equipped with an electron gun to excite the L„ spectrum and to melt the target. The vacuum in the source chamber is ^ 5.10" Torr ; this can rise to 5.10 -7 Torr at liquid phase temperatures. Results shown are from at least 8 runs on different samples. Sponsored in part by DGRST under contract n° 73-7-1586 and "Groupement Regional de Mesures Physiques pour la Chimie Paris Centre (Centre de Spec trochimie ) " . 208 3. Results and discussion : i ) Ordered (0) and disordered SXS Lg emission of Ni in the metal alloys are given Fig. la. The corre are given Fig. lb. The spectra of t than those of the pure elements, th important for the Ni spectra. Such explained by d electron tunnelling broader in the and D alloy respec is 6 % for Fe in either phase. This the number of nearest neighbour s . Th bours in pure Ni but 4 Fe atoms onl the alloy. Disordering would be e this situation. Fe goes from 8 near pure element to 12 nearest Ni atoms account taken for the presence of f be expected to be less perturbed by The XPS valence band spectra o are broader than that of pure Ni , b indicating the lower concentration ii) Lg absorption and emission emission of liquid Fe is indistingu The absorption curves were obt absorption method (5) and the In ( plotted Fig. 4. It is important to tion of the electron beam is invers density of the target, so the amoun the emitted radiation remains the s solid despite a decrease in density 14 % . The absorption curves present sidered to reflect relative changes ficient on fusion. Hence we tentati change in the density of unoccupied tion band is observed. However, as i suits on Fe and Cu (6) no change is experimental limits at the Fermi le absorption curves. This is also tru Co, Ni and Cu as we report elsewher (D) Ni^Fe alloys : the and the and D Ni 3 Fe sponding spectra for Fe he alloys are broader e broadening being more band broadening could be (4). Ni is 2 3 % and 20 % tively ; the broadening must be confronted with ere are 12 nearest neigh- y surrounding each Ni in xpected to attenuate est neighbours in the in the alloy, and ewer Fe atoms, it would di sorder . f the alloys (Fig. 2,3) ut closely resemble it, of Fe. of liquid Fe : the L3 ishable from the solid, ained by the self- *2.5 kV / I 5 kV > is note that the penetra- ely proportional to the t of matter traversed by ame in the liquid and of the liquid phase of ed here can thus be con- in the absorption coef- vely conclude that a states of the conduc- n recent K emission re- observed to within the vel in the emission or e in the Lo emissions of e (3). 4. Conclusion : as expected from the small changes in the coordination numbers of liquid metals no modification is observed close to the Fermi level in the liquid relative to the solid. However 3d band broadening is observed in the and D alloys where a change in coordination number is encountered. A confrontation with conflicting theoretical calculations for the densities of unoccupied states in liquid metals is at present a little hazardous. 209 g c o A "" 2 a J \ c 3 700 710 720 Energy (eV) A — 7 NSr— B B.C — ~Jj 1 '■ -5 Energy relative to Fermi level (eV| Energy relative to Fermi level (eVI Fig. 1 a) Ni b) Fe L 3 emission (A:pure metal ; B : D-Ni 3 Fe ; C : O-Ni 3 Fe) Energy relative to fermi level leV! -10 -5 Energy relative to ferrm level leV) Fig. 2 : XPS valence band (A: Fe; B: Ni ;C : O-Ni 3 Fe; insert unsmoothed 0-Ni 3 Fe) Fig. 3 : XPS valence band (A:0-Ni 3 Fe;B:D-Ni 3 Fe) Jl~ o Ef 5 -5 En»w («V) Fig. 4 : L absorption spectrum of iron Liquid Solid M Fayard Phys Stat Solidi(a) 1_7 407 (1973) al J Phys F:Metal Physics 6 899 (1976) rd References : 1 . Y Calvayrac , 2. C F Hague et 3. C F Hague, in Proceedings of the 3 ra International Confe rence on Liquid Metals, Bristol, 1976 (The Institute of Physics Conference Series, to be published) 4. V L Moruzzi et al Phys Rev B J_0 4856 (1974) 5. R J Liefeld, in Soft X-ray Band Spectra, editor D J Fa- bian (Academic Press, London, 1968) p 133 6. K B Garg, E Kallne Phys Stat Solidi(b) 70 K121 (1975) 210 A NEW COMPARISON BETWEEN EXPERIMENT AND THEORY FOR THE X-RAY K-ABSORPTION EDGE OF NICKEL D. M. PEASE and T. K. GREGORYS Institute of Materials Science University of Connecticut Storrs, Connecticut 06268 *Present Address: Frequency and Time Systems Inc. Street, Danvers, Massachusetts 182 Conant Nagel , et. al . , have calculated the K_ edge absorption spectrum of nickel using an APW approach, in which possible effects of the core hole on the final states are ignored [1], Their calculated curve exhibits maxima at about 3 and 15 eV above the Fermi level, in general agreement with experiment. In addition to these peaks, how- ever, the above authors calculate a shoulder at about 9 eV which they cannot correlate with a corresponding feature on any experimental spectrum. We have resolved in our experimental nickel K edge a simi- lar shoulder occurring approximately 6 eV above the Fermi level, put- ting our results in better agreement with theory than previous spectra. O O o Q. a: o (JT) GO < < J_ 10 ENERGY, eV 30 Fig. 1. Experimental nickel K edge for a 4 ym foil using the (1,1) crystal setting. The spectra were taken with an automatic two crys- tal spectrometer [2]. The x-ray tube had a tungsten target operated at 13 KV and 100 ma. Silicon analyzer crystals in the (1,1) set- ting were used, whose first order rocking curve was 9.5 arc seconds at the nickel K edge. 80,000 count statis- tics and scanning step sizes of h eV were utilized. A four micron nickel foil was used, for which thickness effects will be small for the apparatus used. [3] The spectrum was reproduced with crystals in the (1,3) setting as well. Our ex- perimental spectrum is shown in Fig. 1, and our de- convoluted spectrum at the top of Fig. 2. We point out that Borovskii and Batyrev, although not resolving the shoulder at B in their ex- perimental nickel j< spectrum, do deconvolute their results to obtain a double humped 211 structure somewhat similar to ours in the vicinity of the Fermi level [4]. The feature corresponding to shoulder B is located significantly closer to the Fermi energy in Borovskii and Batyrev's results than in our spectrum. Fig. 2 shows a detailed comparison between theory and experiment. The bottom curve is the unbroadened spectrum of Nagel , et. al . [5]. The central curve shows the cal- culated spectrum after our convolution with a Lorentzian corresponding to the K hole broadening. It may be seen that the theoretical spectrum with K hole broadening shows rough qualitative agreement with the deconvoluted experi- mental spectrum. However, the theoretical spectrum is much sharper than the experimental results, and the first two experimental peaks are shifted to lower energies relative to the theoretical curve by about 2-3 eV. Nagel, et al., point out that there is an important broadening correc- tion which should be taken into account in addition to K-hole broadening, namely the "hot electron" broadening due to the finite time that the excited electron exists in a state above the Fermi level [1]. Fig. 2. Comparison between experi- mental and theoretical absorption edges. From top to bottom are the nickel K edge deconvoluted with the experimental rocking curve, the theo- retical nickel K edge convoluted with a Lorentzian having the K level half width, and the unbroadened theoretical K edge. In conclusion, we note that one of the main reasons experimental and theoretical comparisons such as the above are of interest lies in the possibility of resolving the old question of whether the K_ hole significantly modifies the Bloch states in a metal [6], [7]. From the above it appears that calculations neglect- ing the influence of the core hole on the final state do result in a rough qualitative agreement with experiment regarding the number and position of peaks. However, our results indicate that broadening effects on the final ejected electron states are quite important. In addition, since the two lowest energy experimental peaks are sig- nificantly shifted in energy relative to the calculated peak positions 212 the possibility also exists that core hole effects may modify the positions of spectral features. tThis investigation was supported by a grant from the National Science Foundation. (1) D. J. Nagel , D. A. Papaconstantopoulos, J. W. McCaffrey, and J. W. Criss. Proc. of the International Symposium on X-Ray Spectra and Electronic Structure of Matter, Ed A. Faessler and G. Wiech, 51 (1973). (2) T. K. Gregory and P. E. Best, Advances in X-Ray Analysis ]_5, 90 (1971). (3) Douglas M. Pease, to be published in Applied Spectroscopy. (4) I. B. Borovskii and V. P. Batyrev, Bull. Acad. Sci . USSR 24, 499 (1960). (5) The unbroadened spectrum was obtained by courtesy of D. A. Papaconstantopoulos. (6) L. G. Parratt, Rev. Mod. Phys. 31_, 616 (1959). (7) E. N. Rumanov, Sov. Phys. - JETP 20, 1480 (1965). 213 APPLICATION OF Pt L EMISSION AND ABSORPTION SPECTRA FOR THE INVESTIGATION OF CLUSTER STRUCTURES J. Finster, P. MUller, F. Thiel and A. Meisel Sektion Chemie der Karl-Marx-Universitat DDR-701 Leipzig, Linnestr. 2 The knowledge of the electronic structure of clusters (small aggregations of atoms) is of great interest for seve- ral fields, especially in heterogeneous catalysis, where finely dispersed metals play an important role. However, for a long time the question existed, if these clusters have metallic properties or not. Depending on the choosen criterion, the number of atoms with which such an aggrega- tion starts to be a metal (or a true solid) can vary from appr. 10 (where you can get already a rough picture of the solid band structure) to several hundred atoms (if you con- sider macroscopic properties). Up to now there are only a few investigations which uses X-ray and photoelectronspec- troscopy for the exploration of the electronic structure of clusters [l - 3j. We took as an example platinum and measured at first Lfi emission lines and L-j-jj absorption spectra of the metal and some Pt compounds [4,5]. Additionally, XPS measurements have been made. With the LB., & 2 and Q^ lines we found long-wavelength shifts for Pt(ll) and short ones for Pt(lV) in the order of 0.1 eV relative to metallic Pt. The L 1X1 absorption edge showed shifts of +0.3 eV for Pt(ll) and +0.5 eV for Pt(lV), whereas PtClp (and also the clusters) gave a long-wavelength shift. The changes in the fine structure (especially inten- sity and width of the first absorption maximum) correlate with the changing density of unoccupied 5d states. The X- ray spectra together with the XPS measurements of PtClg, which exists in form of Pt 6 Cl i2 -clusters, account for the 214 existence of metal-metal-interaction £6^# The Pt clusters on a coal carrier exhibit mean diameters of 13, 18, 24 and 45 5, determined by EXAFS jj] • The X-ray spe* ctra of the clusters were measured with a high-resolution focussing spectrometer with linear stepwise movement of the proportional counter and with sample changing in each mea- suring point. The ESCA measurements were performed with the VG- ESCA 4. In both spectrometers the spectra were taken from the original, air-inf lueneed samples and from the samples after in-situ reduction with hydrogen at 150 °C. Thus we could distinguish between chemical effects and cluster- size-effects. The cluster in the 45 fi-sample showed metal- lic behaviour: the spectra wera similar to those of the metals, and there is almost no difference before and after Hp exposure . However, the smaller clusters of this noble metal with a high percentage of active surface atoms had been oxidized after contact with air. For the cleaned samples we found 3 kinds of cluster-^size- effects: 1) The Pt 4f lines show a somewhat lower B.E. in the clusters than in the bulk metal. This can be explained by the combination of the (positive) potential shift and the Negative) polarisation shift of core levels connected with the transition from the free atom to the metal, where the clusters are an intermediate state [8]. 2) The Ljtt"- edge shifts to lower energies in the smallet clusters in agreement with the opposite directions of the shifts of core levels (decreasing B.E.) and of valence levels (in- creasing B.E.), going in the direction bulk metal --> clu- ster — ^free atom. 3) The first absorption maximum of the Ljjj edge is more pronounced in the case of the smaller clusters. This fact (and also the second point) is suppor- ted by a quantumchemical calculation (SCCC calculation of a 13 atom Pt cluster), which shows a higher density of free d states near the Fermi energy» 215 References 1 Lewis P.H.: J.Phys.Chem. 61(1963), 2151 2 Erenburg S.B., GolovinA.V., Noskova S.P., Kuznetsov B.N. and Ovsiannikova I.A.: React. Kinet. Cat* Lett. 1(1974), 507 Ovsiannikova I. A., Erenburg S.B., Khlestov V.B., Gegu- sin I.I. , Topol I. A., Sachenko V.P. and Kovtun A. P.: Izv. Akad. Nauk SSSR, Ser. fiz. 40(1976), 230 3 Borsyak P.G., Katrich G.A. and Samoilov V.S.: Proc. Intern. Symp* "X-ray Photoelectron Spectroscopy", Kiev, June 1975 (to be published) 4 Finster J., Muller P. and Meisel A.: Proc* XVIII 8 Coll. Spectr. Internat., Grenoble 1975, Vol. II, p. 596 5 Muller P., Finster J. and Meisel A.; Izv. Akad. Nauk SSSR, Ser. fiz. 40(1976), 373 6 Finster J., Muller P. and Meisel A.: Z. Chem. (to be published) 7 Keilacker H., Meisel A.: Wiss. Z. KMU Leipzig, Math.- Naturw. R. 22(1 973) , 585 ; Kristallographia (Moscow) 20(1975), 245 8 Finster J.: Wiss. Z. KMU Leipzig, Math. -Naturw. R. 25(1976), No. 4 (to be published) 216 CONFIGURATION INTERACTION INTERFERENCE EFFECTS IN TRF CORE ELECTRON EXCITATION EDGES OF TRANSITION METALS R. E. Dietz and E. G. McRae Bell Laboratories, Murray Hill, New Jersey 0797*+ The shapes of the low-lying core excitation edges in the transition metals are largely determined by an interference between the scattering matrix elements corresponding to the excitation of a core electron to empty d states near the Fermi level, and excitations of d conduction electrons to continuum f states [l]. This result applies to both electron energy loss (ELS) and soft X-ray absorption (SXA) spectros- copies, which give virtually identical lineshapes. The effect of the interference is to distort and shift the peaks in the spectral density from the resonant energy of the discrete d-state density. The inter- ference effect must be taken into account in relating ELS or SXA resonant energies to the corresponding binding energies measured by X-ray photoemission spectroscopy (XPS). We report in Table I ELS peak energies measured in Ni, Pd and Ft together with resonant energies Eo derived from the observed spectra with due consideration of the inter- ference effect. The ELS resonance energies and XPS binding energies [2] shown in Table I are the same. We infer as explained below that the multiplet structure observed in XPS is that of the fully screened conf igur at ion [ 3 ] • Core excitation thresholds in metals as studied by SXA or ELS corre- spond to the transition njn n-1 m+1 c v -* c v and have a threshold energy E =< (c v )> - <^c v )> . Here c and v represent the principal and orbital quantum numbers of, respectively, core and valence electrons, and <( ^> indicates the energy of the lowest energy state of the enclosed configuration. In XPS experiments, the threshold energy for core excitation is deter- mined by the energy for the creation of a fully screened core hole in the long time limit. In the atomic limit we can represent this process by a two-atom excitation, equivalent to the one atom plus metal descrip- tion: „ n m n-1 m+1 n m-1 2cv-4C v +cv +e. ■n _o i -i_l nmn m-1 - „,,,., ,.i For emission of a valence electron: c v — > c v + e . The relaxed binding energy is then the energy difference between core and valence excitations: ., , r / n-1 m+1 x , n m x £ B = - . Thus we find E cv = £g. This equivalence will hold even if c v can be represented by a multiplet or band of states, since the threshold will simply correspond to the occupation of the lowest energy state. Whether the multiplet structure perceived in the spectral density corresponds to the structure expected for the fully screened configura- tion will depend on the relative time scales for the core transition and the screening processes. In cases where the structure in the 217 spectral density is dominated by incompletely screened configurations, as it may be in narrow-band metals or insulators, then the fully screened threshold energy may be difficult to ascertain, and the spectral density will be dominated by bound states. Ni, Pd and Pt are particularly simple to study because these have only one d hole in their ground state, with the final ELS or relaxed XPS configuration consisting locally of a closed d shell. The final state multiplet structure should be simply that of the core hole spin-orbit splitting. Thus a doublet structure should be observed for core levels with I > 0. The components are broadened mainly by Coster-Kronig decay of the core hole, this effect being much larger than s-d hybridi- zation which broadens the final electron state in ELS and SXA. In fact, band structure calculations in Ni, Pd and Pt indicate that the width of the empty d-band states is only ^Jd.2 eV. This means that one can treat the empty d density as a discrete level which would produce a sharp peak in the ELS or SXA spectral density in the absence of relaxation effects. The configuration interaction process which is chiefly responsible for the np core hole decay can be represented by the exchange matrix element <(np, ef;nd',nd)> . Here n = 3> ^; 5 respectively for Ni, Pd, and Pt. This matrix element mixes configurations (possessing a particu- lar total angular momentum j) which result from the discrete p — > d scattering, with configurations which result from d — > ef scattering, as shown in Fig. 1. In this process, each of the J = 3^2 or J = l/2 components of the ^p multiplet of the np5nd-*- y (n+l)s configuration mixes with three continua which are derived from the np^nd°(n+l)s£f configura- tion by combining three of the L-S multiplets of d", namely, -k>, -% and -k), with the f continuum to form 2p continua. In spherical symmetry each core hole component will mix with continua having the same J value, and the spectral lineshapes for each spin-orbit component can be computed simply from the Fano theory for the interference of a single discrete transition with a continuum. In addition to the interference process discussed above, there are a number of less important interference processes which may contribute to the spectral density of the J = 1/2 spin-orbit component. These processes are summarized in Fig. 2. One of them (Fig. 2(b)) is resonant with the discrete p ^d excitation and can lead to interference effects. The nonresonant processes (Fig 2c, d, e) merely contribute to the core -hole relaxation rate T = it SjVjj where the sum is taken over all contributing coulomb and exchange matrix elements (weighted by the density of states). These processes make a significant contribution to the XPS linewidth 2F in some metals. For example, in Ni metal, T(3py2) = °-79 eV while r(3Pl/p) = 1-08 eV [2]. In fourth and fifth row metals, processes (c) and (d) will not exist since the %> and 5p spin orbit splitting is larger than the d bandwidth. We have considered the possibility that departures from spherical 218 symmetry and many-body interactions might also be important in deter- mining the experimental lineshapes. Trial ELS lineshapes computed for cubic potentials in Ni metal are qualitatively similar to shapes computed in the spherical approximation. On the other hand, the line- shapes are very sensitive to many-body interactions which appear to be very weak in the ELS spectra of Ni metal (|a| < 0.02), although they are very important in XPS [3]. 1. 2. 3. REFERENCES R. E. Dietz, E. G. McRae, Y. Yafet, and C. W. Caldwell, Phys. Rev, Letters 33, 1372 (197*0. G. K. Wertheim, unpublished data. S. Hiifner and G. K. Wertheim, Phys. Lett. 51A, 301 (1975). TABLE I. XPS AND ELS CORE EXCITATION ENERGIES ,(2) Ni 3P pa 3/2 3p l/2 3s I*, Up Pt 5p kf, kf J 3/2 1/2 3/2 7/2 5/2 e B (xps)' 65.9 eV 67.6 110.6 51.3 5^ 51-9 71.2 7^.6 E . (ELS) peak 67.0 68.U 110.6 60 58.0 72.0 75-3 E Q (ELS) 66.0 ±0.1 67.7 110.6 52 71.3 lk.6 (n*()s ' w m^ W//////M «f nd (Q) J»3/2 (b) mw/m ** (c) 1 1 — 1 np J =1/2 Fig. 1. Main interference process determining np ELS and SXA line- shapes in n=3j^- and 5th row transition metals. INITIAL EVENT (n H)S m W////A c f nd -. ' (0) np J -3/2 J -1/2 ORBIT COMPONENT NON- RESONANT RELAXATION 0/H/////M (c) (d) (e) 3 /2> '1/2 219 Fig. 2. Some additional processes affecting np n /r , excitation. VALENCE BAND AND CONDUCTION BAND SPECTRA OF TRANSITION-METAL COMPOUNDS Kenjiro TSUTSUMI , Kouichi ICHIKAWA, and Osamu AITA College of Engineering, University of Osaka Prefecture Mozu, Sakai, Osaka 591, JAPAN Transition-metal compounds are of fundamental interest in solid- state physics. It is not possible to adequately describe the optical, electronic and magnetic properties of many first-row trans it ion -metal compounds within the theoretical framework provided by conventional band theory. The results of the energy band calculations which have been carried out for 3d transition-metal monoxides clearly predict that the transition-metal monoxides should be conductors [l ,2] . However, ex- perimentally the oxides MnO through NiO are insulators, though the oxide TiO is a good conductor. Determination of the electronic structures of these materials is essential to an understanding of these properties, and x-ray spectroscopy and x-ray photoelectron spectroscopy are powerful means for studying these structures. However, only a few investigations have been made on soft-x-ray absorption[3] and emission-band spectra of these substances. In the present study, the M~ _ emission-band spectra of transition metals and their compounds, such as* Ni , NiO, NiCl p , NiBr , Co, CoO, CoCl , CoBr , etc. were obtained by using a Henke-type x-ray tube and a Vodar-type spectrometer consisting of a concave grating with the radius of 200cm and 1200 grooves per mm. In addition, the x-ray photoelectron spectra of the valence bands and the transition-metal 3p states of these substances were obtained by using an electron-energy an- alyser of hemi-spherical type with the radius of 12.5cm. All the exper- iments were carried out under the clean high vacuum. Also, the M photoelectric-yield spectra of the transition-metal compounds had "Been obtained with a usual x-ray tube and the same Vodar-type spectrometer as mentioned above [U]. It is well known that the feature of the photoelec- tric-yield spectra is quite similar to that of the absorption spectra [5]. Besides, the M absorption spectra of the transition-metal hal- ides had been obtained by using a soft-x-ray spectrometer consisting of a plane-glass grating with 1080 grooves per mm and a concave mirror[6]. In this case synchrotron orbital-radiation from a 1.3GeV electron syn- chrotron had been used as a continuous light source. The M emission spectrum of these substances shows a structure accompanied 'with a tail (in some substances, very remarkable structure) in the high-energy region of the emission band. The photoelectron spec- trum of the valence band shows detailed structures. The M „ absorption spectrum of the transition-metal halides shows the fine structures on the low-energy side of the absorption threshold, and photoelectric-yield spectrum of the transition-metal monoxides also shows the similar struc- tures. All these emission, absorption, photoelectric-yield and photo- electron spectra are compared one another. For the accurate comparison, the energy scale of the photoelectron spectrum is measured from the peak of the transition-metal 3p spectrum of these substances. Some of such comparisons are shown in Fig.l. Such comparisons show the following re- markable features: (l) The shapes of the M emission-band spectrum and the x-ray photoelectron spectrum(XPS) of tne^same substance are quite 220 CoM^EMISSION CoM n ABSORPTION Co METAL different each other. The structures which are observed in the high-en- ergy region of the x-ray emission band are not observed in XPS. How- ever, the peak of the band in XPS nearly coincides with the main peak in the x-ray emission-band spectra. (2) Even in the case of the compounds the energy gap is not observed between the absorption or photoelectric- yield spectra and both the x-ray emission-band spectra and XPS. (3) In the absorption and photoelectric-yield spectra the structures are ob- served on the low-energy side of the absorption threshold of all the transition-metal compounds except for the nickel compounds. The structure observed in the high-energy region of the M ' emis- sion band appears not to be due to the M component in the usual mean- ing, because its intensity ratio to the main peak of the emission band is sometimes much larger than the ratio generally expected (about 1:2) and changes with the substances. It is well known that the characteris- tic x-ray lines of the transition- metal compounds show the asymmet- ric shape and/or sometimes show the remarkable structures [7 ] • It is interpreted by the electro- static interaction of a core hole created by x-ray transition with the d valence electrons [7 ,8], which gives rise to the multiplet struc- tures of the lines. Recently Asada et al.[8] calculated the shape of the K$_ „ line and the 3p-XPS of nickel 'compounds on the basis of the ligand field theory for molecular cluster in which the d electrons are mainly localized, and showed that the line broaden- ing is due to the multiplet struc- ture arising from the configura- tion p d in a cubic field. Their result shows that such multiplet structures extend over ten elec- tron volts on the high-binding- energy side of the state with the maximum multiplicity. According to this conception, it might be considered that the high-energy structure of the emission band may be due to the multiplet structure caused by the interaction between the 3d electrons and the inner- core p hole at the initial state of x-ray emission, that is, due to the multiplet structure arising from the configuration 3p 3d at the initial state of the M e- mission, where n is the numoer of the 3d electrons of the substances CoMuEMISSION CoMu EMISSION CoM 2J YIELD CoO CoM^ABSORPTION CoCU 50 55 60 65 PHOTON ENERGY ( eV ) 70 221 Fig.l. The M p _ x-ray emis- sion band spectra, "Cne 1VL ab- sorption spectra, the M ' photo- electric-yield spectra, and the photoelectron spectra(XPS) of the valence bands of metallic cobalt, CoO and CoCl . in question. Similarly, it might be considered that the structure which appears on the low-energy side of the absorption threshold in the M absorp- tion and M photoelectric-yield spectra may be attributed "60 the mul- tiplet structure arising from the configuration 3p 3d ' in the process of x-ray absorption. Kotani and Toyozawa[9] discussed the soft-x-ray absorption process of metal with an incomplete shell and suggested that the final state of the d level of the excited atom is lowered down due to a core hole left behind and sometimes is formed below the Fermi-level, though in the initial state of the absorption the unoccupied d level is above the Fermi -level. Similar phenomenon might occur in this case, and some of the 3p 3d " multiplet states may be formed below the conduction band. This may give rise to the low-energy structure of the absorption threshold. The main absorption on the high-energy side of the absorp- tion threshold may be caused by the transition to the empty Us band and some of the 3p 3d multiplet states mixed with this band. The x-ray photoelectron spectrum of the valence band is considered to show the most reliable feature of the electronic state of the valence band and its main peak appears to show the d character of the valence band of the substance in comparison with the M emission band, absorp- tion and photoelectric-yield spectra. The detailed structure in XPS are interpreted in terms of multiplet structure at excited state[lO]. The tail observed on the low-energy side of the peak may be due to the p character of the anion[lO] . As a conclusion, the soft-x-ray emission and absorption spectra of the transition-metal compounds are accompanied with the multiplet struc- tures which are caused by the interaction between the core hole and the localized d electrons in these substances, and the results appear to support the model containing both localized and one-electron band states [8,11]. 1 2 3 1+ 5 6 7 8 9 10 11 References L.F. Mattheiss, Phys . Rev. B jj_, 290,306 (1972). J. Yamashita, J. Phys. Soc . Jap. 18, 1010 (1963). F.C. Brown, C. Gahwiller, and A.B. Kunz , Solid State Commun. 9., 1+87 (1971). K. Tsutsumi and S. Nakai , Physica Fennica 9_, Suppl. 7h (197U). W. Gudat and C. Kunz, Phys. Rev. Lett. 29, 169 (1972). S. Nakai, H. Nakamori, A. Tomita, K. Tsutsumi, H. Nakamura, and C. Sugiura, Phys, Rev. B 9, 1870 (197*0. K. Tsutsumi and H. Nakamori, J. Phys. Soc. Jap. 25, lUl8 (1968). S. Asada, C. Satoko, and S. Sugano, J. Phys. Soc. Jap. 37., 855 (1975). A. Kotani and Y. Toyozawa, J. Phys. Soc. Jap. 35, 1073,1082 (1973) D.E. Eastman and J.L. Freeouf, Phys. Rev. Lett. 3^_, 395 (1975). D. Adler and J. Feinleib, Phys. Rev. B 2, 3112 (1970). 222 INTERPRETATION OP THE RHENIUM Lttt ABSORPTION DISCONTINUITY H ;T RHENIUM METAL AND IN SOME OP ITS COMPOUNDS A. 7. PENDHARKAR and C. MANDE Department of Physics, Nagpur University, Nagpur (India) The shape and fine structure of the Re X-ray Itqt absorption discontinuity have been studied in rhenium metal, seven octahedral rteoReClg, K^ReBrg, (tyH)oReCl6, (dipyH^ReClg, Re(dipy)Cl/L, K^ReO^tCN^ and ReO^j and three tetrahedral (KReO^., TTaRe04, NH^ReO^.) compounds, using a Cauchois type Dent crystal X-ray spectrograph of diameter 40 cm, equipped v/ith a well tested mica crystal. Microphotometer traces with magnification x100 of the recorded spectra were taken on the Spectroline Scanner manufactured by the Applied Research laboratories, California, U.S.A. The shape and the absorption maxima in the extended fine structure obtained for rhenium metal can be interpreted on the basis of the reported band structure of the metal and Iytle's theory. It has been shown that an absorption maximum lying at 30 e7 from the main Ljjt discontinuity can be explained using the concept of electronic plasma in solids. The main absorption discontinuity for all the compounds is found to split into two components [1] whereas in the metal the discontinuity is not split. The splitting and near edge structures in the discontinuities of the ien t &m a m compounds lying within 30-35eV have been interpreted with the help of suitable qualitative molecular orbital diagrams. It is possible to assign specific electron transitions for the different spectral features in the discontinuities on the basis of the M. 0. diagrams, taking account of the dipole selection rules. In the absorption process, the initial level from which the electron is ejected is ^£3/2 • ^ e can interpret the absorption maxima of the ReLju discontinuity as transitions of the 2?3/2 electrons into suitable vacant M. 0. levels. In all the cases except that of Re(dipy)Cl4, the p(^ and *rc) orbitals of the ligands are considered for interactions in constructing the M.O. pictures. In the case of Re(dipy)Cl4, the f2,2*] dipy ligand behaves as a strongs* donor because of which one has to consider the interactions of mainly the p(o") orbitals of the chlorine ligands and the p( in these compounds. Table II: Bond lengths (r^ ) in A.U. obtained from the fine structure of the Ljjj edge. n (in A) Compound AE r 1 (in A) ( X-ray diffraction data) K 2 ReCl 6 27.6(e-<) 2.34 2.37 K 2 ReBr6 23.2(e-Y) 2.55 2.50 (p3rH) 2 ReClg 29.0(e-/) 2.28 (dipyH) 2 ReCl5 2S.9(e-Y) 2.29 Re(di P y)Cl 4 33.9(e-Y} 2.11 (av.) E 3 Re02(ClT)4 44.8(f-6) 1.84(av.) Re0 5 44.5 (e-nf) 1.84 1.867 KRe0 4 52.2(f-6) 1.70 1.77 NaRe04 50.4(f-6) 1.73 1.68 M^ReCty 43.7(f-6) 1.86 1,84 Assuming that the fluctuations of the absorption coefficient are nearly sinusoidal in nature in the region of the escape peak, it is possible to extend the applicability of Levy's theory, originally developed for 224 the K discontinuity to the Ljjj and other X-ray discontinuities as well. The peaJ<: just; beyond the M.O. region is considered as the escape neaJ^. Utilizing the observed energy differences (£E) between this escape peaic and the subsequent absorption minimum, we have been able to obtain the bond lengths in these comnounds with resonaoie accuracy. The standard error, obtained statistically, in the values of &fi is found to be within + 2 eV and therefore the errors in the determination of the bond lengths lie within + 0.07 A. Table II shows that the agreement between our values and those obtained from X-ray diffraction work is quite satisfactory. It is, thus, possible to emnloy the X-ray adsorption edge fine structure method to determine the bond lengths of the compounds with sufficient confidence. Reference 1) Pendharkar, A. 7. and Mande, C. Chemical Physics (W.G.) 7 (1975) 244-254. 225 COHERENT- PSEUDOPOTENTIAL- PAIR CALCULATION FOR X-RAY PHOTOEMISSION STUDIES OF AG-PD ALLOYS Vipin Srivastava and S.K.Joshi Physics Department jRoorkee University ?Roorkee 2^+7667 ?India. In the recent past there has been considerable activ- ity) both theoretical and experimental |-^] ?for the determ- ination of the density of electronic states in disordered alloys. X-ray photoelectron spectroscopy (XPS) has emerged as one of the most powerful techniques for getting a direct view of the occupied electron states of such systems. On the the- oretical side simplified models are being employed to deal with real alloys. In the Ag-Pd system the lattice constant changes mar- kedly with composition giving rise to an appreciable change in the site energies and bandwidths.The densities of states of Ag and Pd are also very dissimilar in nature. Though the coherent potential approximation (CPA) gives moderately good agreement with experimental data? it can not be held as a promising scheme for an adequate understanding of complex systems like Ag-Pd alloys. We propose here a scheme that can incorporate the special features of the Ag-Pd system menti- oned above. The agreement of our results with XPS data is heartening. THEORY AND RESULTS'. The present scheme is an extension of our earlier work [if] based on the pseudopotential concept. We have considered two-site scattering in an effective medium framework to take into account off-diagonal disorder more rigorously. The Hamiltonian of the system is? I n ) knm^l ' ... CD where site energies? e and hopping integrals? h j are ra- ndom variables and satisfy the following equality for Ag-Pd system? I |n>e h e pd h p , p , V(E)(=<(E-H)-1». is related to an effective medium propagator, as > = G + GG, ... Of) where T is the scattering matrix, and the effective medium is denoted by the Hamiltonian H = I|n>LI 2 is made self-consistently by putting 3 -<(H-H) / [l-(H-H)G]>= 0. ... (6) It is a formidable task to solve eqn. (6) exactly. We appro- ximate T by a two-site scattering matrix, and m obtain two self -consistent coupled equations in £, and £p • I 2 ) > = °» •'• (7a) = 0, ...(7b) where n and m are two nearest neighbour sites. The self-energies 5% and Y.? have been obtained by sol- ving (7) iteratively for 1+0 at.VT Ag , 60 at.*/. Pd alloy .The various input parameters have been taken from ref .3. The density of states for the alloy is found from the formula p( E ) = -tT 1 Im |n> [l-O.lf^iSl ] , ... (8 ) .Pd where |n> - A- f P (E ' )dE ' 1 -^2- y (E-.I 1 )/(l-Z 2 )-E'+e pd Figure 1 shows the results for P(E) for the alloy under consideration. Comparison has been made with the CPA results and the optical density of states (XPS).The struct- ures in the present result are distinctly close to the ones shown in the experimental result, and may be assigned to the structures in the parent densities of states. The posi- tions of the prominent peaks are indicated in the figure. The present calculation shows excellent agreement with esperiment. 227 references: 1. C.Norris and H.P.Myers, J. Phys. Fl ,62(1971) . 2. S.Hufner, G.K.Wertheim and J.H.Wernick, Phys .Rev.BS >^5ll (1973). 3. G.M. Stock, R.W.Williams and J.S.Faulkner, J. Phys.F3,l688 (1973). k» V. Srivastava and S.K.Joshi, Proceedings of the IV Inter- national Conference on Vacuum Ultraviolet Radiation Phys- ics (Hamburg ,1971*) } Phys. Rev. B12, 2871(1975). /. ../ • . *\. they were corrected using a ^ a ' _ ^•-'"' .' L(3p Pd'. '*•'•-..•.. method which will be described g T'*t*T"7*T?"V**". ../ . . .."'.* elsewhere. The L3 absorption ^ .' '• spectra were recorded using H .•* \ the continuum of a gold anode, b) -••' ""v. They were corrected for the ** ,Vh «' background accompanying the bremsstrahlung as reported in (3). Results and Discussion , ._..-•••* + c) LP 2 PdH x - . Lp 2 Pd Luc — ^1 *■ - *■ *■- u»^ * * 4- * > m 1 1 1 ~- The corrected and norma- lized Lp2 emission spectra shown on Pigs. 1a, b are al- 7 Vrn -zinrs / TT \ 7-ion most identical in shape and ylbv j\0 ( eV ) t> 1 80 . . . mi ~ ,f -, . n. K v ; position. Therefore the dif- ference LP2 PdHx - Lp2 Pd is given on Pig. 1c on an enlarged scale . (2 .7x) . The region where according to EASTMAN et al. transitions from the additional energy band in PdH x should oc- cur is marked by arrows. As can be seen there is no correspon- ding feature in the x-ray spectrum of PdH x . Prom Pig. 1c one has to conclude that in the energy region in question L^2 PdH x is even less intense than L(32 Pd. In the adjacent region bet- ween 3164 eV and 3167 eV the intensity of the PdH x spectrum is slightly higher which might be regarded as some indication for an additional energy band. There is some ambiguity in the relative positions of the emission spectra, as it is not possible to determine the Per- mi edges in the spectra without further information. If one assumes the Permi edges to be given by the points of inflexion of the absorption edges shown on Pig. 2, the spectrum of Pdf^ would have to be shifted by 0.5 eV towards lower energies in order to achieve coincidence of the Permi edges in the emis- sion spectra. Then the difference L(32 PdHx -' LP2 Pd becomes positive in the region between 3164 eV and 3172 eV with a maximum at 3171 eV. This again would not comply with the ex- perimental findings of EASTMAN et al. The low lying x-ray emission band, which is well pro- 230 02 -P •H 2 eh - / : • p ft —I P 1 '. P-* L-, Absorption Spectrum of PdH Pig. 2 A 1 Pp L-* Absorption Spectrum of Pd o ft o ■ H EH • o CD pq Photon Energy (eV) 3150 3200 3250 I I I..... nounced in the Nb L(3 ? spectrum of NbH x ? is absent or has a very low intensity in the case of PdH x . The corresponding energy band obviously has a very low density of states at the Pd atoms or a symmetry different from s and d. In contrast to the emission spectra the absorption spectra show significant differences. The first peak P-| decreases. In- stead of the peak P2 , which disappears completely, a new line P3 arises between P-| and P2 . The interpretation of these re- sults has to be postponed until appropriate calculations will be available. The extended fine structure regions marked with A,B,A',B' are rather similar. The distances in energy AE bet- ween corresponding features are smaller in the spectrum of PdH x due to the lattice expansion. Using theAE^l/a2 dependence we found the lattice parameter a to be increased by (3.7 + 0.4)$. As the increase of a at the low concentration limit of the p phase amounts to 3.5$ it is assured that the specimens of PdHx were of rather pure |3 phase. It is intended to complete this investigation by studying the corresponding transitions to and from L-| which should give information on the p-like character. Acknowledgements The author is indebted to Prof. J. Peisl and to Prof. A. Paessler for several helpful discussions. Thanks are also due to cand. phys. B. Eoltz for technical assistance. Literature: (1) D.E. Eastman, J.K. Cashion, and A.C. Switen- dick, Phys. Rev. Letts. 27, 35 (l971).fe)E. Gilberg, phys. stat. sol. (b) 69, 477 (1975) ;"T3) M.J. Hanus and E. Gilberg, J. Phys. B 9, 137 (1976) C 3 I CHARACTERISTIC AND CONTINUOUS X-RAY EMISSION MEASUREMENTS ON TiNi Helmut Foil Physikalisches Institut der Universitat 7500 Karlsruhe, FRG A special problem which arises in connection with the alloying of Ti with Ni is the possibility of a charge transfer. Investigations on this question have been perfor- med by Kallne [1] and Kolobova and Trofimova [2] . For clari- fication of this problem we have investigated the electronic DOS of the occupied and unoccupied part of the conduction band of the ordered alloy TiNi. The electronic DOS of the unoccupied part of the conduction band can be investigated by means of continuum isochromats . Recently Nagel et al. [3] have given an anticipated shape of such a continuum isochromat for TiNi. These calculations are based on so-called local DOS of TiNi as have been given by Papaconstantopoulos et al. [4]. A comparison of the theore- tical expectation with the measured continuum isochro- mat is shown in Fig. 1. The largest discrepancy between the two isochromats is the first high maximum of the theoretical isochro- mat immediately neighbouring the Fermi edge which is completely missing in the experimental isochromat. This high maximum of the theoretical curve corre- sponds to a high electronic DOS above the Fermi edge and arises according to Nagel et al . [3] from the unoccupied d-electron sta- tes localised at the Ni- sites in TiNi. The lack of such a high maximum in the experimental curve can be understood by a local trans- fer of electronic charge from Ti-sites to the Ni- sites on alloying. i intensity 1 1 T 1 TiNi A continuum- isochromat 10 i i \ \ \ . / / ./ / \ • i i i * • • 3 \ * • 05 i / \ / \ / /. i S \ / / / • / E-E F /. eV n •• i 1 i i i 2 U 6 8 Fig. 1 Comparison of the theoretical and experimental isochromat. The theoretical isochromat (Nagel et al . [3]) is dashed lined. The Fermi edge Ep is zero of energy. The curves are norma- lized to the same hight of the second peak. Further arguments for a charge transfer from Ti- to the Ni-sites arise from a comparison of our measured isochromats of Ti, Ni and TiNi (Fig. 2) There is a conspicuous simila- rity of the TiNi-isochromat with the Ti-isochromat especial- ly with regard to the intensity in the maximum. Concerning the high intensity of the Ni-isochromat this result can 232 only be explained by a completely filled local d-band of the Ni-spheres in TiNi. continuum - isochromols ii Fig. 2 Continuum isochromats from Ni, Ti and TiNi. Measured with a quartz crystal in 1 st order of reflection. Threshold voltage - 1.5 kV. The Fermi edge is zero of energy. ••' E-Ef Supplementary to isochromat spectroscopy we have investiga- ted the occupied part of the conduction band by measuring LjTj-emission band spectra in the pure elements and in the ordered alloy. Here our conclusions are based mainly on the positions of the Fermi edges at the respective emission bands. With the exception of the TiLjjj-spectrum from TiNi all these positions are determined from additional measure- ments of self absorption spectra. Fig. 3 shows the NiLjjj -bands in pure Ni and TiNi. Most important in our connection is the shift of the position of the Fermi edges at the spectrum. On going from pure Ni to TiNi the shift of the position of the Fermi edge towards the bottom of the spectrum in TiNi can be interpreted in terms of a filling up of the local DOS within the Ni-sphere of the ordered alloy TiNi. It supports the charge transfer concept from Ti to Ni . Fig. 4 shows the TiL-ry^-bands in pure Ti and TiNi. The pre- sentation is the same as that of Fig. 3. Because in TiNi the Fermi edge could not be localised by a pertaining self absorption spectrum , at present we cannot draw any conclu- sions from the positions of the Fermi edges in favor of charge transfer but on the other hand there is no evidence against charge transfer. There are arguments for the assumption that the high ener- getic peak of the TiL III -spectrum from TiNi does' nt reflect local DOS but possibly arises from cross transitions from the local Ni-d-band to the TiLm- level . On this basis fur- ther arguments for a charge transfer from Ti to Ni can be given. Normally one would expect that the area of the TiL^y-band from TiNi is half the area of the TiLjjj-band from pure Ti . 233 100 075 025 1 1 _ intensity 1 ft t i ' • iiL Ni L m -spectrum * t - • 1 - *ESS«V • t & * s - 1 # / '*.. A ; » ° # • • * •« _^. * ' ' • t TiNi •••_^_ 100- 075- 050 Q25 025 * i \ Ni l_ ,,, - spectrum . 2.70V* ; T- E. ev 025 Intensity Ti L,i, - spectrum __J — « 2.90 eV ■'*«♦♦ intensity TiNi / • Ti L m -spectrum 4.75 eV 840 845 850 855 860 Fig. 3 NiLj j -r- -emission band spectra from Ni and TiNi . Measured with an OHM-crystal in 4 th order of reflection. Excitation energy: 2.5 keV. The ordinal scale is the same for both spectra. -*-♦ ♦ ♦ ♦ ♦' eV 445 450 Fig. 4 TiL-j- j j -emission band spectra from Ti and TiNi. Measured with an OHM-crystal in 2 nd order of reflection. Excitation energy: 2.5 keV. The ordinat scale is the same for both spectra. Regarding the high energetic peak in the TiLj jj-spectrum from TiNi as the result of cross transitions, the area due to the Ti-d-band in TiNi is significantly less than the expected 50 %. This can be interpreted in terms of a local charge transfer from the Ti- so the Ni-sites. In the case of the NiLjj^-bands (Fig. 3) the area of the Ni-band from TiNi is significantly greater than the half area of the band from pure Ni. From this the same conclusion regarding charge transfer can be drawn. References J. 2 [3] [4] Kallne, E: J. Phys . F. Metal Phys . 4 167 (1974) Kolobova, K.M., Trofimova, V.A. : Proc. Int. Symp. Kiev 1968 (Institute of Metal Physics Academy of Science of the Ukrainian SSR) pp. 172-83 (1969) Nagel, D.J., Papaconstantopoulos , D.A., Mc Caffrey, J.W., Criss, J.W.: In X-ray Spectra and Electronic Structure of Matter pp. 51-80 ed. by A. Faessler and G. Wiech, Munchen (1973) Papaconstantopoulos, D.A., Mc Caffey, J.W., Nagel, D.J.: J. Phys. F 3, L 26 (1973) 234 RESOLUTION-ENHANCED Cu AND Co K* l>2 X-RAY EMISSION SPECTRA OBTAINED BY THE DECONVOLUTION METHOD Jiro KASHIWAKURA, Yohichi GOHSHI and Isao SUZUKI Toshiba Research and Development Center Komukai- Toshiba, Saiwai, Kawasaki, 210 Japan Introduction It is well known that K^, 2 X-ray emission lines of the iron- series first transition elements in chemical compounds show very- broad line width and depart from a single Lorentzian distribution form. An elucidation of these experimental facts has been an objective of a number of theoretical studies. [ 1-3] In an X-ray emission process, two hole states arise, either of which may be studied by X-ray photoemission technique. According to the theory of Weisskopf and Wigner, the lifetime widths of the initial and final hole states should contribute additively to the width of the X-ray emission spectra. Therefore appearance of fine structures due to multiplet splitting in the X-ray emission spectra is hindered by the large lifetime broadening factor. However, as is shown in the previous papers [4,5], application of successive pseudo-deconvolution method taking the lifetime broadening factor as a deconvoluting func- tion to resolution enhancement treatment of the transition element K(Ai2. X-ray spectra makes it possible for fine structures to appear. The amount of fine structures is largely influenced by the number of unpaired 3d electrons, which also depends on the nature of the chemi- cal bond in the compounds. The purpose of the present paper is to show fine structures of the K^, z X-ray emission spectra of copper compounds CuCl and CuF z • 2H2.O, and of cobalt acetyl acetonates Co(AA) 2 and Co(AA) 3 . Experimental The original Kod 2. spectra of copper and cobalt compounds were measured with a prototype TOSHIBA AFV 701 two-crystal X-ray spectrometer [6] . The tungsten target tube was used to produce primary exciting X-rays and was operated at 35KV-25mA. Si (220) crystals were used as analyzer crystals. The scanned 2d regions for the cobalt and cupper compounds are from 55.38 to 55.78 degrees and from 47. 04 to 47. 54 degrees, respectively. Method The pseudo-deconvolution technique, whose mathematical formu- lation is given in the following form in the frequency domain, was used. G^ (W) b G^w) + [G (u) - G« H (w)x L(u)] (1) 235 Here, G (uj), L(cj) and G-^u)) are the Fourier transform of the original spectrum, the Lorentzian distribution function expressing the lifetime broadening shape and the deconvoluted spectrum after n iterations, re- spectively. Though the exact values for the lifetime width of Co and Cu atoms are not known, 1. 7eV and 2. OeV lifetime width values were used for Co and Cu atoms, respectively, which were estimated from the values given in a previous article [7] . In order to prevent the enhancement of the noise component con- tained in the spectra during the deconvolution process, the feedback term of Eq. (1) was smoothed n- 1 times, using smoothing functions determined by the least- squares sliding polynomial method [8] . The frequency characteristics of these smoothing functions depend both on the number of polynomial fitting points and on the degree of polynomi- nals. An appropriate smoothing function was decided upon through deconvolution treatment of the simulation spectra having a Lorentzian contour, which was formed by taking into account the experimental conditions and the measured spectra of the compound having no un- paired d electrons. The smoothing function determined in this way was a quartic 17-point function for the cobalt compounds and a quartic 15- point function for the copper compounds. Results In order to correctly judge the fine structures appearing in the resolution enhanced spectra, it was necessary to calculate the amount of false peaks or ringings caused by the deconvolution process. It was determined from the calculation on simulation spectra, whose results are shown in Table 1. Resolution- enhanced Cu and Co K^( 2-^-ray spectra are shown in Fig. 1 and Fig. 2. According to the Nefedov theory [2] ,when there are no unpaired d electrons, both K^ and Kc*2 spectra are expected to be composed of a single peak. This seems approximately correct in the Co(AA) 3 and CuCl compounds, though the spectra of the latter com- pound show some structure in a lower energy side of the main K^ 2 peak. As the Co(AA) z compound is known to have three unpaired d electrons, the resolution- enhanced Kc*, and K^ spectra are expected to be composed of four and two peaks, respectively. Though it is not clearly separated, the obtained K^ z spectrum seems to consist of three peaks. The high resolution Cu K^ z spectra of CuF 2 • 2H2O rather resemble those of CuCl. As the CuF 2 • 2H 2 compound is known to have one unpaired d electron, its high resolution spectra should give two peaks for the K^ ( and K < v2 spectral lines. However, it is doubtful whether free spin localization on the Cu atom is firmly made. References 1 K. Tsutsumi, J. Phys. Soc. Japan, 14, 1696(1959) 2 V.I. Nefedov, Izv. Akad. Nauk. SSSR, Ser. fiz. , 28, 816(1964) 3 J. Finster, G. Leonhardt and A. Meisel, J.de Phys. , 32, C4, 218 (1971) 236 4 Y. Gohshi and J. Kashiwakura, Physica Fennica, 9, 327, 330 (1974) 5 J. Kashiwakura and Y. Gohshi, Spectrochim. Acta, 30B, 471 (1975) 6 Y. Gohshi, Y. Hukao and K. Hori, Spectrochim. Acta, 27B, 135 (1972) 7 L. G. Parrat, Rev. Mod. Phys. , M» 630 (1959) 8 A. Savitzky and M. J. E. Golay, Anal. Chem. , 36, 1627 (1964) Table 1 Amount of false peaks or ringings Element FWHM of Simula- Deconvolution Percent of maximum false :,!V tion spectra width 5 ' peak height with regard to peak maximum (%) Co 18. channels 14.24 channels Cu 15.7 channels 12. channels 10.4 (8.8) 11.2 (8.9) * Using a one-fourth value of this, deconvolution treatment was carried out four times. ** The entries in the parenthesis are values for noise free spectra. CuFj-2'rlzO CuO. Fig. 1 High resolution Cu K<* ia spectra V^CV'-VrVi A Co(AA) 3 Fig. 2 High resolution Co K^ ( spectra 237 "A NEW COMPUTER CONTROLLED SOFT X - RAY SPEKTROMETER" H.-E. Goldstein, R. Pfliegl, H. Kirchmayr Institute for Experimental Physics Technical University Vienna Karlsplatz 13, A-1040 Vienna /AUSTRIA The activity in the field of Soft X - Ray Physics within the Institute for Experimental Physics is based on experiments performed in the 1950 's by H. Herglotz and coworkers. ("Study of Structural Detail by X-Rays of Wavelength greater than 4 8," Advances in X-Ray Analysis, Vol. 14, Plenum Press 1971) In the last three years a completely new Soft X-Ray Spectrometer has been designed and built, trying to combine the technical advantages of different commercially available components in the field of vacuum, spectrometry, registration and computer science to a unique new appara- tus. Thus we have put great weight on a sophisticated fully automatised vacuum system (Leybold), capable of 10"° Pa in the sample chamber (see fig. 1) in which the facilities to clean the sample surface (sputter gun, scraper) and in which the electron gun are positioned. This elec- tron gun (focus 3x7 mm , max. current 30 mA) is home made and allows a normal incidence of electrons as well as a normal take off of the X-Rays, thus minimising the self-absorption. The spectrometer is based on a Hilger & Watts vacuum spectrometer (E 580) adapted for photoelectric scanning, utilizing a blazed grating (Bausch & Lomb, 600 mm , 3°31' blaze angle) with a radius of 2 m according to the Rowland radius of 1 m. In the spectrometer tank there is a pressure of 10~6 Pa. The entrance slit has the function of separation to the sample chamber. rentrancs slit row! and sample motor channel tron spektrometer tank \ electron gun scraper-* sample chamber fig. 1: scheme of the spectrometer 238 Throughout the wavelength region of 50 to 1000 A we expect to gain a resolution of at least 0,3 eV. The dedection system consists of a channeltron, which is moved along the Rowland circle (Valvo B 312-BL) by means of a step and scan motor (Bautz, Slo Syn). Both are controlled by a CAMAC system in connexion with a process computer (PDP 11/05 Digi- tal Equipment) which control Is the complete experiment and is also responsible for the fully automatic running and supervising of the ex- periment during an extended period up to several days. (See fig. 2) Furthermore the PDP 11/05 allows the control 1 of a large number of parameters, e.g. of the pressure and composition of the residual gas, of the sample temperature, the electron current (from filament to sample) of fluctuations of the excitation, voltages, etc., during the whole ex- perimental time. Therefore a distinct improvement of the reproducibility of the spectra is achieved. The concentration and primary treatment of the results is also done by the process computer PDP 11/05, but for the unfolding of the spectra and for the theoretical analysis there exists a connexion with a large computer, (PDP 11/45) the central computer for the Physics Institutes and also a large CYBER 70 computer. Simul tanously an X-Y plot may be obtained during the run of the experi- ment. First results are presented. channel tron fig. 2: schematic registration diagram 239 Ultra High Resolution Capabilities of A 5M Grating Spectrometer In The 10 to 250 A Region George Andermann, Lars Bergknut, Marri Karras and George Griesehaber Department of Chemistry University of Hawaii Honolulu, Hawaii 96822 Our recently acquired Grating Measurements Ltd. (GML) 5 meter grating spectrograph has a number of interesting features. The standard features include highly precise and accurate "reference" Rowland circle railings as well as carefully aligned primary slit, grating and photographic assemblies. The optical elements may be demounted and reinserted without disturbing the alignment. The range of our spectrograph is from 10 to 250 A. Using a high voltage spark for a source GML personnel obtained in first order a spectral resolution of about .017 eV at 130 eV, i.e., a resolving power of about 7500, thus demonstrating ultra high resolution capability. The standard GML spectrograph has been adapted by our group for molecular electronic structural characterization via x-ray emission studies. In our arrangement the identical spot on a sample may be viewed by the grating optics at any angle of incidence which itself may be varied continuously from to 6°. A simple modular photoelectric attachment has been designed by our group which allows an easy insertion of the photographic detection assembly. The unit is currently under evaluation with respect to resolution and intensity capabilities using conventional photon irradiation of samples. * Prof. Karras spent his sabbatical at the University of Hawaii. His regular address is Department of Electrical Engineering, University of Oulu, Finland. 240 K ABSORPTION SPECTRA OF FLUORINE IN ALKALIHALIDE CRYSTALS S. Kiyono, Y. Hayasi and T. Muranaka Department of Applied Physics, Faculty of Engineering, Tohoku University, Sendai, Japan Recently, several papers were published on measure- ments of soft X-ray spectra with a concave grating grazing incidence vacuum spectrometer. However, as yet there have been only a few works on the spectra studied 10 ^ 30 A region. This is probably because of the complexity in ex- perimental methods and technics. We have designed and constructed a spectrometer oper- ated by new mechanism <> . The center of Rowland circle is not fixed but moves around a fixed X-ray source, and a flow proportional X-ray counter moves also on this moving Rowland circle. Both crystal and detector move with high precision without backlaches (< 1 ym) along the Rowland cir- cle (R = 300 mm) , and accurate spectra can be recorded in the range of 11.43 A ^ 19.68 A. The spectrometer is operated by a simple pantagraph mechanism which provides precise straight motion along bear- ing V-slots and rotation around pivots. Since a guiding circle and gears are not needed, it is comparatively easy to construct a high precision spectrometer. A glancing angle of the analyzing crystal from anticathode is always kept constant and the displacement of the center of the crystal corresponds to the difference in X-ray wavelength. An X-ray tube with tungsten target was used as a source of continuum X-rays. The tube was operated at 1.3 kV, 10 mA. The anticathode voltage was determined by the condi- tion that the 2nd order reflection of the lowest energy X- ray in the spectrum did not appear. The output pulses of the detector were counted for 20 seconds at each point. The intensity transmitted through the substrate was approximate- ly 5000 counts per 20 seconds. In this apparatus the ab- sorption coefficient was determined by observing the differ- ence in transmission of the two samples [1] . The measure- ment of transmission intensity of two samples were carried alternatively. The apparatus ran automatically for about 4.5 hours to obtain a set of data (201 data points). The samples used in this investigation were prepared by vacuum evaporation upon aluminum thin foil (^ 5000 A) at pressures of about 2 x 10" 5 Torr. Two samples of different thicknesses, were prepared at each evaporation. In the case of LiF the thicknesses of the two samples were 600 A and 8000 A, respectively. But the LiF spectra were not so dif- ferent from the one obtained by the difference method of transmission with the thicker sample and the substrate only. Therefore we determined the absorption coefficient of other 241 6.4 A BoF. fit Of ^Vw^^yiA, Fig »«.t>a«kv. (b) €V M ,J ff v i '.'J''*~''l'*!~''T*f ,. ->e 2,6 2.4 2,0 ." ! .2 L0 •>^ v VVs vr S^V^j|AWVl*w-> "SA" 09 Q8

i o >2C Fig. 172 2. 16,4 A Fig 3. 16.4 * samples by the difference in the transmission of one sample and a substrate. Effects of small pinholes in the substrate were negligible compared to the transmission through a sample. At present we have managed to overcome the experi- mental difficulty of measuring absorption coefficient of such a hygroscopic sample as KF by the subsequent evapora- tion of carbon thin film on the sample. Characteristic of the reflection intensity of mica analyser crystal is showed in Fig. 1(a). An anomalous ap- peared near at 710 eV. In Fig. 1(b), the absorption coeffi- cient of aluminum substrate is showed. It is clear that the effect of anomalous reflection and fluctuation of the incident X-ray almost disappeared. We obtained the fine structure of the fluorine K absorption spectra in alkali halide (LiF, NaF) and alkali-earth fluoride (MgF 2 , CaF 2 , SrF 2 , BaF 2 ). In Figs. 2 and 3 these spectra are showed, respectively. In the measured spectra the absorption peak positions and relative intensities were almost consistent with those obtained by Zimkina et. al [2], [1] A. Milgram and M. Paker Givens, Phys . Rev. 125 , 1506 (1962) . [2] T. M. Zimkina and A. S. Vinogradov, Journal de Physique, 32, 278 (1971). 242 A HIGH-RESOLUTION X-RAY SPECTROMETER: DESCRIPTION AND PRELIMINARY EXPERIMENTAL RESULTS Will iam C. Saiider Department of Physics Virginia Military Institute Lexington, Virginia 23669 and Robert E. LaVilla Optical Physics Division National Bureau of Standards Washington, D.C. 20234 The availability of crystals of high perfection has made possible a variety of novel X-ray diffraction devices. For example, a single crystal machined into a form that would allow an X-ray beam to diffract succes- sively from two different crystal planes has been proposed as a monochrom- ator [1]. This monolithic monochromator is equivalent to a conventional X-ray double crystal spectrometer with a fixed inter-crystal dihedral angle. Calculations [1,2] have identified several near coincidences between wavelengths of prominent characteristic X-ray lines and the wavelength transmitted by some silicon and germanium monochromators. These calculations were carried out under the assumption that the beam lies in a plane perpendicular to the line of intersection of the diffrac- ting planes (the so-called plane of dispersion). Mery limited tuning of the characteristic wavelength is possible if the temperature of the monolith is changed. The passband wavelength of such a device can be varied over a much larger range by varying the angle i> between the incident beam and the plane of dispersion. One method of accomplishing this would be to rotate the monolith about an axis that simultaneously lies in the plane of dispersion and is perpendicular to the incident beam. The diffraction process can be visualized by representing it in reciprocal space as a vector tetrahedron defined by the wave vectors of the incident beam (£ ), the beam travelling between the two diffracting planes {ti ) , and the exit beam (£). The base of this tetrahedron, bounded by the reciprocal lattice vectors ftj and ft 2 of the diffracting planes and the vector ft = ft x + ft 2 is the plane of dispersion. From such a geometrical representation, it is straightforward to determine the tuned wavelength of the device: ->- X = (sin a/H) cos ty where a is the angle between "flj and H 2 and <|> is the angle between "£ (and therefore also Ki and t) and the base plane. If one employs this device in an arrangement that allows ty to be varied, then he has a monolithic (tunable) double crystal spectrometer (MDCS) that functions over a narrow wavelength range, but one that can have a large dispersion if tp is suffic- iently small . 243 The high dispersion of the MDCS makes this spectrometer suitable for the study of X-ray line shapes. In order to test this concept, we fabricated an MDCS from dislocation free silicon; the first and second Bragg diffrac- tions were of the type 444 and 111, respectively. By operating this MDCS so that ty lay in the neighborhood of 9°, we were able to use it to examine the Cu Kai ,2 spectrum from a commercial X-ray diffractometer tube. Previ- ous observations [3,4] have shown this spectrum to consist of a pair of smooth but asymmetric lines, but our data show definite evidence of underlying structure. We attribute this structure to electric dipole transitions between the double vacancy states [1 s 1 3d 9 X » 3 D -*■ 2P 5 3d 9 1 » 3 PDF and Is^p 5 X ' 3 P -> 2p 5 3p 5 1 ' 3 SPD]. In order to support this interpretation, we have carried out non-relativistic atomic model calcula- tions for the positions and relative strengths of the multiplet transi- tions. We find that the principal features of the observed spectrum are predicted by the theoretical model. We shall discuss (1) the experimental arrangement of the MDCS, (2) the reasons for the apparently greater resolution of the MDCS as compared to other double crystal spectrometers, and (3) the comparison of the experimental spectrum with the theoretical spectrum predicted by our model to determine the intensities and widths of the multiplet transitions. References 1. R.D. Deslattes, Appl . Phys. Lett. 12, 133 (1968). 2. M. Hart, Rep. Prog. Phys. 34, 435 (1971). 3. For earlier work on the copper Kai, 2 spectrum, see K. Tsutsumi and H. Nakamori , Proceedings of the International Symposium "X-ray Spectra and Electronic Structure of Matter ", (Munchen, 1972), V.l, p. 100 and references therein. 4. P.H. Citrin, P.M. Eisenberger, W.C. Marra, T. Aberg, J. Ultrainen and E. Kallne, Phys. Rev. BIO, 1762 (1974). 244 HOLOGRAPHIC TRANSMISSION GRATINGS: A NEW ANALYSER IN THE X-RAY REGION E.Kallne, Los Alamos Scientific Laboratory, P.O. Box 1663, Los Alamos, N.M. 87545, USA H. W. Schnopper ,L. P. VanSpeybroeck , J . P. Del vai 11 e ,and A. Epstein , Center for Astrophysics, HCO/SAO, Cambridge, Mass. 02138, USA R.Z.Bachrach, XEROX Research Centre, Palo Alto, Calif .94304, USA J.H.Di jkstra and L. J. Lantwaard, Laboratory for Space Research, Utrecht, The Netherlands The low efficiency of high resolution analysers together with the problem of overlapping orders for grating instruments in the soft x-ray region has already limited the variety of experiments which are feasible. Holographic transmission gratings are made using the photolithographic technique previously employed for producing zone plates [1,2]. Although intended primarily for use in a grating spectrometer in the High Energy Astronomical Observatory HEAO-B for extra-solar x-ray astronomical studies the gratings will be available in the near future for laborato- ry applications. The gratings consist of a thin gold wire system support- ed by a fine and a coarse random structure. Since the thin wires are not opaque to x-rays in the region of anomalous dispersion it is of importance to measure the efficiency over a large wavelength region. The gratings can be constructed to achieve first order transmission as large as 25% in the region of anomalous dispersion. The potentially achievable resolution exceeds one part in 10 3 . Future tests are planned to deter- mine the resolution experimentally and extend the efficiency measure- ments to higher energies. Q s 3 \ EXIT MIRROR DETECTOR Fig.l FOCAL PLANE OF M 2 (07m) VODAR GEOMETRY GRAZING INCIDENCE MONOCHROMATOR BEAM DEFLECTOR (15m) FROM SPEAR (6m) Fig.l s performed on Project[3]. earlier [4]. entrance sli of about 70 region of in description hows tb the 4° The gra The ex t S 3 of cm from terest of the e apparatus for the grating tests. The tests were beam line of the Stanford Synchrotron Radiation zing incidence monochromator has been described it mirror M 2 is adjusted for best focus on the 0.5mm a Mullard channel plate array located at a distance the grating. The detector can be scanned over the in the focal plane by a stepping motor. The detailed experimental procedure as well as the theoretical 245 analysis of the data is described elsewhere [5] over the energy range 45-275 eV. 10 190 eV Data were accumulated Several typical data scans are shown in Fig. 2 for two different gratings with 1000 1/mm. a) shows grating #1 , E=95eV in first order and E=190eV in second order. In the labelling of orders the top num- bers refers to 95eV and the lower one to 190 eV x-rays. b) gra- ting #l,190eV, little second order from the monochromator is pre- sent, c)grating #2, E=190eV.The difference in intensity relative to first order for or- ders two through five in c) when compared to the same orders in b) is indicative of a different fractional open grating spacing a/d for each grating. The broad structure of Fig. 2 the zero order is attri- buted to the low quality focus of the exit mirror. A disturbing feature is the presence of second order from the monochromator which contributes to zero order from the test grating. Cal ibration data were taken by scan- ning the monochromator with the test grating in place at zero order and again with the grating removed from the beam. The grating is modeled as an array of wires with rectangular cross sections. The number of counts received in a given order m as a function of photon energy (or wave number q) is calculated from the N-slit inter- ference pattern which is modulated by the single slit diffraction pattern appropriate to the fractional slit opening a/d. The interference between the wave coming through the slit opening and the attenuated, phase-shifted wave coming through the wire is included in the calculation. By using previously measured values of the refractive index in this energy region [6], we have constructed curves of efficiency vs. photon energy based on the above model. Fig. 3 shows the results of these calculations together with the experimental data. It is interesting to notice that the ratios in a) are energy dependent, which may be an indication of non-rectangu- lar wire cross sections. Further development of the model of the grating in terms of a more complex wire cross section is in progress. 5 JL J_ J_ 100 200 300 400 DETECTOR INDEX UNITS 500 600 246 20 0.13 ~ 0.10- 005 0.0 1.5 r ..o o -r- 0.5 o.o 0.15 ^. 0.10- 0.05- 200 Fig. 3 PHOTON ENERGY «V 300 a) shows the relative efficient, cy of orders two through six compared to first order. b) gives the first order to zero order ratio values which can be used to obtain the grating thickness. c) gives the absolute efficiencies for the first or- der. The values in the experi- mental data may be low compa- red to the predicted values because of difficulties in ob- taining absolute normalization to the incident beam. For fu- ture applications it is in- teresting to point out that the effects of the interfe- rence term between waves go- ing through the slit opening and the waves coming through the wire can be used to advan- tage. A proper choice of gra- ting material and thickness will minimize zero- and maxi- mize first order transmission. In addition, even orders are cancelled when the slit ope- ning and wire sizes are equal. This research has been partially supported by NSF grant No.DMR 73- 07692, in cooperation with SLAC and ERDA and by NASA contract NAS 8- 30751. 1. Dijkstra,J.H. , and Lantwaard,L.J. , Optics Comm. ]_5,300 (1975) 2. Dijkstra,J.H. , Space Science Instr. in press (1976) 3. Winick,H., in Vacuum Ultraviolet Radiation Physics, eds. E.E.Koch, R.Haensel and C.Kunz, Pergamon Vieweg, 1974, p. 776 Brown, F.C., Bachrach,R.Z. , Hagstr6'm,S.B.M. , Lien,N., and Pruett,C.H., in Vacuum Ultraviolet Radiation Physics, eds. E.E.Koch, R.Haensel and C.Kunz, Pergamon Vieweg, 1974, p. 785 Schnopper,H.W. , VanSpeybroeck,L.P. , Delvaille,J.P. , Epstein, A. ,Kallne, E.,Bachrach,R.Z. , Dijkstra,J.H. , and Lantwaard,L.J. , Proc. from International Workshop on Synchrotron Radiation Facilities, Quebec, Canada, June 1976 6. Hagemann, H.-J., Gudat,W., and Kunz,C, J .Opt.Soc.Am. 65,742 (1975) 4. 5. 247 VAPOR X-RAY SPECTRA OF RARE-EARTH METALS I. A. Brytov, L.E. Mstibovskaya, N.I. Komyak and L,G. Rabinovitch X-ray Institute 1, Stakhanovtsev, Leningrad, 195112 USSR A vapor-jet source with a supersonic speed of the jet formed by an axi symmetric Laval nozzle has been developed. The source is placed into a vacuum chamber coupled with a PLASMA-type X-ray spectrometer [1], To excite X-rays, a high-perveance three electrode electron gun is used. The supersonic jet flowing out into vacuum has sharp boundaries within which a region of constant density and vapor speed is maintained. Intensity assessment dictated by nozzle parameters, heating tempera- ture of the metal to be analyzed and anode current is made for Dy Ma band excited in atomic vapor. The intensity is calculated to be 10 12 - , v J sec with allowance made for the spectrometer geometry and efficiency the recorded intensity should be 10 u quanta [2]. Ma bands are obtained for Yb, Dy and Eu in vaporous and solid states Ma-band width of atomic Yb is four times less than Ma-band width of Yb in solid state. When passing from metal to atom, Ma line shifts by 1.5 eV towards long wavelengths. The spectrum of atomic Yb reveals an extended short-wavelength structure. Similar differences are observed for Dy and Eu in vaporous and solid states. A problem of mul tiatomic-particle/cluster/generation in a super- sonic jet is discussed. References 1. I. A. Brytov, M.C. Goldenberg, E.A. Oblenskii, N,I. Komyak et al Sbornyk, "Apparatura i metody rentgenovskogo analiza", vypusk XII, 3 SKB RA, Leningrad, Mashinostroenie (1973). 2. I. A. Brytov, L.E. Mstibovskaya, L.G. Rabinovitch, Izvestiya AN SSSR. Seriya phys. 40 (1976). 248 DETERMINATION OF THE DEPTH OF IMPURITY ATOMS IN BULK MATERIAL BY PROTON INDUCED X-RAYS 0. Benka, M. Geretschlager, A. Kropf and H, Paul Institut Fur Physik J. Kepler Universitat Linz A-4045 Linz-Auhof, Austria An attempt is made to determine the target composition by proton induced X-rays in the simple case of one layer of foreign atoms in a known bulk material. For this purpose, the X-ray yield Y(E]l ) is measured at various energies Ej and at energies Ej - e, where e is taken as constant. If the foreign layer is infinitely thin, then its depth x can be deter- mined by comparison to a calibration function f(E) = Y(E)/Y(E-e) measured beforehand on a pure sample of the foreign material, if the stopping power Si of the bulk material is known as a function of energy. If the layer is not infinitely thin, the depth can still be determined by iteration. For proton energies E x of about 0.5 - 1 MeV we found a value e = 0.2 MeV to be most appropriate, if K-lines of elements with Z ^ 30 are to be measured. An error of about 5 keV in the energy loss Ex -E = S^q can be expected. To try the method, Ag-Cu-Ag and Ge-Cu-Ge sandwich targets were measured, with depths up to 1 mg/cm 2 . For comparison, reference targets of all layers were prepared separately and measured by the backscattering technique. The deviations of the individual depth values measured by X-rays from the backscattering results were about 2-3% and hence consis- tent with the expected error. In addition, it was possible to determine the surface density of foreign atoms from the absolute X-ray yield. The measured results can also be compared to yield ratios calculated by means of a computer program. Because of the good elemental discrimination of the X-ray technique, this method can be applied in cases of nearby elements, and can thus give important information additional to that obtainable from backscattering analyses. 249 HIGH RESOLUTION L X-RAY EMISSION SPECTRUM OF ARGON J. Nordgren, H. Agren, C. Nordling and K. Siegbahn, Institute of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden. Abstract . A high resolution L x-ray emission spectrum of gaseous argon has been recorded, using a holographic grating spectrometer at grazing incidence. The spectrum has consider- ably better resolution and contains a great deal more satel- lite lines than our previously reported spectra (1,2). We have mounted a 3m-holographic grating with 24 00 grooves/mm in our spectrometer at a grazing angle of 87°. Electrons of 10 keV were used for excitation and Kodak SC5 plates for de- tection of the x-rays. The holographic grating yields con- siderably higher dispersion than our former ruled grating. In fact, using a 10 ym entrance slit we obtain a width of the spectrometer function which is not greater than 50 meV in this energy region. This width is about one third of the natural width of the main x-ray lines. The energy calibration was made in second order against spark induced spectral lines from highly ionized silicon, aluminum and oxygen. As can be seen in the figure the L line is rather broad, which is in accordance with the high Coster-Kronig decay rate of the L hole. The other two diagram lines, L and L T / are separated by 2.148eV and their width is « 0.19eV. Around 210 eV there is a group of satellite lines of consider- able intensity. Some of these were observed in our previous spectrum and interpreted as L~ ~>-M x-ray transitions to the 3p4 n d( 2 S) states (see table if. The main part of the lines in the spectrum are found on the high energy side of the L TT ,L lines. Some of them can be attributed to transitions promoting an L-hole to the M shell while having a "spectator" hole in the M shell (see table I) . A great deal of the lines are due to transitions in multiply ionized atoms created by Auger cascades from the Is hole state, which the 10 keV impact electrons are likely to pro- duce. This is supported by the observation that some of the lines are much narrower than the main lines and the fact that the fluorescence yield tends to increase with higher degree of ionization. The line energies are listed in table II. As demonstrated in this work, grating spectrometers possess very high capabilities as resolution and energy measurements are concerned. Together with the straightforward dipole selec- tion rules this makes soft x-ray grating spectroscopy a powerful tool for molecular (2) as well as atomic studies. Reference 1/ L. Werme et al. C.R. Acad. Sc . Paris t279 (29 juilett-74). 2/ L. Werme et al. Z. Physik A272, 131-141 (1974). 250 ARGON L X-RAY EMISSION SPECTRUM H MULTIPLY EXCITED INITIAL STATES L-n L in MULTIPLY EXCITED FINAL STATES 10 15 20 25 30 35 U> 45 50 55 60 65 70 75 80 85 90195 j 100 105 110 115 120 [ (111 if "' hy (eV) _L_j j— 300 -r i- 250 !! I ill lill J Li ! 200 40 ~Zb Table I ~50~ 55 60 A (A) Energies and assignments of some of the Ar L x-ray lines Line no Energy (eV) Assignment 4 309.64 84 224.899 85 224.590 86 224.142 87 223.563 88 223.468 90 222.408 91 •■' 222.079 92 221.537 93 221.405 99 219.389 100 217.364 105 212.144 108 210.032 110 209.548 115 207.402 L -M 3 3 L M ( P ) -M M ( P) ii, in 11,111 \ r iiijiiY L M ( P ) -M M ( P) II, III II,III V o ; 111,111] ' L M ( S) -M M ( P) II, III II,III^ ; I II,III V -J L M ( D, ) -M M (~ P) lj ii,iir 1 ii,in v r 1 1 1, in 1 ; L II,III M II,III ( V^II,!!!^ P) L II # III M II # III ( J D 2 ) - M I M II / III ( 1 P) L II,III M II,III ( D 2 ) " M I M II / III ( P) L II" M I ^^III^II.III^^V-VlI,!!^ P) L III- M I L -M ( P) -M M ( P) II, III II,III V ; I II,III V ' L i:[ -3s 2 3p 4 3d( 2 S) L i;EI -3s 2 3p 4 3d( 2 S) L I]; -3s 2 3p 4 4d( 2 S) L II:E -3s 2 3p 4 4d( 2 S) 251 Table II . Argon L x-ray energies. The accuracy is better than 10 meV for the main part of the lines. Line Line Line no Energy (eV) no Energy (eV) no Energy 1 336.20 42 245.039 83 225.233 2 315.67 43 244.648 84 224.899 3 313.06 44 244.408 85 224.590 4 309.64 45 244.250 86 224.142 5 298.43 46 243.948 87 223.563 6 294.77 47 243.682 88 223.468 7 288.10 48 243.021 89 223.193 8 280.29 49 242.760 90 222.408 9 278.43 50 242.407 91 222.079 10 272.55 51 242.118 92 221.537 11 270.922 52 241.975 93 221.405 12 270 .135 53 241.486 94 221.276 13 269.586 54 240.766 95 221.111 14 268.206 55 240.058 96 220.968 15 266.371 56 239.811 97 220.452 16 265.667 57 238.940 98 219.976 17 264.415 58 238.584 99 219.389 18 264.143 59 237.883 100 217 .364 19 263.563 60 235.152 101 214.818 20 262.752 61 234.849 ' ■•■ 102 214.358 21 262.509 62 234.689 103 212.647 22 261.449 63 234.394 104 212.464 23 260.272 64 234.034 105 212.144 24 259.604 65 233.158 106 211.232 25 258.729 66 232.939 107 210.556 26 257.473 67 232.702 108 210.032 27 257.214 68 232.517 109 209.804 28 255.944 69 232.162 110 209.548 29 255.514 70 231.972 111 208.967 30 254.345 71 231.071 112 208.852 31 253.308 72 230.175 113 208.111 32 252.048 73 229.561 114 207.937 33 251.674 74 228.904 115 207.402 34 249.629 75 228.599 116 205.952 35 249.300 76 227.946 117 205.788 36 247.273 77 227.474 118 205.198 37 246.999 78 227.309 119 204.695 38 246.814 79 227.005 120 201.815 39 246.579 80 226.052 121 200.707 40 245.572 81 225.871 122 198.435 41 245.283 82 225.579 123 194.565 252 THE USE OF LONG WAVELENGTHS FOR LOW"ANGLE SCATTERING Yasuo SIOTA and Mamoru YOKOTA Research Institute for Science Education, Miyagi Univ. of Education, Aramaki, Aoba, Sendai, Japan This report concerns with both our present work of low- angle X-ray scattering with long wavelengths and future use of synchrotron radiation as a very intense source of light for low- angle scattering with long wavelengths. Several important advantages are gained. First, the effects of multiple scattering and refractions become small for long wavelengths. Second, owing to the large angle of scattering, an accurate determination of the central portion of the scat- tering pattern is possible and an important information about large particles is obtained. Third, low-angle scattering due to double Bragg reflections (,l) could be removed by using long wavelengths. Finally, the use of long wavelengths sup- presses the continuous background radiation against the characteristic radiation proportional to the atomic number of the target in an X-ray tube. Few workers (^2), (3) have tried investigations in a long wave length region. Perhaps this is due to the necessity of hard working in a vacuum, low inten- sity of scattered X-ray and high absorption by the sample. We have studied the low-angle X-ray scattering by poly- styrene latex spherical particles and succeeded in obtaining several well-resolved peaks of higher orders. Close agreement between observed and calculated curves was obtaind. 253 The source was an Al or C tube of Pierce type. For record- ing, a Kodak SWR-plate or a proportional counter was used. The counter was followed by a pulse height discriminator in connection with automatic scanning and recording devices. A speical attention was paid for sample preparation. Figs.l and 2 represent observed and slit-corrected scat- tering curves ^4) of polystyrene latex of diameter 0.234 u with Al-K radiation and of l.OlLawith C-K radiation, re- spectively. The numbers labelled by K=2,3,4 correspond to the orders of the peak positions of the intensity maxima calcu- lated in the Rayleigh-Gans theory for a uniform sphere. An 12 10 at o E 8 m z UJ I— z - I, 1 V I I I | I I I I | t 1 POLYSTYRENE LATEX 0.234^ Al-K \ k=2 1 1 - \ 1 '•■ \ 3 '• \ 1 - V 1 s OBSERVED - CORRECTED •t. 1 1 1 1 1 1 L .J L.. L. J 1 1 12 10 8 1 z Ul V.--'' \ 1 ■ ■ ■ ■ 1 ■ ■ ■ POLYSTYRENE LATEX i 011 ^ C-K ■ M k=2 - \ v •. \ 3 \\ I - 4 I - \>« I V. 5 W - * c c B5ERVED ORRECTED V ,,,, 1 1 1 _ .01 .1 5 1 1.5 2 S 2 (xlCT** 4 ) 01 05 .1 .2 3 A .6 8 1.0 12 S 2 (xict 5 a- 2 ) 40 60 20 (min ) 40 60 80 2e(min ) 20 Fig.l. Curves of polystyrene latex of diameter 0.234/xwith latex of diameter l.Oll/xwith 20 Fig. 2. Curves of polystyrene Al-K radiation C-K radiation. 254 additional peak A is caused by interparticle interference C5), which was clearly observed by using long wave-lengths. There is a limit in sampling times, in spite of a high power X-ray tube and a high sensitive detector. We are now planning to use synchrotron radiation from a 1.3 Bev electron synchrotron at the .Institute for Nuclear Study, University of Tokyo, for the low- angle scattering with long wavelengths in o a range of 50~-'100 A. The application of synchrotron radia- tion to low-angle scattering has been made at DESY (6). A grazing- incidence spectrograph with high resolution is used. Experiment at any desirable wavelengths is possible by moving a slit on the Rowland circle continuously. First, we will investigate the same sample as studied by our X-ray tube. Details of experimental arrangements and technical considerations will be reported in the conference. The authors appreciate ES-Machine group and INS-SOR group at the Institute for Nuclear Study, University of Tokyo, for their assistance. They are also greatly indebted to the In- stitute for Solid State Physics, University of Tokyo. References (1) A.Franks and K.Thomas, Proc. Phys. Soc. B. 11, 861 (1958). (2) K.L.Yudowitch, J.App.Phys. 2_0_, 174 (1949). (3) B.Henke and J.W.M. DuMond, Phys. Rev. 8£, 1300 (1953). (4) J.Soller and J.Baldrian, J.App.Cryst. 7, 398 (1974). (5) U.Bonse and M.Hart, Z.Phys. 189 , 151 (1966). (6) J.B.Leigh and G.Rosenbaum, J.App.Cryst. 1_, 117 (1974). 255 X-RAY DETECTION FOR MEASUREMENT OF INNER SHELL IONIZATION BY RELATIVISTIC ELECTRON IMPACT* H. Genz, D.H.H. Hoffmann, W. Low and A. Richter Institut fur Kernphysik, TH Darmstadt, 61 Darmstadt, Germany The measurement of the absolute yield of characteristic x rays emitted from a target bombarded by particles has become one of the major techniques in the determination of inner shell ionization [l,2]. Electron induced ionization has predominantly been restricted to K-shell ionization at nonrelativistic and ultra relativistic energies [3]. The lack of data in the intermediate range has now been overcome by measuring the K and L x-ray production cross section between 15 and 70 MeV [4-6]. The present work is motivated by this lack of data, by the lack of fully relativistic theories and by the speculation of a possible scaling behaviour of the cross section. In the present work we report on the first L x-ray production cross section for energies between 15 and 70 MeV with electrons from the Darmstadt linear accelerator (DALINAC) . The recent considerable improvements of its beam quality and transport system [7] enable x-ray detection at low background. The electron beam impinged on thin self supporting targets of Au and Bi (- 200yg/cm ) inside a scattering chamber and was then collected by a magnetically suppressive Faraday cup located about 5.3 m downstream. The produced x rays were detected with a Si (Li) detector. By means of a 20um Al foil placed between tar- get and detector M-shell x rays were hindered from reaching the detec- tor. For the measurement of the angular distribution of the emitted photons the detector can be placed under 14 angles from 45 to 165 . In order to avoid pile-up of two events due to the detection of two x rays within a single machine pulse of 6ys duration every second photon detected within this time interval was electronically rejected. The beam current was kept at about 0.6 nA (i.e. 3x10 electrons per linac pulse) corresponding to about 0.1 detected event per machine pulse. A typical L-shell x-ray spectrum obtained by bombarding a Bi target with 60 MeV electrons is shown in fig. 1. The spectrum clearly exhibits a low and flat background. The solid line represents a fit of several asymmetric Gaussians to the data points after subtraction of the background. The total cross section for L-shell ionization is determined from C7 m = I N. /[n tw e(Aft/4TT)] f (1) TOT 11 ° L where N. is the number of i-subshell photons corrected for absorption in the target, absorber and window of the scattering chamber, N the . Oo — number of incident electrons, t the target thickness in atoms/cm , (jO L 1 Supported in part by Deutsche Forschungsgemeinschaft 256 4000 0) c c o £Z U 1/1 ? 2000 o u L °l 8 10 Bi X-Ray Spectrum E o =60MeV 10 12 14 Energy / KeV Fig. 1 L-shell x-ray spectrum observed with a Si (Li) detector by bombarding a Bi target with electrons of E = 60 MeV o the average L-shell fluorescence yield [8], e the detector efficiency and A£2 the solid angle subtended by the detector. The first results on the L-shell ionization cross section for Bi are shown in fig. 2 to- gether with the values by Park et al. [9] at much lower and by Middle- man et al. [lo] at much higher electron energies. The solid line repre- sents a theoretical prediction by Gryzinski [ll]. It is interesting to note that the cross sections do not scale when plotted in the form suggested by this theory, i.e. a, TOT versus E /I, I being the aver- I I L L-SHELL IONIZATION CROSS SECTION • PRESENT DATA o MIDDLEMAN o o o o 1000 z — a PARK # - —GRYZINSKI CALC. • *• % 500 CO - < |2 Bi I *\9 100 I I I I 10 100 1000 o n A _ 1 1 SCALING BEHAVIOUR OF L-SHELL IONIZATION CROSS SECTION - ■ ^k — " — * « »Au ( 1 1 'Bi E c /MeV Fig. 2 L-shell ionization cross sec- tion for Bi with theoretical prediction [ll] V) 10 10 9 10 E„/l (MeV) Fig. 3 L-shell ionization cross section in the 01 vs E /I represen- tation 257 age L-shell ionization energy, but they do scale in the form O • I versus E /I. They then exhibit the same "scaling behaviour" (fig. 3) as observed for the K-shell [4]. The L /L ratio of x rays from Bi and Au has been measured at E = 60 Mev. The result for the case of Bi is plotted in fig. 4 to- gether with the values obtained from ref. [<9] and [lo]. There is clear- ly an increase of the ratio by about 14% over the considered energy region. This might be explained qualitatively by the fact that L x-rays result predominantly from 3p-2s and L from 3d-2p transitions. Because of their spatial extension 3d electrons are stripped off pre- ferably to 3p with increasing bombarding energies and then L R /L should also increase [12], 0.9 ? 0.8 _ Bi CO. 0.7 0.6 x Park et al. • Middleman et al. o Darmstadt 10 100 1000 E^MeV 28 20 « 28 20 12jr- ■c L /l_ e Intensity Ratio MeV E = 60 MeV - o Au • Bi Scofield -,U I f- 90 180 Photon Detection Angle / Degrees Fig. 4 L R / L ratio versus bombarding energy Fig. 5 Angular distri- bution of the V L £ ratio Figure 5 displays a preliminary angular distribution of the L /Lp ratio as obtained at four different angles together with a re- lativistic Hartree-Fock model prediction [13]. This prediction assumes isotropy of the ratio. The experimental angular distribution is in- deed isotropic within 8%, the uncertainty still being large at pre- sent. Table 1 lists the measured L /L p ratios for Au using different experimental methods of creating L-shell vacancies as well as the cal- culations by Scofield. Apart from the values of the measurement of ref. [16] there is an overall agreement between all ratios. Finally, the spectra have been investigated for possible energy shifts of x-ray lines. Therefore the peak positions in the spectra have been compared with a careful calibration using standard low energy x-ray sources. In the case of Ag for example we detected an average energy shift for K lines of about 150 eV. This might reflect 258 effects of multiple ionization seen also in the production of x rays by heavier particles . TABLE I L /L n ratios of Au a I X-ray fluorescence [14] Proton bombardment [15] Electron Theory bombardment 25 keV 60 MeV [16] [13] 18.72 ± 1.2 19.7 ± 1.0 25.2513.0 19.9 ±1.1 19.8 We should like to thank Drs. Folkmann and Liesen from GSI for the kind loan of the Si (Li) detector. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] C.J. Powell, Rev. Mod. Phys. 48 (1976) 33 D.H. Madison and E. Merzbacher, in Atomic Inner-Shell Processes, B. Crasemann, ed. , Acad. Press, Inc., New York (1975), p. 11 Proc. Second Int. Conf. on Inner Shell Ionization Phen., Freiburg 1976, ed. R. Brenn and W. Mehlhorn, Fakultat fur Physik, Universitat Freiburg H. Genz, D.H.H. Hoffmann, A. Richter and E. Spamer, ref. [3] Abstracts p. 229 S. Morita, ref. [3] D.H. Madison, ref. [3] H. Miska, H.D. Graf, A. Richter, R. Schneider, D. Schiill, E. Spamer, H. Theissen and 0. Titze, Phys. Lett. 58B (1975) 155 W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark, CD. Swift, R.E. Price and P.V. Rao, Rev. Mod. Phys. 44_ (1972)716 Y.K. Park, M.T. Smith and W. Scholz , Phys. Rev. A12 (1975) 1358 L.M. Middleman, R.L. Ford and R. Hofstadter, Phys. Rev. A2 (1970) 1429 M. Gryzinski, Phys. Rev. A138 (1965) 336 B. Crasemann, private communication J.H. Scofield, Phys. Rev. A10 (1974) 1507 J.H. McCrary, L.V. Singmann, L.H. Ziegler, L.O. Loomey, CM. Edmonds and C.E. Harris, Phys. Rev. A5_ (1972) 1587 J.R. Chen, J.D. Reber, D.J. Ellis and T.E. Miller, Phys. Rev. A13 (1976) 941 S.I. Salem, D.C Clark and R.T. Tsutsui, Phys. Rev. A5 (1972) 2390 259 A NEW TYPE OF KOSSEL-BORRMANN RADIATION FROM GERMANIUM CRYSTAL* K. Das Gupta Department of Physics and Engineering Physics Texas Tech University, Lubbock, Texas 79409 Two regular Kossel lines have been observed in germanium crystal with wavelengths of 1.134 and 1.246 A due to germanium KBi and Ka 1>2 radiation. Two additional Kossel-type lines on the low energy side of germanium Ka 1>2 with wavelengths 1.391 and 1.544 A have also been ob- served. The energy of these newly observed lines correspond to the kinetic energies of the Auger electrons of germanium involving K and L levels. The newly observed radiation is characterized by the following properties: (i) a non-linear rise in intensity with pumping, (ii) anoma- lous mass absorption coefficient in aluminum and silicon so far studied, (iii) preliminary results reveal an unusually narrow fundamental width of the newly observed lines. Kossel cones of semi-vertical angle a are generated in good single crystals due to internal Bragg interference of characteristic x-ray lines of the atoms of the crystal by sets of lattice planes (hk£) given by the equation 2cosa=X | r (hk£) | . The axis of the Kossel cone is the direction of the reciprocal lattice vector r(hk£). Borrmann effect is characterized by an anomalous transmission, that is a low mass absorp- tion coefficient y/p , when a collimated beam of x-rays is set at the Bragg angle for a set of lattice planes of the crystal. In studying Kossel lines from germanium single crystal, the mass absorption coef- ficients y/p for germanium K3i and Kcti , 2 radiation of wavelengths 1.129 and 1.256 A respectively were expected to be absorbed by the germanium crystal of thickness 1.2 mm. I have observed strong Kossel lines K^ and K 2 , Fig. 1 (a), (b) , and (c) , due to germanium 1.129 and 1.256 A in crystals of thicknesses 1.2-1.3 mm. The crystal is cut parallel to (111) planes and is excited by x-rays from silver, molybdenum, copper, and co- balt target radiation in different sets of experiments. Kossel lines Kj and K 2 were observed with target radiation at 20, 25, 30, 35, and 40 keV and tube currents between 30-10 mA. Because of the high penetrability of Kossel lines Kj and K 2 through thick germanium crystal, these lines have been designated as Kossel -Borrmann lines. In addition to the lines Ki and K 2 , I have observed two more Kossel-Borrmann type lines Aj and A^ Fig. 1 (a), (b) , and (c) , of longer wavelengths than germanium Ka lines. The lines Ai and A 2 have been observed in different sets of experiments when germanium crystal was irradiated by the target radiation from sil- ver, molybdenum, copper, and cobalt operated at 20, 25, 30, 35, and 40 keV and tube currents 30-10 mA. Some of these preliminary results using copper target radiation as the exciting source have been reported. [1] It has been established by a series of experiments with more than 20 different pieces of germanium crystals that the new type of Kossel- Borrmann lines Ai and A 2 are generated in the germanium crystal and not at the target of the x-ray tube that excites the crystal. We have mea- sured the increase in intensity of the unusually strong portion of Aj and A 2 lines at the terminal with increase of the x-ray tube current from molybdenum target that excites the germanium crystal radiation. We have observed a non-linear rise in intensity of Ai and A 2 with increase 260 TARGET A l G£ 4 h Fig. 1(a) Silver Target 30 kV, 20 mA 15 hrs. exposure Fig. 1(b) Copper Target 35 kV, 10 mA 20 hrs. exposure MOLYBDENUM TARGET CE HI Fig. 1(c) Moly Target 35 kV, 15 mA 10 hrs. exposure Fig. 1(d) Moly Target with Nickel Filter 35 kV, 15 mA 15 hrs. exposure Fig. 1(a) » (b) , and (c) : Kossel-Borrmann lines K^ , K 2 and Kossel-Borr- mann type lines A^ , A 2 from Ge {220} planes. The collimated beam of x-rays from the target strikes normally the Ge crystal of thickness 1.2 mm cut parallel to (111) planes. Fig. 1 (d) : Kossel-Borrmann lines Kj , K 2 , and Kossel-Borrmann type lines Aj are absorbed with a 0.015 mm thick nickel filter. 261 of the tube current. We have checked at the same time that the inten- sity of Ka radiation from molybdenum monochromatised with a silicon crystal increases linearly with increase of the tube current. Prelim- inary results with a multi-channel analyzer reveal an unusual narrowing of Aj and A 2 , similar to the narrowing of lines reported earlier by Das Gupta. [2] In a series of experiments, I have studied, in collaboration with Peter Seibt and James White, the mass absorption coefficients of Aj and A2 with aluminum and silicon filters. The values of y/p are suprisingly low by a factor of 40-50. This work is currently being continued with an energy sensitive detector and generating Aj and A 2 at various po- tentials of the x-ray tube that excites germanium crystal radiation. I have reasons to believe that Auger electrons from germanium involving K and 1.2,3 levels and K and L^ levies could generate Kossel type elec- tron cones in germanium crystal with the same set of {220} lattice planes. In earlier papers [3,4] I have tried to explain the origin of low energy satellites in soft x-ray band spectra from solids to be due to a radiative Auger-Raman process in crystals. An understanding of A^ and A 2 lines as a stimulated Kossel-Borrmann radiative Auger-Raman pro- cess will be reported in a separate article. *This work has been supported by the Robert A. Welch Foundation and the Air Force Office of Scientific Research. [1] K. Das Gupta, J. Appl. Phy. , 47, 2765, (1976). [2] K. Das Gupta, Phys. Letters, 46A, 179, (1973). K. Das Gupta, Colloquium Spectroscopicum Internationale XVII, II, 482, (1973). [3] K. Das Gupta, Nature, 166, 563, (1950). [4] K. Das Gupta, Nature, 167, 313, (1951). 262 THEORY AND MEASUREMENT OF X-RAY DIFFRACTION FROM SEVERAL ACID PHTHALATES D. M. Barrus, R. L. Blake, and A. J. Burek* University of California, Los Alamos Scientific Laboratory P. 0. Box 1663, MS 436 Los Alamos, New Mexico 87545 Acid phthalate crystals have been widely used in the laboratory and cosmic x-ray spectroscopy because of their large interplanar spac- ings, reasonable diffraction properties, and availability in large sizes with good quality. Liefeld (1) evaluated KAP by double spectrometer measurements, after which this crystal was widely used. Burek, Barrus, and Blake (2) - prompted by concern that variations among samples could limit the validity of higher precision measurements - studied several samples of KAP from several sources and under a variety of experimental conditions. They found only minor variations among samples. For prac- tical purposes all KAP without obvious visible flaws could be considered the same. Nevertheless we were keenly aware of the need for some analyt- ical guidelines for the evaluation of additional crystals, especially for long wavelength x-ray spectroscopy where we were unable to find any application of diffraction theory in the literature. Elimination of this difficiency was undertaken (2,3) with results that have been grat- ifying not only for KAP but also for several other crystals of impor- tance in soft x-ray studies. The basic theory of x-ray diffraction in crystals has been avail- able for a long time (4) . Successful application to long wavelengths (5"<-25 A) is critically dependent upon knowledge of the ultrasoft x-ray absorption coefficients for atoms in the crystal structure , especially near the edge frequencies because anomalous dispersion dominates the dif- fraction properties. We have now extended both the calculations and measurements to several additional crystals. In this report results will be given for the most readily available acid phthalates and some interesting properties will be noted. Calculations far more extensive than shown here are available on request. The table summarizes the calculated and average-measured values of the single crystal coefficient of reflection, R c , at characteristic line wavelengths. All calculated values are from Darwin-Prins theory. For each order of reflection the upper number is the calculated R and the bottom number is the measured value, with error estimate replacing the power of 10 designation. Quoted errors are estimates of upper bounds to systematic effects - statistical errors being neglibible. Individual specimens can vary outside these limits due to poor production or han- dling procedures. KAP shows excellent agreement over a wide wavelength range and three orders of reflection. When reflection coefficients are small the calculated values are very sensitive to small errors in atomic locations and measurements are sensitive to systematic errors; hence, agreement within a factor two should be considered good when R c < 10 RAP shows good agreement in three orders of A1(K) but the measured values fall below calculated values at longer wavelengths. This probably means the Rb absorption coefficients at long wavelengths are larger than our input values. We believe this same factor is responsible for the excess of calculated values for T&AP, the effect in this case reaching all the 263 way down to 8 A. Uncertainties inherent in our present knowledge of anomalous dispersion effects combined with uncertain absorption coeffi- cients in Rb and Til are sufficient to account for any discrepancy pres- ently found between calculated and measured values. Note the good agree- ment between calculated and measured values from KAP, NaAP, and NH^AP in three orders of reflection. When displayed graphically against complete calculated curves the measurements show remarkably good agreement. However, it has long been known that rocking curve profiles and peak reflection coefficients pro- vide far more sensitive tests of the quality of crystals for spectros- copy. Unfortunately our laboratory facilities do not include a double crystal instrument required for such measurements. In order to achieve at least a qualitative evaluation of acid phthalate rocking curve widths we employed the Ne ls-*3p absorption line technique suggested by Liefeld (5) . The figure shows this sharp-line profile measured with nominal one arc minute FWHM collimation of the Ni L(3 line passed through a Ne absorp- tion cell and diffracted from KAP, RAP, and T£AP. Detailed comparison shows KAP resolving power very slightly superior to RAP as predicted by calculations. T#AP has such poor resolving power that the line is hard- ly distinguishable, also in agreement with theory. NaAP and NH AP are not suited to this technique. Some conclusions to be drawn from this work are as follows. RAP, because it has twice the reflectivity of KAP and nearly equal resolving power, should replace KAP as a standard for general spectroscopy. For quantitative analysis where reflectivity is most important T&AP is far superior at all useful wavelengths. Both RAP and T&AP have good ratios of first to all higher order reflections. NH^AP has the interesting property that the second order R c exceeds the first order by a factor two or more from 15 to 60 degrees of theta angle, and above 68 degrees. It is particularly useful for high dispersion measurements around 12 A. We have been able to resolve the solar NeX resonance doublet with this crystal in a rocket experiment. References 1. Liefeld, R. J. Hanzely, S., Kirby, T. B. and Mott, D. 1970, Advances in X-Ray Analysis, 1_3, 373 (results were general knowl- edge as early as 1963) . 2. Burek, A. J., Barrus, D. M. and Blake, R. L. 1974, Ap . J., 191 , 533. 3. Burek, A. J. 1976, Space Science Instrumentation, to be published 4. Batterman, B. W. and Cole, H. 1964, Rev. Mod. Phys . , 36^, 681. 5. Liefeld, R. J. 1965, Appl. Phys. Ltrs, £, 267. *Work performed under the auspices of the U.S. Energy Research and Development Administration. 264 CALCULATED AND MEASURED R OF ACID PHTHALATE CRYSTALS c WAVE- KAP RbAP T£AP NaAP NHi^AP ORDER LENGTH (A) (001) (001) (001) (002) (002) n 1.54 3. 14x10 " 5 6. 19x10 ~ 5 1. 20x10 "" 2.76xl0" 5 £ i.59xl0" 6 1 3.59±5% 1.9 2x10 " 6 9.97xl0" 6 3.57xl0" 6 1.36xl0" 6 3.67xl0" 5 2 1.88±5% 3.15xl0" 7 7.85xl0" 6 2.08xl0" 5 2.16xl0" 6 1.92xl0" 6 3 8.34 7.93xl0" 5 1.04X10" 1 * 2.56x10"" 6.15xl0" 5 1.12xl0" 5 1 8.45±2% 1.10±2% 2.79±2% 6.21±2% 1.12+2% 3.46xl0" 6 3. 9 7x10 " 7 3.45xl0" 5 3.17xl0" 6 2.63xl0" 5 2 3.27+4% 2.94±4% 3.59±4% 3.39±4% 2.58±4% 2.40xl0" 8 7.87xl0" 6 1.15x10"" 3.42xl0" 6 6.26xl0" 6 3 4.41±6% 4.83±6% .90.6±6% 5.75±6% 7.35±6% 14.6 5.77xl0 -5 1. 16x10 _lf 2.39x10"" 3.30xl0" 5 6.09xl0" 5 1 5.49±5% 18.3 5.04xl0" 5 l.llxlO" 1 * 2.57x10"" 2.53xl0" 5 4.86xl0" 6 1 5.21±2% .896±2% 2.00±2% 2.67±2% 5.20±3% 21.7 5.35xl0" 5 1.34x10"" 3.65x10"" 1.90xl0" 5 9.12xl0" 6 1 5.61±10% 1.43xl0" 5 23.6 1.21x10"" 5.23x10"" 2.77xl0" 5 6.02xl0" 5 1 1.78±4% .733±4% 2.81±4% 2.94±4% 6.66±4% 24.3 2.87xl0" 5 2.1 3x10 ~" 7.63x10-" l.lOxlO" 5 ' : 3. 36x10 " 5 1 2.85±15% ————— — __ — — CO N CO odd If) Tf d d ro CJ — odd i i "" " i i i 1 "" 1 ' 1 -w in ro 2; Q. fO 1 ■» • ^/ < I a. C i - ! ,Sl 1 r i i \ i 1 \ ° ) " / \ ill 1 1 O rO in CJ _ 2; ) 1 CD _J UJ < c d cx> in d d =r(2 arcsin nA/2d + arcsin - ||l-(nA/2d) - 267 where d is the lattice const In practice, this expression tion for a small source (abo the crystal. When using mica tion order n can have relati more accurate measurements i sideration the refraction in This is done in a convenient lattice constant d n for each with calibration of the spec all wavelengths to the corre ord er f "A = nTV d eq In Fig. 4 the dispersion for shown • ant and will g ut 1 mm one ca vely hi t is ne dex of way by order tra it spondin n order of diffraction, ive a very good approxima- ) situated about 1 m from n expect that the diffrac- gh numbers. Therefore, for cessary to take into con- the crystal for X-rays. calculating a corrected n of diffraction. Working is convenient to reduce g equivalent of first i/* n the first order diffraction is Spectra . In Pig. 5 two spectra recorded by the spectrograph are shown • One of these represents ordinary or continuous X- rays and the other flash X-rays from a Cu electrode. As seen, the lines from the FXR discharge are broder than those from ordinary X-ray tubes. - 5 - 10 - 15 — I — 0.05 1 — - 0.06 1 — 0.07 1 — 0.08 eq A d> /d-fc A eq' mm -1 Fig. 4 . Theoretical first order dispersion versus wavelength Fig. 5 * Cu-spectra. Continuous (upper) and flash X-ray source. (l) M. de Broglie and F.A. Lindemann, Compt. Rend. 158 , 944 1914. 268 X-RAY SPECTROSCOPIC INVESTIGATION OF ENERGY BANDS FINE STRUCTURE AND THE INTERPRETATION OF CONDUCTIVITY CHARACTER OF PHOSPHOROUS COMPOUNDS OF VARIOUS CHEMICAL BOND TYPES A.N. Gusatinski, M.A. Blokhin, G,I. Alperovich, M,A. Bunin, I, A. Topol Department of Solid State Physics, Rostov State University 344006 Rostov -on-the-Don, USSR In [1] it was shown that the energy distribution of local partial electron states density of p- and s-symmetry (with d-admixture) for the third period elements is well reproduced by X-ray K- and L2 3-spectra. Fluorescent K-bands, K-absorption and L2 , 3-emission spectra of phos- phorous in semiconductor compounds of types A^B' and aHbIVcV 2 and in the 3d-transition metal monophosphides had been studied, The Ti M2,3~ emission band was investigated in the TiP-compound. The phosphorous K- and L2 3-spectra were matched to a common energy scale with the aid of the PKa-line for the same compounds. The P K-spectra were corrected for the inner energy level width using a method, which ensures small boundary distortions. As an example for the A B compounds the results of X-ray spectral study of InP (Fig, la and b) are compared with the calculated N(E) distri- bution (Fig. Id and e) and with the X-ray photoelectron spectra (Fig. lc) , Such a comparison was also made for GaP , The positions and related ampli- tudes of individual elements of the curves in the Fig. lb,c,e are similar to each other, F- and G-maxima of the absorption spectra (Fig. la) and of the N(E) curve (Fig, le) are in accordance also. All this shows that for polyhedra of phosphorous atoms the curve of local states density distribu- tion reproduces well such a distribution for the whole crystal, This can be explained as the bonds in such materials are mainly of a covalent type and that both types of atoms are mutually identical surrounded with atoms of the other type. As can be seen from Fig, la the 1-st subband (A) con- tains mainly s-states, the 2-d, 3-d and 4-th subbands (B,C,D) - mainly p- states but with some s-states admixture. The comparison of various emission spectra series for various compo- nents of indium phosphide justifies an assumption of d-states admixture in polyhedra containing the indium atoms. The MO calculation confirms this assumption. For ZnGeP2 (an isoelectronic analog of GaP) a comparison of phospho- rous K-spectra with the calculated N(E) curve shows a correspondence of separate elements of these curves (Fig, 2), III V Phosphorous K emission and absorption spectra in A B compounds corrected for the inner level width allows us to determine the energy gap AE, which (in the accuracy limits for measuring this quantity) is equal to the forbidden band width Eg for these compounds as determined by other physical methods [1] . As appears from the above there is a sufficiently large p-state density both near the top of the valence band and near the bottom of the conductivity band, Thus, the combined effect of several physical causes leading to a difference between AE and Eg in this special case is not greater than the error in the AE determination, The main structure features of the investigated X-ray emission and absorption spectra of phosphorous in monophosphides of Sc , Ti, Cr and Mn are similar in all these compounds. As an example the emission K-bands 269 %M A B CD FG a tf 4 Bcp -jo 10 E ; eV Fig. 1. InP: a) X-ray K (thick line) and L2 3 (thin line) phosphorous spectra, b) Local states density in polyhedra of phosphorous atoms, derived from the X-ray spectra. c) X-ray photoelectron spectrum of the valence band [3] . d) Calculated N(E) curve. JL e) Calculated N(E) curve, convolu- ted with a Lorentz curve of 1.2 eV width. and the absorption K-spectra of phospho- rous in TiP and MnP are shown in Fig, 3, The corrected spectra slightly overlap (^0.4 eV) each other, but this overlap- ping is within the limit of experimental errors. Therefore, we can conclude that these compounds must have a metallic conductivity. According to [4] TiP does have a metallic conductivity. 270 E,eV Fig, 2. ZnGeP 2 : X-ray PK- spectra (a) , valence band states density after convolution with a gaussian [2] (b) . The emission K- and L 2 3- bands of phosphorous and the M2 s 3~bands of titanium in TiP are shown in Fig. 4. In these spectra one can see a display of three main energy subbands A, C (with a shoulder B) and D. The intensity ratios of these subbands are different for the spectra of various series and components , The A and C subbands in the considered spectra have a genetic connection to the s- and p-states of the phosphorous atoms, respectively, and the D subbands - with the d-state of titanium (Fig. 4). The s-like subband A is not reproduced in ? he phospho- rous K-spectra. Apparently an admixture of p-statas of phos- phorous is practically absent in this region, The appearance of a high energy shoulder in the K-emission spectra of phospho- rous, which is prominent in ~J Fig. 3. Fluorescent PK-bands in MnP (a) and TiP (b) ; experimental (thick lines) and corrected for the inner level width (thin lines) , phosphorous compounds with transition elements, is connected with an admix- ture of a fraction of phosphorous p-states to the crystal valence band, which contains mainly d-states of the transition metal. In the L2 3-spectra of phosphorous the faint peak D corre- sponds to this shoulder. As can be seen on the K- and L2 , 3-spectra of the phosphides of Sc, Cr, Ti and Mn the intensity of the D structure features increases with the atomic number of the transition element. In the titanium emission M2 3-spectrum the main peak corresponds to the subband D, Thus, the results of X-ray inves- tigations can give important information on the energy band structure and on the electric conductivity type for compounds of the considered classes. The authors express their deep gratitude to N.A, Gurunova, A.S. Borshchevski, V.D. Prochukhan, V.I, Torbov and V,I. Chukalin for the compounds they had synthesized and placed at our disposal for this investigation, and to L.M, Monastirski 271 mo mo e,»v w 120 ISO E.eV E.eV Fig. 4. Emission bands of TiP: a) PK-band. b) PL 2 3-band. c) T1M2 3-band. and I,G. Shweizer for their aid in the experimental part of this work. References 1. A.N, Gusatinski, in "X-ray Spectra and Electron Struc- ture of Materials", Kiev, 1969, p. 328 (in Russ.) . 2. C.V. de Alvarez, M.L. Cohen et al, Phys. Rev. B 10, 596 (1974). 3. L, Ley, R.A. Pollak et al , Phys, Rev. B 9, 600 (1974). 4. I.R. Fakidov, V.P. Krasov- ski, Physika Metallov i Metallovedenije 7, 156 (1959) (in Russ.). TARGET K X-RAY PRODUCTION FOR HEAVY IONS MOVING IN THIN SOLID FILMS' Tom J. Gray, Patrick Richard, R. K. Gardner, K. A. Jamison, and J. M. Hall Department of Physics, Kansas State University Manhattan, Kansas 66506 There have been several works reported [1-4] on the production of target x rays as a function of target thickness for various heavy ion projectiles incident on thin solid films. Betz et al . [5] reported a new technique for measuring inner-shell atomic lifetimes by measuring the projectile x-ray yield vs target thickness. The approach of the latter group was to account for the microscopic interactions affecting the pro- jectile K shell as the incident ion moved through the solid at high ve- locities. The results of their work are dependent on the rate equation which relates the K-shell single-vacancy population, Y-^, to the K-shell vacancy production cross section, a v , the quenching cross section, ctq, and the natural decay cross section, a T : (1) dY /dX = oil - Y-) - (a_ + 1 v 1 Q a T )Y 1 Hopkins [2], Groeneveld et al . [3] and Feldman et al . [4] have used a similar approach to that of Betz et al . as a starting point for their respective studies of film thickness on target x-ray production. We have studied the target x-ray production vs target thickness for various incident charge states of the projectile at high energies. The initial system studied was CI ions on thin solid Cu targets. It has been shown by Winters et al . [6] that the target x-ray production rate for gas targets under single collision conditions increases by fac- tors of 2 or greater for H-like incident projectiles on argon. Admix- tures of the bare nucleus or H-like component in a beam is expected to enhance the x-ray production rate. Shown in Fig. 1 are the results of measurements for CI on Cu at 60 MeV for three different target thicknesses. Beginning with Eq . (1) and assuming that there are two components in the ion beam within the targets; those with a K vacancy, Y^, and those without a K vacancy, Yq, the target K-shell x-ray production cross section averaged over the target thickness is rT (2) u» 40 °KX " 1/T Kx "p"30 20 [o ko Y o + o T ] dX where c^q = target x-ray cross section for the Yq component, and o"jq = target x-ray cross section for the Y]_ component. The resulting expression for a^ is 10 I I I I I l a q+ 0N cu Cu px (pg/cm 2 ) • EO • 28.9 • 92.1 u II ■ Cu K X-RAYS 7 I I I I 10 II 12 13 14 IS 16 17 q Fig. 1 °KX = a K0 [1 + (a " 1) Q v /a " ((«-D/ a T )( CT v / a " A)(1 " ex P(" aT )>] (3) 272 where A is the initial fraction of ions with one K-shell vacancy inci- dent on the target, a = a v + oq + a T and a = OkI^KO* Experimentally, a is determined for vanishing target thickness The measurements and model calculations for 60 MeV CI ions on Cu are shown in Fig. 2. The relevant para- meters obtained from the model calcu- lations are given in Table 1. At energies of 1-2 MeV/amu the two component model begins to break down as the atomic number of the pro- jectile is decreased. The projectile must then be described by three com- ponents Yq, Yx and Y2, where Y2 is the fraction with 2 K-shell vacancies. Using the solution of Allison [7] for the 3- component system an effective cross section ojqj f or target x-ray production is formulated analogous to the 2-component system. Solutions of the form 1 1 ■ 1 t 1 1 1 — r Cl q *0N Cu 10 # L7I MeV/ AMU - jV A 16 + 8 Okx ^J • 9 + 6 *^j^A»l 4 - , 2 " """ A«0 1 1 , 1,1,1. KX % a K0 {l + (a-l)[f lYl+ f 2 Y 2+?1 ] + (3-l)[f 3Yl +f 4 Y 2 +5 2 ]> ■ 40 80 120 Px (jig/cm 2 ) Fig. 2 160 where y. = exp(r.T)-l; f. = f.(r.,C.,T) and £. = B, . (a , ) . 1 i 1111 1 1 v.. The quantities r^ and C-^ are, respectively, the eigenvalues of the di- agonalized coefficient matrix of the rate equations and the constants determined from the boundary conditions. 4800 Fig. 3 gives measurements of o^x f° r Si on Cu at a bombarding energy of 48 MeV Similar measure- ments have been made for Al and F on Cu at energies of 48.5- and 38.0- MeV, respectively. Model calculations for the 3-component system are shown in Fig. 3. Work is in progress on the Oj^b) interpretation of the projectile cross ' sections obtained from the model cal- culations of a^x in terms of single 1600 collision cross sections. 3200 I 1 I I 1 I l 1 1 I 1 I 1 I 1 I i_ 20 40 60 80 100 px(ug/cm2) Fig. 3 273 TABLE 1 Values of the parameters for 60 MeV CI on Cu Present Work Other Sources _ nA -19 2 , .--19 2 [6] a 3.5x10 cm ^6*10 cm l J a' 15.4xl0" 19 cm 2 15.7xl0- 19 cm 2 a 8.1 8.4 -21 2 a vn 1.18x10 cm -2 w — 2.80x10 o^ — 7.07xlO~ 19 cm 2 K 03 — 0.443 cu REFERENCES * Work supported in part by the U. S. Energy Research and Development Administration under Contract No. E(ll-l)-2753, and the Faculty Research Fund, North Texas State University. Presently on leave from North Texas State University. [1] W. Brandt, R. Laubert, M. Mourino, and A. Schwarzschild, Phys. Rev. Lett. 30, 358 (1973). [2] Forrest Hopkins, Phys. Rev. Lett. 15, 270 (1975). [3] K. 0. Groeneveld, B. Kolb, J. Schader, and K. D. Sevier, Z. Physik A 277, 13 (1976). [4] L. C. Feldman, P. J. Silvermann, and R. J. Fortner, Nuc. Instr. Meth. 132 , 29 (1976). [5] H. D. Betz, F. Bell, H. Panke, G. Kalkoffen, M. Solz, and D. Evers, Phys. Rev. Lett. 33, 807 (1974). [6] L. Winters, M. D. Brown, L. D. Ellsworth, T. Chaio, E. W. Pettus, and J. R. Macdonald, Phys. Rev. A 11, 174 (1975). [7] S. K. Allison, Rev. Mod. Phys. 30, 1137 (1958). 274 AR ha, K8, ArjD h-REC X-RAY ENERGIES AMD INTENSITIES US AR +12 -*C-F0IL THICKNESS j|\ | / f— | |—t __ ^ | J^^K |— i K A II 3R —| f~, i __ I ^^ Jfc tj pv « • 3^ J^ ^( F.Folkmann, h.-O.Groeneveld, P.Mokler, J.Schader, h. D.Sevier *G.S.I., Postfach 541, 61 - Darmstadt, Id. Germany. **I.h.F. f August-Euler-Str. 6, 6 - Frankfurt/Main 90, U. Germany Investigation of X-ray emission from the system Ar -*■ Ni (on C-substrate) or -*C-foil with a Si(Li) spectrometer enables one to study the projectile and target or only the projectile X-ray emis- sion cross section, respectively, with varying target thickness. The first article in this series treated the Ni Kct and K0 intensi- ties and energies /V. The results were similar to an earlier study of Ne -*A1 of varying target thickness /2/. The present report deals with the Ar ha, 8, and -REC energies + 12 2 and intensities using 56 Me\7 Ar -*C-foil (8 to 440 fjg/cm thick) at the UNILAC at Darmstadt. The foil normals bisected the beam- Si(Li) spectrometer right angle. A 19 urn Al-foil was used as ab- sorber, a 19 urn hostaphan foil acted as vacuum chamber window which was situated 3 mm (of air) from the 12.7 urn Be-foil spectro- meter window. The detector acceptance solid angle was 0.75% of 4TI, and the beam current was integrated by use of a Faraday cup (2D mm tf) 20 cm behind the target. Figure 1 shows a typical measured spectrum, the components being clearly distinguishable. The intensity maximum near 1.4 keV/ may be due to h-f luorescence radiation from the Al absorber foil. Figure 2 shows the average X-ray production cross sections for the Ar hO, hfl, and K-REC spectral components: These values are calculated by dividing the absorption and solid angle correct- ed Gaussian-fitted and integrated peak intensities by the number of projectiles per run and the used foil thickness (measured by alpha-scattering) expressed in units of atoms/cm . (Absorption of the Ar ha radiation is less than 4% in the thickest C-foil.) Such a cross section calculation is quite suitable for the Ar h-REC radiation, which originates within the foil. However, the Ar ha Recipient of an Alexander von Humboldt scholarship. 275 and Kf3 radiation originates both from within and from without the foil. As the foil thickness increases, the relative radiation con- tribution from outside the foil decreases. This variation need not be linear, depending on solid state effects. Qualitatively, the data can be easily understood. First, the general weak fall in average cross section values for all three rays is due to projectile energy loss in the foil. This loss is 2 estimated to be -12 MeV after traversing a 500 ug/cm thick C-foil. One may extract from such measurements the energy dependence of projectile K X-ray yield for a given target material. (The extra- polation of this component toward smaller thicknesses is drawn in.) Secondly, one observes an initial increase in the average Ar K-REC production cross section with thickness, and this tends to saturate. This tendency can be fitted in the first approximation by the for- mula (KR) oc 1 + (expC-CT-rX ) - 1)/oVx , where x is the foil thick- T a T o a ness and oL is the sum total of all excitation and de-excitation cross sections for projectile K-vacancies /1/. Thirdly, the Ar K& and K8 production cross sections are made up of an in-foil contri- bution, similar to the H-REC case, and a post-foil contribution from the decay of the excited projectiles after the foil, with mean fluorescence yields uj # and <*> respectively. The latter con- tribution to the mean cross section will have the general form (KAB)OC (1 - expC-tf-pX ))/oVx . The total Kct and KG production T o T o cross sections will be expected to have the general form (*Oc£?(KR) + w (KAB) = «' + (S- «T)(1 - exp(-tf x x ))/tf_x , To To which describes in general the upper two curves in Figure 2 when co > c*>'. Of course, to and co'may vary with target thickness, be- cause the average projectile excitation state may be a function of the duration of the ion's being in the foil. Also, the foil thickness dependent variations of the X-ray peak centroid energy values, shown in Figure 3, indicate larger changes with foil thickness for the thinner foils than for the thicker. This may result from mean projectile state variation with penetration depth in the foil, as above. These and other points will be discussed. 276 References: /I/ K. D. Sevier, F. Folkmann, K.-O. Groeneveld, P. Mokler, and J. Schader, 5th International Conference on Atomic Physics, Berkeley, California, July 26-30, 1976. /2/ K.-O. Groeneveld, B. Kolb, J. Schader, and K. D. Sevier, Z. Physik A277(1976) 13. Figure 1. Ar K X-ray spectrum (1.4 MeV/amu) Ar + ' 2 bombarding 113 ug/cm^ thick carbon foil. from a 56M«V Ar ♦«2 C-FoKTOng/cm 2 ) I.Ar M i-.tr m 3: Ar K-REC ~ 5 t* e.o e.o 10.0 12.0 u.o ie.o X-RAY ENERGY KEU J-* Figure 3. Ar K X-ray energies as functions of C-foil thick- ness. Mote transient and gen- eral features, analogous to those seen in Figure 2. Dash- ed curves to guide the eye. Figure 2. Average Ar K X-ray pro- duction cross sections as functions of C-fail thickness. Mate the tran- sient components for x ^ 120ug/cm2 and the projectile straggling de- pendent general decrease with in- creasing foil thickness. Dashed curves to guide the eye. ,•21 xto' afc.) yon > moo 3. SO I " h *° so 56 MeV Ar C-Foil Ar KB -r' » § 4S00 "* Mr «-. *-f xso 22 8 6 2 X» 23 cm 2 5 4 ^Sj 3 Effective C-Foi Thickness (wgfcm 2 ) (*,) • 56 MeV Ar* 12 ► C -Fo* Ar Ka -■*---. v.. ArK0 • ■ Y" 1 Ar K-REC ■ 100 200 300 400 Effective C-Foil Thickness ((jg/cm 2 )(x.) 277 ABSOLUTE MEASUREMENTS OF L-SHELL EXCITED AR PROJECTILES EMERGING FROM CARBON FOILS BETWEEN 100 AND 800 KEV P. Ziem, R. Baragiola, and N. Stolterfoht Hahn-Meitner-Institut fur Kernforschung Berlin GmbH 1000 Berlin-West 39, Germany The effect that the degree of projectile ionization becomes much higher when heavy ions pass through solids rather than gases is explained in the Betz-Grodzins model (1) by assuming inner shell excitation of the projectile in the solid. Outside the solid the excited states prefer- entialy decay via nonradiative transitions enlarging the ion charge- state. Recently, in the case of Ar ions incident on Carbon targets (2, 3), in- vestigations have been made to determine the influence of inner shell vacancies on charge-state distributions. The measurements of the abso- lute Auger yield (3) have shown that the observed Ar L-excitation can- not account for the differences in the charge-state of ions emerging form solids and gases. In this work we extended the earlier experiments by measuring electron yields at angles as small as 5 making use of the Doppler-ef feet. Due to shifting of the electrons to higher energies it was easier to discriminate the autoionization emission from the lower background. 10° 10' 400-keV Ar + C 5° -+- ■+- -t- \m 15* 308 350 400 450 500 Electron Energy [eV) Fig. 1 The electron yield of 400-keV Ar ions incident on 2 2yg/cm C-foils observed at 5°. The C K-emission at 140° is added to the background. The inset shows the Auger yield after background sub- traction. Also given are theo- retical transition energies for different multiple ionized initial states. 278 Fig. 1 shows the electron emission of 400-keV Ar ions having passed a 2yg/cm C-foil using a spectrometer with 1.3% resolution, the observa- tion angle being 5 . Autoionization electrons (at 50 eV) and Auger elec- trons (150 to 300 eV) of the target and the emerging projectile are de- tected apart from the continuous background. In the reverse direction (140 ) only C K-Auger electrons have been observed with the same inten- sity as in forward direction (3) . Apparently, due to multiple M-shell ionization of the Ar ions within the first four C-layers, MO-swapping occurs so that C K-electrons can be promoted. The inset of Fig. 1 depicts the Auger electron emission at 5 after sub- tracting the background. The labels denote the theoretical energies of electrons produced by L M ^~ M 9 -, M ~(i=0,1..4) transitions (4) indi- eating that the step-like shape of the peak is probably due to satellite 2 Auger transitions; whereby, the L M state is the most likely exci- ted one (in agreement with ref . (5) ) . The peak intensity near 300 eV is caused by transitions involving electrons which are excited to upper bound states. A detailed discussion comparing Ar-CH experiments will be given at the conference. Fig. 2 The electron yield for 400 keV ions observed at 30 showing the autoionization electrons between 20 and 35 eV, > a TJ LU ■o NT 2 10" 400-keV Ar + C 30° \ s — t » — — 1 i 1 1 ( H 1 10 20 30 40 50 £0 70 86 90 100 Electron Energy leV] The new experiments enabled a better detection of the Ar autoionization electrons as seen in Fig. 2. The plot indicates that this emission is superimposed on a steeply increasing background which makes detection difficult. Nevertheless, we could estimate that the yield of autoioniza- 279 tion electrons was nearly equal to the yield of Auger electrons. Thus, we may conclude that the autoionization process strongly contributes to the charge-state increase of ions emerging from the surface. The fraction f of L-shell ionized Ar ions passing C-foils with energies L from 100 to 800 keV (3) has been reproduced within 20%. Also the same 2 2 fraction f was found for 2yg/cm and 10yg/cm C-foils. Hence, it Li appears that the f equilibrium is already reached at 100 A (thickness 2 L of 2yg/cm C-foils) . This result allows for estimating the upper and lo- wer limit of the lifetime x and the production cross section a v of Ar L- vacancies in C-foils; this estimation is similar to the procedure used — 18 "? in ref. (6). It follows for 400-keV Ar projectiles that 17 > 3.6*10 ' cm and t£ 4.3" 10 sec. This lifetime t is smaller by a factor of two than that obtained from the analysis of thick target x-ray yield (2) . Suppo- sing an underestimation of collisional quenching in ref. (2) the diffe- rences in the fraction f between x-ray yield (2) and Auger yield measu- rements (3) could be discerned. We are indebted to G. Wustefeld for his assistance during the experiments Footnotes and references. + Permanent address: Centro Atomico Bariloche, 8400 S.C. de Bariloche, R. N. , Argentina 1) H. D. Betz, L. Grodzins Phys . Rev. Lett. 25(1970)211 2) R. Fortner, J. D. Garcia Phys. Rev. A12 (1975) 856 3) R. A. Baragiola, P. Ziem, N. Stolterfoht (Sec. Int. Conf. on Inner Shell Ionization Phenomena, Freiburg 1976, Abst. of pap. p 109) 4) F. P. Larkins J. Phys. B4 (1971)1 5) A. B. Wittkower, H. D. Betz Atomic Data 5(1973)113 6) K. H. Schartner, Th. P. Hoogkamer, P. Woerlee, F. W. Saris Nucl. Inst. Meth. 132(1976)35 280 CONTINUOUS THERMAL X-RAY SPECTRUM FROM HOT PLASMAS. BREMSSTRAHLUNG AND RADIATIVE ELECTRON CAPTURE PROCESSES* C. M. Lee and R. H. Pratt Department of Physics and Astronomy University of Pittsburgh Pittsburgh, Pennsylvania 15260 The x-ray emission from a plasma consists a continuum of free- free bremsstrahlung, free-bound electron capture radiation, and bound- bound line radiation [1] . We have attempted to carry out systematic theoretical surveys of both the bremsstrahlung process [2,3] and the direct radiative electron capture process [4,5]. Both processes are described as single electron transitions in a relativistic self-con- sistent screened central potential, using full relativistic partial wave expansion calculations which include all important photon-multipole contributions. Theoretical bremsstrahlung energy spectra k(da/dk) from neutral atoms (Z = 2-92) with incident electron energy 1-500 keV are now available [2]. Similar analysis for the bremsstrahlung energy spectra from atomic ions is in progress [3]. Regarding the direct radiative electron capture process, we recently proposed a simple theoretical method for calculating the needed cross sections [4], Applying quantum defect theory, the radiative capture and the tip bremsstrahlung pro- cesses can be treated together because, at atomic distances, bound and continuum wave-function shapes, of energies close to the ionization threshold, are similar and vary slowly with energy. As a result only two smoothly varying quantities, the quantum defect and the cross section density, need to be calculated for each partial wave channel of the final-state electron. This then suggests a convenient way to carry out systematic analysis of radiative capture cross sections. We have reported some preliminary results [4,5] of such analysis. The bremsstrahlung and the direct radiative capture processes give rise to the continuous x-ray spectrum from a plasma. The con- tinuous spectrum [1] usually consists of the continuous thermal x-ray spectrum and a runaway tail at higher photon energies due to non- thermal high energy electrons. From the cross sections for these two basic processes, the radiation power loss density of the thermal x-rays (defined as power loss per unit volume per unit photon energy, e.g. Watt/cm 3 keV) can be calculated as (dw th /dk) = I n n, (dw* h /dk) , i X where n e and n^ are the densities for electrons and for atomic ions of the ith kind respectively. The "specific radiation power loss density" (dW^"/dk) , defined as power per unit density of the ith kind of atomic ion per unit photon energy, e.g. Watt cm 3 /keV, is related to the basic cross sections through the following Maxwellian folding, 281 dW th = 1 dk n k a CT) <$Ck-T- e )f-, (T,T )dT n ' n 1 Max * e -00 da (T,k) ( )dT dk Max e where k is the photon energy, T the electron kinetic energy and ^Max^-»^e) tQe Maxwellian energy distribution of the electron at the electron temperature T e . Also a*(T) is the direct radiative electron capture cross section into the unoccupied bound state with binding energy e_; the summation here covers all unoccupied states. Finally, da^-(T,k)/dk is the bremsstrahlung cross section from the ith kind of atomic ion. In Fig. 1, we plot the specific radiation power loss density dw£"/dk for Ne-like Mo ions vs. the photon energy k at various electron temperatures T e = 0.4, 0.8, 1,5, 3, 6, and 9 keV. We also present the corresponding partial specific radiation power from the bremsstrahlung process, indicated by the dashed lines in Fig. 1. At low electron temperatures, the direct radiative capture process is dominant for continuous thermal x-ray radiation. However, at higher electron temperature, the bremsstrahlung process will have an appreciable contribution and will be even more important than the direct radiative electron capture process. In such a semilog plot, the continuous thermal x-ray intensity has almost a linear dependence on photon energy k with a slope equal to about -0.434/T e . Thus, a complete set of such data, (i.e. extended to various atomic ions) would be help- ful for quick estimates and/or checks of the average electron tempera- ture, electron density and atomic ion densities in a hot plasma. > QJ O -o > QJ 6 o o c o w V> E a* 5 i -fir 80 20 40 60 Photon Energy k ( keV ) Fig. 1. Specific radiation power density (Watt cm 3 /keV vs. photon energy k (keV) 282 -30 l i i i i i ' T ♦ Completely stripped Mo ion 10 ■ Ne-iike Mo ion - ':■••. • Ar - like Mo ion " »*♦!>■ m - ■ ■ * " m ■ * ■ • -32 #, " ♦ : ■ • . 10 ♦ ■ . • * : ■ Te = 9 kev I . ♦ " _ * ♦ ; ♦ a ■ ♦ ■ • - m ♦ ■ ♦ • . ~"34 ■ ♦ ■ 10 — ♦ * *■ ■ ♦ • * ♦ • - -36 * ■ . Te = 3 keV 10 : ♦ ♦ ; - -38 Te = 0.8 keV . 10 i i i i i ♦ i i 20 40 60 Photon Energy k ( keV ) Fig, 2 "Reduced" specific radiation power density vs. photon energy. 80 In order to examine the validity of the conventional effective charge approximation for the bremsstrahlung process, we present, in Fig. 2, the "reduced" partial specific radiation power loss density, (l/Zf) (dW-^ /dk) vs. the photon energy k for bremsstrahlung from Ar-like, Ne-like, and completely stripped Mo ions. Our data here indicate inadequacy of the effective charge approximation, understandable since such a hard-photon bremsstrahlung process involves small distances where an adequate treatment for the screening effect is necessary in the case of partially ionized atoms. Finally, for the total radiation power loss, one should integrate over the whole photon energy range and should also include the con- tribution of the "discrete line" spectrum and the "runaway tail" in addition to that of the thermal continuous x-ray spectrum. At higher electron temperature, the bremsstrahlung process will become more important. References * Supported in part by the National Science Foundation. 1. S. Von Goeder,W. Stodiek, H. Fishman, S. Grebenschchikov and E. Hinnov, Nuclear Fusion 15, 301 (1975). 2. C. M. Lee, L. D. Kissel, R. H, Pratt and H. K. Tseng, Phys. Rev, A, 13, 1714 (1976). 3. C. M, Lee and R. H. Pratt, Bull. Am. Phys. Soc. 21, 574 (1976). 4. C. M. Lee and R. H. Pratt, Phys. Rev. A12, 1825 (1975). 5. C. M. Lee and R. H. Pratt, (to appear in Phys. Rev. A, 1976.) 283 RELATIVE INTENSITIES OF ION- INDUCED Ka X-RAY SATELLITE SPECTRA OF Si AND Mg AS A FUNCTION OF THE CHEMICAL ENVIRONMENT Robert L. Kauffman, L. C. Feldman and P. J. Silverman Bell Laboratories Murray Hill, New Jersey 07974 High resolution spectra of ion-induced Ka x-rays contain a number of satellite lines which are due to multiple L-shell vacancies present at the time of K x-ray emission. The in- tensity of the satellite lines is greater than that observed for x-ray bombardment and in some cases the satellites may dominate the spectrum. In a recent letter the relative intensities of the satellite lines for the third row ele- ments of Si and S are observed to depend upon the chemical environment of the element when 2 MeV/amu and Ne projec- tiles are used [l]. Such dependences have been explained by changes in the L-shell decay rate. The systematics of such changes suggest that interatomic transitions are a major contribution to the effect. In this abstract preliminary results are reported of the relative intensities of x-rays from Mg and Si compounds using proton and He projectiles. Dependence of the satellite intensities on the chemical com- pound in these collision systems is also observed. Possible effects of the chemical environment on the production of the multiple L-shell distribution is discussed. In this experiment thick targets of Mg and Si compounds are bombarded with beams of protons and He + at 1.9 MeV. The x- rays are resolved using a flexed mica crystal in first order. Typical spectra from Mg compounds produced by 1.9 MeV He are shown in Fig. 1. The spectra are taken in scans of decreasing wavelength in constant 20 steps of 0.02°. The first peak at about channel 25 is the Ka]_ 2 peak. The higher energy peaks correspond to transitions with n L-shell vacancies accompanying the K shell vacancies and are design- ated KL1, KL2, . . . Kcq_ 2 i n this nomenclature is KLO. From these scans peak areas can be extracted and relative inten- sities are obtained. In Table I the relative intensities, I(n), of the satellite lines normalized to Ka]_ 2 are given. Errors due to counting statistics and peak area extraction are less than 3$» The relative intensities of the satellite lines in the compounds are decreased with respect to the element. This is opposite to the trend observed from x-ray fluorescence whose values are also listed in Table I. The changes in satellite intensities of the ion-induced measurements can be explained by the interatomic Auger hypo- thesis, but the theory would not predict the x-ray fluore- scence results. Another possible mechanism which can 284 800 600 400 - 200 - 400 - I 200 1500 1000 - 500 - •*. Mg KG! X RAYS • • - - He + MgF 2 - . . 1.9 Mev • _ . • . • *• • • • •• • . • * — - • . • _ • • • « ' '. * VSv^ "» > • He +Mgo 1 ' , % 1.9 Mev '\ % " • • • •" v^ *• • • •• •» i % J — • He + Mg • 1.9 Mev •'. .N . • v . • • . V _ • • _ • • • • * • • * .. ' • • • * • _# %t «/ <■".• . V-TV__ 50 100 CHANNEL NO. 150 Fig 1 1-9 MeV He induced Ka structures of Mg compounds. The peak at channel 25 is the Ko^g, line. qualitatively predict the changes in the ion-induced satel- lites is the variation of the L-shell ionization probability, p T . P T should be related to the L-shell ionization cross section which varies with binding energy, U L , as Ul or U L in this energy range [ 3 ]. In Table I the U ?p binding energy of the various material determined from ESCA measurements are given. Using such arguments the correct sign of the change and the correct order of magnitude can be predicted. The S results are also consistent with such arguments. The Al results, which are not in agreement with the interatomic Auger hypothesis [2], cannot be understood in this forma- lism. A more thorough investigation is needed before a quantitative comparison can be made. 285 Table I The Relative Intensities of the Ka Satellite Lines for Mg and Si Compounds p 1.9 MeV He 1. 9 MeV Fluore- scence [2 3 U 2p [4,5l 1(1) 1(1) 1(2) 1(3) 1(1) (eV) Mg MgO MgF 2 0.21 0.21 2.45 2.32 2.26 1.82 1.54 1.47 0.47 0.39 0.37 o.i4o 0.158 48.9 50.8 53.5 Si SioN4 Si0 2 0.18 0.17 0.17 I.65 1.46 1.52 0.78 0.67 0.68 0.12 0.09 0.10 0.078 0.090 99. 101.8 103.0 References [l] R. L. Watson, T. Chiao, and P. E. Jensen, Phys . Rev. Lett., 35, 254 (1975). [2] J. Utriainen, M. Linkoaho, E. Rantavuori, T. Aberg and G. Graeffe, Z. Naturforch. 23a, 1178-82 (1968). [3] J. H. McGuire and P. Richard, Phys. Rev. A 8, 1374-84 (1973). [4] G. Wertheim, private communication. [5] R- Nordberg, H. Brecht, R. G. Albridge, A. Fahlman and J. R. Van Wazer, Inorganic Chem. 9, 2469-74 (1970). 286 IMPACT PARAMETER DEPENDENCE OF NONCHARACTERISTIC RADIATION EMITTED IN Cl - Cl COLLISIONS I. Tserruya Max Planck Institut fur Kernphysik, 69 Heidelberg, Germany H. Schmidt-Bocking, R. Schule, and K. Bethge Institut fiir Kernphysik der J. W. Goethe Universitat 6 Frankfurt/Main, Germany R. Schuch and H.J. Specht Physikalisches Institut der Universitat Heidelberg 69 Heidelberg, Germany The structureless shape of the non characteristic radiation (NCR) emitted in heavy-ion-atom collisions makes it diffi- cult to associate (in a clear cut way) this radiation with transitions between molecular orbitals transiently formed during the collision. In this work we present results of a new experimental ap- proach to the problem, namely measurements of the continuum radiation upon the impact parameter of the collision /1/. Such measurements are expected to show a strong dependence of the cross section on the impact parameter. A 35-MeV Cl beam was used to bombard thin targets of NaCl on a carbon backing. X rays emitted at 90° were detected with a Si (Li) detector in coincidence with particles scat- tered ct laboratory angles of 1.5, 3, 6, 7, 13, and 25° corresponding to impact parameters of b = 4 50 to 25 fm. Scattered-particle detection was accomplished by the use of a parallel plate avalanche detector with an azimuthal 2ir geometry. The coincidence spectrum is only slightly different from the single spectrum, normalised at the ClK x rays. The measured photon emission probabilities for different x-ray energy intervals are given in Fig. 1, as well as the Cl x-ray emis- sion probability. The photon emission probabilities are qui- te insensitive to the impact parameter of the collision, similar to the characteristic x-ray emission probability. A small increase for small impact parameter and high x-ray energies is in qualitative agreement with what is expected from induced transitions. Quasistatic /2/ and dynamic /3/ theories, however, predict strong dependence of the NCR yield and shape on the impact parameter of the collision. One may think of several reasons of the similitude of "sing- les" and "coincidence" spectra. If the NCR is produced most- ly in a two-step process, i.e. production and decay of the vacancy in two subsequent collisions, the information on the impact parameter may be lost. In a one-step process the va- cancy might be produced only at the moment of closest ap- proach of the two nuclei, and the radiation is emitted in the separating system, by this removing all interference effects. 287 c o > .on- t 1 — r • o •S 10 D a \ c o o Q. -:.» 10 .-s X LU © •• 10' -J 1. I, i 1 — r CI K x-roys E x =5.5-7keV • • • E x =7-I0 keV - E x = 10-15 keV ~ I0 2 b(fm] Fig. 1 I0 3 For the clarification of this point , we un- dertook the measure- ment of the NCR exci- tation function for similar systems using gaseous and solid tar- gets. The spectral shape of the NCR-continuum is very similar for both types of targets at 35 MeV in accordance to previous results. At low energies, how- ever, considerable differences are seen, the NCR yield almost vanishing for gaseous targets. + supported by a Mi- nerva fellowship; present address: Weizmann Institute of Science, Rehovot, Israel. /V I. Tserruya, H. Schmidt-Bocking, R. Schule, K. Bethge R.^chuch, and H.J. Specht, Phys. Rev. Lett. 36 0976) /2/ W.E. Meyerhof et al., Phys. Rev. Lett /3/ j.h. Macek and J.S K. Smith, 75. 32. (1974) 1279. Briggs, J. Phys. B7 (1974) 1312- B. Muller, and W. Greiner, J. Phys. B8 (1975) 288 1.0 0.5 OjO -/h 1 1 / 1 r NORMALIZED REC-YIELD ANGULAR DISTRIBUTION AND PROJECTILE -ENERGY DEPENDENCE OF THE RADIATIVE ELECTRON CAPTURE X RAYS R. Schule and H. Schmidt-Bocking Institut fur Kernphysik der J. W. Goethe Universitat 6 Frankfurt/Main, Germany I. Tserruya" 1 " Max Planck Institut fiir Kernphysik 69 Heidelberg, Germany X-ray spectra induced by energetic heavy-ion collisions show a peak-like continuum at x-ray energies above the characteristic K-lines of the projectile, which is due to the radiative capture of target electrons into the pro- jectile shell /1/. We investigated the angular distribution of these x rays for 20-, 30- and 1 1 5-MeV 32 S ions on Be, C, and Ni targets. Fig. 1 shows for 115 MeV incident energy the resultant distributions . The experimental results are in good agreement with a pure sin^O distribu- tion in the rest frame of the pro- jectile, thus in- dicating the di- pole nature of the radiation emitted in the capture process. 32 For S ions in the range of bom- barding energies from 5 to 115 MeV incident on Ni targets, we stu- died the energy dependence of the radiative electron captu- re (REC) . The centroid energy of the REC peak was found to depend linearly on the bombarding energy, if one allows for an increase of the projectile K-shell binding energy in function of the charge state and hence in function of the bombarding energy. The width of the REC peak, however, is proportional to the ion velocity. The ratio of the width and the projectile ve- locity is supposed to yield some information on the momen- tum distribution of the electrons captured. The value of the average kinetic energy of the target electrons derived from the data, 113 eV, is in reasonable agreement with the expected one for Ni M-shell electrons, 80 eV. This over- 289 -U L, /A 30" 60° Jk 30" 60 *i J I l 0° 30° 60" 90° H.AB Fig. 1 estimation of the average kinetic energy, however, seems to be a common result in all REC investigations /2/. The REC cross section Greq was obtainted from the yield ra- tio of REC to characteristic x rays, v /y K x ray REC y = n v rad REC projectile energy ( MeV ) Here n denotes the number of target atoms per unit volume, A r ad the decay constant for radiative decay of the projecti- le K vacancy and v the projectile velocity. The REC cross sections obtained in this way are given in Fig. 2. We compare our re- sults with the for- mulation of the REC cross section in the Bethe-Salpeter theory /3/ and the Born approximation /4/. The Bethe-Sal- peter theory is supposed to be re- levant for this ca- se, since it is more appropriate for slow collisions. In both theories we made the assump- tion that 1 8 elec- trons, the number of M- and N-shell electrons of nickel, contribute to the capture process. The theories are also gi- ven in Fig. 2 by the curves labelled B and BS for the Born approximation and the Bethe Salpeter theory, respectively. A qualitative agreement with the Bethe-Salpeter theory is observed, the discrepancies ranging from a factor of 7 at the lowest energy to a factor of 2 at the highest energy measured. The Born cross section, although closer to the ex- periment for energies exceeding 60 MeV, fails completely to describe the shape of the excitation function. The discrepancy between the experiment and the Bethe Salpe- ter theory may be partially due to the way the experimental cross sections were deduced. For \. a A we adapted the neutral atom value /5/, since the real value for these highly ion- ized projectile states is unknown. One can estimate, however, that the real value of ^ ra( j should be smaller, thus decrea- sing the experimental cross sections. Also the determination of the yield of S K x rays may be in error due to the absor- bers used in the measurements. In Fig. 2 only the statisti- cal errors are given, the absorber correction is estimated to be correct within a factor of 2. Considering these uncer- Fig. 2 290 tainties, the description of the excitation function by the Bethe Salpeter theory is quite satisfactory. + Supported by a Minerva fellowship; present address: Weiz- mann Institute of Science, Rehovot, Israel. /*\/ H.W. Schnopper et al., Phys. Rev. Lett. 29 (1972) 898; P. Kienle et al., Phys. Rev. Lett. _31 (1973) 1099. /2/ H.D. Betz et al., "The Physics of Electronic and Ato- mic Collisions, Review Papers and Progress Reports", University of Washington Press, Seattle (1975). /3/ H.A. Bethe and E.E. Salpeter, "Quantum Mechanics of the One- and Two-Electron Atoms", Handbuch der Physik, Springer, Berlin (1957) p. 408. /4/ M. Kleber and D.H. Jakubassa, Nucl. Phys. A252 (1975) 152. /5/ E.J. McGuire, Phys. Rev. A2 (1970) 273; D.L. Walters and C.P. Bhalla, Phys. Rev. A3 (1971) 1919. 291 CONTINUOUS X-RAY SPECTRA BELOW 2 MEV IN RELATION WITH NUCLEAR RESONANCE Y. Cauchois Laboratoire De Chimie Physique 11 , Rue P. Et M. Curie 75231 Paris Cedex 05, France ABSTRACT NOT AVAILABLE 292 SOLAR X-RAY ASTRONOMY Allen S. Krieger American Science & Engineering, Inc. Cambridge, Mass. Introduction Solar X-ray astronomy is a branch of astrophysics. As such it is concerned with determining the properties of the solar corona from its radiations. Soft X-rays provide an advantageous waveband for ex- amination of the lower corona. Soft X-rays are thermally emitted by plasmas with temperatures in the range of 10°K or more, therefore they are (along with XUV radiation) the characteristic emission of the coronal plasma. There is no background radiation at soft X-ray wavelengths from the lower, cooler regions of the solar atmosphere. Thus the corona can be observed in projection against the disk without ambiguity. This property provides coronal physics with (quite literally) a new perspec- tive on the corona which is not available at visible wavelengths. It is now possible to produce X-ray emitting plasmas under laboratory conditions. Many of the experimental and analytical techniques which have been developed for coronal studies may also be applicable to these laboratory plasmas. Accordingly, before proceeding on a short tour through the coronal zoo, it would be appropriate to review the tech- niques with which these results were obtained. Detection Techniques At this time solar soft X-rays are observed by three techniques: 1) Broad-band soft X-ray flux measurements are usually obtained with gas filled counters. Such counters are usually designed to have very good time resolution, and high efficiency. 2) High spectral resolution is achieved by Bragg reflection crystal spectroscopy. Recently, most crystal spectrometers have been preceded by multi-grid collimators in order to reduce the field of view. The collimators serve two purposes. They reduce the angu- lar spread of the incident radiation to a width less than that of the crystal rocking curve in order to maximize the spectral resolution, and they restrict the field of view to a single solar feature. 3) High spatial resolution is obtained through the use of grazing inci- dence optical systems. At the present time, photographic film is almost always used as the image detector and full disk photographs of the X-ray corona can now be obtained routinely. 293 In the future, X-ray spectrometers will be coupled to X-ray telescopes. This will permit the acquisition of data combining both high spatial and spectral resolution. This advance has required the development of systems with higher efficiency than have been available in the past. Interpretation of Solar X-ray Measurements The X-ray spectrum I (X) emitted from a volume V on the sun may be written as: I (X) = L F [X, T (r)] N 2 (r) dV J V u — e — (1) where N e , and T are the electron density and temperature respectively at a point _r in V. F (X, T) is a spectral power function which depends only on atomic physics and solar abundances. A number of estimates of F (X, T) have been published. If the corona or any coronal feature were isothermal, two measurements of I (X) or I (X) dX na or an> of p2 J ^ would suffice to reveal both the temperature and the emission integral /, . N 2 dV. V e In actuality, the corona is not isothermal. It is made up of loop like structures of various dimensions, each of which possesses its own temperature distribution. Accordingly, it is customary to rewrite equa- tion (1), /T 2 Y (T) F (X, T) dT (2) T 1 where Y (T), called the differential emission measure represents the total emission integral within the volume V at temperatures between T and T + dT. It can be shown that N Y (T) = ? i f N 2 (r) | VT| X dS (3) S.(T) i where the sum is over elementary volume elements Vj each possessing its own temperature and density distribution, and the integral is a sur- face integral over the closed isothermal surface S^ (T) at temperature T. Unless high spatial resolution is achieved the measured Y (T), a sum of the elementary Y* (T), may not resemble the individual Yj_ (T) very closely. 2g4 Equation (2) is not easy to invert because coronal lines are typically formed over a range of temperatures which is large compared to the vari- ations in Y (T). Individual line intensities are not independent. Thus, equation (2) is mathematically ill-conditioned. A number of approximate methods have been developed for its solution. Solar Coronal Structures Study of soft X-ray images of the corona has allowed us to identify five types of coronal features which emit X-rays continuously, three classes of transient X-ray brightening s, and two types of coronal features which do not emit X-rays. The five types of coronal structures which emit X-rays continuously are active regions, the interconnections between active regions and their surroundings, large scale coronal arcades, X-ray bright points, and regions of disorganized coronal structure. The three classes of transient X-ray brightenings are solar flares, bright point "flares", and filament or prominence eruptions. The two types of features which do not emit X-rays are coronal holes, and filament cavi- ties. The nomenclature of solar physics is often obscure to the non- specialist, but all of these are coronal structures whose morphological and physical characteristics can be defined in detail. Some of the relationships described above have been well known for many years (e.g. active regions and solar flares emit X-rays), and they have been extensively studied. Others are brand new. Both bright point "flares" and the transient X-ray brightenings associated with filament or promi- nence eruptions were discovered from observations obtained by Skylab. 295 K-SHELL EXCITATION AND X-RAY SPECTRA IN HOT LABORATORY AND ASTROPHYSICAL PLASMAS Leonid P.Presnyakov P.N.Lebedev Physical Institute, USSR Academy of Sciences, Moscow, USSR At present time the most effective methods of X-ray spectroscopy diagnostics are based on measurements of re- lative intensities for resonance and satellite lines of highly charged ions in plasmas [1-3] . The following pro- cesses are important for spectra formation: i) dielectro- nic recombination, ii) direct K-shell excitation. The last one is less investigated. The problem of excitation of highly charged ions by electron impact is considered. The system of clouse coupl- ing integral equations is solved for the case Z ^ 1 » where Z— I is the ion charge. The representation obtain- ed for the radial Green function of the Coulomb field per- mits construction of a solution in the form of correct ex- pansion in small parameter Z - ' • The asymptotically exact expression for the scattering matrix contains two terms which describe respectively potential and resonance scat- tering.. Coupling of open channels leads to small correc- tions in the parameter 2""' "k° "the potential scattering, whereas the resonance contribution has the same order of magnitude as potential scattering, and in number of cases it is dominant [4-5] .As to the potential scattering, the electronic exchange effect should be taken into conside- ration [7]. For any specific ion the following selection rule is valid: either resonance contribution or exchange effect is important [6] .In a case of K-shell excitation of many-electron ions one should take into consideration presence of equivalent electrons in an initial and final channel [8]. The scattering theory under consideration permits to obtain a regular asymptotic expansion for au- toionization rate coefficients. Results of numerical cal- culations are given both for resonance lines and satelli- tes. X-ray spectra of solar flares and laser produced plasmas are discussed. References. 1. A.H.Gabriel. Mon. Not. Roy.Astr* Soc. 1o0 ? 99 (1972) 2. C.P.Bhalla, A.H.Gabriel, L.P.Presnyakov. Mon. Not. Roy.. Ast. Soc. 172,359 (1975) 3. L.A.Vainstein, UTTTSaf ronova. Short Communications Phy- sics. Lebedev Inst. 3. 4 ° (1972). 4. L.P.Presnyakov, A.M.Urnov. Sov. Phys. - JETP 4J^ 31 (1975) 296 5. L.P.Presnyakov, A.M.Urnov. J.Phys. B.8^ 1218 (1975) 6. L.P.Presnyakov. Uspekhi Fys. Nauk. 112749 (W) 7. L.A.Vainstein. Sov. Phys. - JETP, 4^32 (1975) 8. L.P.Presnyakov. Apleton Laboratory Keport No.I.M.jby (1975). 297 X-RAYS FROM TOKOMAKS W. Stodiek Princeton University Plasma Physics Lab Princeton, New Jersey 08540 ABSTRACT NOT AVAILABLE 298 300 - 500 X LASERS AND POSSIBLE LASERS OF SHORTER A I.I, Sobelman P.N. Lebedev Physical Institute Moscow, USSR ABSTRACT NOT AVAILABLE 299 ELECTRON TEMPERATURE AND DENSITY MEASUREMENTS FROM LASER PRODUCED PLASMAS* T.C. Br i stow Laser Energetics Laboratory University of Rochester Rochester, New York 14627 One of the most important measurements in laser produced plasma research is the determination of the electron density and temperature. These measurements are crucial for understanding such basic problems as thermal conduction, ablation, and compression in laser fusion experiments, as well as studies of the possibility of soft x-ray laser action in this environ- ment. Typical conditions in laser plasmas are electron temperatures of 1 keV and electron densities of 10 2 * cm" 3 . A measurement of these conditions can be determined from relative soft x-ray line intensities. However, the results are often complicated by the non-steady state nature of the plasma. Previous interpretation of these intensities have used only a few of the observed lines, as well as an assumption of steady state ionization models (e.g., corona model). For laser plasmas the line intensities can be effected by a non-steady state population density of the ground level. The result is that steady state models will then incorrectly predict the intensities of the emitted line radiation. It will be shown in this work that one can determine the electron density and temperature for non-thermal, non-steady state plasmas. The method consists of examining relative line intensities from an ion using the Colli si onal -Radiative model. Implicit in this model is the use of a non- steady population density of the ground level. Results will also extend the collisional-radiative model to include helium-like ions. The extent to which departures from steady state conditions occur will be examined for various times and Z dependencies. An illustration of the above method will include experimental spectra of an aluminum plasma, produced by irradiating a slab target by a 10 11 watt, 10~ 10 sec laser pulse, focussed to 10 15 watts/cm 2 . The spectra includes both the Lyman series of hydrogen and helium-like ions. Results will include electron density and temperature measurements using the collisional radiative model, and a comparison of these results with those obtained from steady state models. • Research supported in part by the National Science Foundation and by ARPA, Contract No. N00014-67-A-0398-0017. 300 K X-RAY EMISSION SPECTRA FROM A HIGH POWER DENSITY PLASMA T. N. Lee U.S. Naval Research Laboratory Washington, D.C. 20375 Vacuum spark discharges have been used as a source of EUV and x- radiation since at least the 1890's [1] ; however, in spite of its long history, this extremely simple device still finds a place in the modern laboratory. In general, when such a device is operated with an in- creased energy input, it is known [2], [3], [4] to emit the K x-ray radiation of highly stripped, high-Z atoms. This line radiation origi- nates from one or more small (~ 10" 9 - 10~ cm 3 ), high-temperature (<~ 10** - 10 8 °K) plasmas, The x-ray energy density (in both line and bremsstrahlung radiation) in such a plasma volume reaches a value of 10 s - 10 8 J/cm 3 in a time interval of about 5 x 10" 9 sec, giving a power density of 10 14 - 10 16 watts/cm 3 [5]. In addition to the highly concen- trated hot plasmas, the discharge also produces somewhat cooler, low- energy- density plasmas. Accordingly, the integrated spectral contribu- tions from all the components of different plasma temperatures and states makes it difficult to unambiguously interpret the spectra obtain- ed, unless one can also produce spatially resolved spectra with a reso- lution of a few tens of micrometers. Another difficulty in understand- ing the x-ray spectrum obtained with multiple discharge exposures is a consequence of the shot- to- shot nonreproducibility of the discharge, i.e., such spectrum is an integration of a large variety of spectral features emitted by individual discharges. In this study, space-and-time -resolved K x-ray line spectra emit- ted by a vacuum spark plasma are analyzed in order to better understand the physics of the x-ray spectrum. These spectra are obtained with a single discharge exposure. The vacuum spark source used here is a laser- pulse-triggered discharge and is essentially the same device used in the previous investigation [6] . The capacitive discharge takes place be- tween a bullet-shaped anode tip and a relatively flat cathode which is separated from the anode by a gap of approximately 5 mm. The anode material used here is iron. After triggering, the discharge current reaches its maximum value of 250 kA in about 2 usee. A flat LiF analyz- ing crystal is used, and the spectrum is recorded on Polaroid film in an XR-7 film back. Spatially resolved (in an axial direction) spectra of the discharge x-ray emission is obtained by simply mounting a 150 to 250 um-wide slit (oriented perpendicular to the discharge axis) onto the x-ray window (125 um-thick Be-foil). Pinhole (50 um in size) x-ray pho- tographs are also taken simultaneously with each spectral exposure to aid in the interpretation of the spectral data. Fig. 1 shows three microdensitometer tracings taken by scanning across three different axi- al locations of the discharge gap in a space-resolved spectrum. The three locations correspond respectively to a plasma cloud near the anode tip (1st trace) and two axially well- separated (600 um in distance) point plasmas which constitute the main x-ray emitting plasmas in this particular run. The 1st tracing suggests that the plasma cloud emits 301 predominantly Kcc-type transition lines mainly from Fe II through about Fe X, according to the normal line intensity ratio between a K a and Kg line. One of the point plasmas (2nd trace) is hot enough to produce the 2p->ls transition lines of Fe XXIV, Fe XXV, and H-like Fe XXVI ions; whereas the other point plasma (3rd trace, the farthest from the anode tip) does not emit these lines. Negligibly weak Kp-type (3p -+ Is) lines in the 3rd trace , however, indicates that this relatively cool point plasma emits predominantly Kcx-type lines arising from Fe XI through Fe XVIII ions. It is likely that the main contribution to this feature may be Fe XVIII ions which are produced by innershell ionizations of Ne-like closed-shell Fe XVII ions. Examination of a number of pinhole x-ray photographs and spectra obtained indicate that a single, isolated hot point plasma is rarely produced but generally accompanies a cooler point plasma (or a small cloud) occurring in the immediate vicinity (< 25 - <~ 100 (am) . For instance, the point plasma which produced the spectrum indicated in the 2nd tracing of Fig. 1 is surrounded by a small plasma cloud, according to the monitoring x-ray pinhole photograph. However, on several occasions, we were able to obtain spectra emitted by Fe XX iV ls 2 n« - l%2oat Fe II F« XXIV lS'n/-H2pn VACUUM SPARK SOLAR FLARE NRL -0S0 6 Fe II K a Fig. 1 - Microdensitometer scans of a space-resolved K x-ray spec- trum of iron. Scan 1 is taken at the plasma cloud near the anode, and scans 2 and 3 are at two separated (600 urn) point plasmas, respectively. Fig. 2 - Microdensitometer scan of a space- resolved K x-ra> spectrum emitted by a well-isolated point plasma. Also shown is a corres- ponding Fe x-ray spectru n . [7] of the solar flare for comparison. , . Note the negligibly weak Fe II K a line in both cases. 302 what is believed to be an isolated point plasma. Such a spectrum is shown in Fig. 2, where a microdensitometer scan of the point plasma is shown along with a corresponding Fe spectrum [7] of the solar flare (NRL-OSO 6) for comparison. Note the strong Fe XXV ls2p -* Is 2 and Fe XXIV ls2p nX -» Is 2 ni lines with negligibly weak emission of the Fe II - Fe XVIII Kct and K{B lines. This result contradicts the previous assumption [8] that a laboratory transient plasma inevitably produces K transition lines of lower stages of ionization due to the extremely transient ionizing condition (in this experiment, ~ 10 sec). On the other hand, the result is in good agreement with a recent study by Feldman, et al. [9], who deduced the spectral contributions from a two- temperature plasma based on space-resolved x-ray absorption measure- ments. Time-resolved x-ray line radiation of Fe XXV ls2p -» Is 2 and its satellite lines are obtained by properly positioning an x-ray detector and a slit at the film plane of the crystal spectrometer. The data is analyzed by comparing the signals with the simultaneously obtained pin- hole x-ray photographs or the space-resolved spectra (time integrated) obtained with the second LiF analyzing crystal. The result will be described. I would like to thank Mr. R. H. Dixon for reading the paper and Dr. R. C. Elton for helpful discussions. [1] R. W. Wood, Phys. Rev. V, no. 1, p. 1 (1897). [2] L. Cohen, U. Feldman, M. Swartz, and J. H. Underwood, J. Opt. Soc. Am. 58, 843 (1968). [3] T. N. Lee and R. C. Elton, Phys. Rev. A3, Soi (1971). [4] J. L. Schwob and B, S. Fraenkel, Space Sci. Rev. 13, 589 (1972). [5] T. N. Lee, Ann. New York Acad. Sci. 251, 112 (1975). [6] T. N. Lee, Astrophys. J. 190 , 467 (1974). [7] G. A. Doschek, J. F. Meekins, R. W. Kreplin, T. A. Chubb, and H. Friedman, Astrophys. J. 170, 573 (1971). [8] A. H. Gabriel, M.N.R.A.S. 160, 99 (1972). [9] U. Feldman, S. Goldsmith, J. L. Schwob, and G. A. Doschek, Astrophys. J. 201, 225 (1975). 303 SPATIALLY-RESOLVED SPECTRA FROM EXPLODED-WIRE PLASMAS* C. M. Dozier, P. G. Burkhalter and D. J. Nagel Naval Research Laboratory , Washington, D.C. 20375 Exploded-wire plasmas are used to excite x-ray transi- tions in highly-ionized atoms (1) . X-ray emitting plasmas are produced by passing energetic currents through thin metallic wires stretched between the output electrodes of electron-beam generators. Spectra for high atomic number elements have shown that high ionization states are pro- duced. For example, 51-times-ionized gold has been ob- served (2) . It has also been observed that the high ioniza- tion states are not produced uniformly along the length of plasma, but are related to pinch and flare regions that occur along the plasma length (3) . The spatial information from the earlier work was somewhat limited. The purpose of this paper is to report newer results of spatially-resolved spectra from several exploded-wire plasmas. Plasmas formed from exploding wires have rather complex structures. Figure 1 shows an x-ray pinhole image which exhibits tightly-pinched regions plus more extended flares between the pinches. The x-ray spectra from exploded wires contain three types of features: (a) thermal emission from high temperature (^ 1 keV) pinches, (b) thermal emission from cooler plasma (^ 0.1 keV) , and (c) inner shell transi- tions excited by non- thermal electrons (3) . Space-resolved spectra obtained in this work yield two types of results. Firstly, they permit association of spatial regions (pinches and flares) with spectral features (thermal and non-thermal emission) . Secondly, it is possible to examine pinch-to- pinch variations in the emitted spectra. FLARES PINCHES Fig. 1. X-ray pinhole image of exploded wire plasma showing pinch and flare regions. $*f? h- / z Ul J o / o f , i X. 1 | CL n »/ fl i < 1 A/ ViAjVAa 1 a: J 1 M ^VK'fy W* o v r II 1 ul \ii N %J " \- V « Wv* VV' "N o r fT* r I fc . Q. / V* Www h^ ft*»V 1.5 Fig. 3. Densitometer traces of Al spectra from two pinched regions. 2.0 ENERGY (keV) 2.5 In summary, spatially-resolved spectra have provided valuable insight into the origin of the different types of x-ray emission in exploded-wire plasmas. The spatial origin of various x-ray spectral features were determined and variations in x-ray intensity along the wire were obtained. * This work was partially supported by DNA and ERDA. (1) D. Mosher, S. J. Stephanakis, I. M. Vitkovitsky, C. M. Dozier, L. S. Levine and D. J. Nagel, Appl. Phys. Lett. 23, 429 (1973). (2) C. M. Dozier, P. G. Burkhalter and D. J. Nagel (to be published) . (3) P. G. Burkhalter, C. M. Dozier and D. J. Nagel (to be published) . (4) D. Mosher, Phys. Rev. A 10, 2330 (1974) . (5) D. B. Brown (private communication) . 306 PICOSECOND PROXIMITY-FOCUSED X-RAY STREAK CAMERA A. J. Lieber, H. D. Sutphin, and C. B. Webb University of California Los Alamos Scientific Laboratory Los Alamos, New Mexico 87545 It has been recognized for several years in the LASL laser-fusion program that x-ray diagnostics with temporal resolution better than 1 ps and good spatial resolution are essential for understanding the basic laser-fusion process. Compression instabilities are predicted to be 1 to 2 ps. Therefore, a program was initiated to develop a new streak camera with picosecond x-ray resolution, since all existing cameras were based upon a streak tube capable of delivering only 10 to 20 ps resolu- tion in the design limit. Among the old tube's weaknesses are its pinhole electron geometry requires operation at low peak conductance or gain to reduce the effect of space-charge distortion at the pinhole and the loss of temporal and spatial resolution. Expensive follow-on intensifiers must be used in an attempt to restore system gain for recording. The overall length of the basic tube of 22 cm from photocathode to phosphor allows longitudinal photoelectron velocity dispersion to reflect as intolerable time disper- sion for true picosecond operation. Finally, such features as overall package size, vacuum compatibility, dynamic range, and trigger jitter limit the utility of the overall camera package as a practical diagnos- tic in the laser-fusion laboratory where experimental space around the target is at a premium, and the cost of each shot requires a record each time. Our camera, the Pico-X, was developed primarily as an x-ray diag- nostic although application of the design to the visible spectrum rep- resents an advance in the state-of-the-art of these cameras as well.[l] A schematic of the tube is shown in Fig. 1. MCP COLLIMATOR PHOTOCATHODE ALUMINIZED PHOSPHOR FIBEROPTICS TRACE Fig. 1. Schematic of proximity-focused streak tube 307 The tube utilizes a microchannel plate in a new manner--as a pas- sive collimator for transverse photoelectron velocity control .[2,3] The overall distance of 3 cm from photocathode to phosphor minimizes longi- tudinal electron dispersion without the need for a lens for longitudinal velocity selection. Such a lens would result in a longer tube which in turn would require high selectivity and reduced sensitivity. In this type of intensifier resolution and conduction are practically independ- ent eliminating the need for an expensive high-gain follow-on intensi- fier. Proximity-focused devices require maximum electric fields to map photoelectrons from cathode to phosphor making them ideal for producing maximum photocathode extraction fields at the same time. Peak extrac- tion fields generated between polished plates far exceed those that can be generated using the grid structure of the old tube, thereby yielding the highest possible photocathode sensitivity. The overall limit on tube length has required care be taken in the design of the sweep electrodes. Our plates were designed using a com- puter simulation code. [4] A comparison of the prototype Pico-X with a standard visible RCA C 73435 (which is the basis for most x-ray tubes) is shown in Fig. 2. Using this tube, an instrument package that is vac- uum compatible and small enough to fit inside the chamber without block- ing the field of other diagnostics has been developed. This camera is capable of taking 24 frames without breaking vacuum--a fact that has greatly speeded data recording. To ensure a streak each cycle of the laser, a new low-jitter power supply had to be developed. Basic to this system is a laser triggered solid dielectric spark gap which has shown less than 20 ps jitter in over 400 cycles. * ^*)5> --** Fig. 2. Comparison of prototype Pico-X with standard RCA C 73435 streak tube. 308 Streaks formed when a 200-ym-diameter-nickel ball two Nd:YAG laser beams are shown in Fig. 3. The left tically delayed from the right by 20 ps for calibratio sweep. Quality of the profiles allows quantitative de files. Data will be presented showing the irradiation diameter-glass microballoons using the dual beam laser elude a trace showing an instability of less than 3 ps of a microballoon. This serves to verify, experimenta ical prediction of 2.7 ps resolution for the prototype should be capable of 0.6 ps resolution). is irradiated by beam has been op- n of the camera nsitometer pro- of hollow 50-ym- . These data in- in the collapse lly, the theoret- (the design Fig. 3. Sweep calibration using x-rays generated when nickel ball is irradiated by a dual beam Nd:YAG laser of 70 ps :ion. REFERENCES 1. "Pico-X" patent waiver applied for by General Engineering Applied Research, Inc., 260 Sheridan Avenue, #414, Palo Alto, CA 94306. 2. A. Lieber, R. Benjamin, H. Sutphin, and C. Webb, Nuc. Inst, and Methods, 127. (1975) pp 87-92. 3. C. Webb, A. Lieber, H. Sutphin, and R. Benjamin, Rev. Sci. Instrum, 47, 1 (Jan 1976) pp 149-150. 4. S. Gitomer, R. Benjamin, W. Hall, A. Lieber, and H. Sutphin, IEEE Conference on Plasma Science, Ann Arbor, MI, May 14-16, 1975. 309 THEORETICAL INVESTIGATIONS CONCERNING THE EVOLUTION OF THE ATOMIC EFFECTS CONTRIBUTION IN THE SPECTRA (kO TO *l-00 eV) F.Combet Farnoux and F.Keller E R "Spectroscopic Atomique et Ionique" Universite Paris-Sud Batiment 350 - 91^05 Orsay (France) The atomic origin of inner shell ionization processes in the photoabsorption and electron energy loss spectra obtained with solid state samples is well known now. However, the exact formulation and the importance of the atomic effects (compared with the environment effects) vary with the energy range and the elements considered. We will give a brief review of these spectra recently studied both by optical absorption using a synchrotron light source and by elec- tron energy loss spectroscopy, in the energy range from 40 to A-OOeV. Among them, we will mention: the rare gases (np and (n-1)d ioniza- tion) , Ag,Sn,Te,Cs,Ba and the rare-earth metals (kd ionization), Na, Mg,Al (2p ionization), some transition metals Sc ,Ti,Mn,Ni, Ir ... (np ionization) , and some heavy elements (Au,Hg,Bi,U ...). We will emphasize the various atomic calculations of photo- ionization cross sections O"- which have been performed to interpret these spectra; they are relevant to various techniques, among them: independent particle models taking into account some final state correlations, as we use for heavy elements, many body perturbation theory as used by Kelly (1), random phase approximation with exchange, as used by Amusia (2) and Wendin (3) • The comparison of these calculations with spectra obtained from gaseous and solid samples allows us to distinguish several situations, according as we consider the atomic configuration of the ionized element or the energy range. A) If the photon energy TTO ^ E (generally less than 100 eV),the calculated structures of > l) we have for the screened cross section the simple result, ,r- rt c/ N / N Cx2, r ^8 3Ul .110 1 1 . r 310 102TU 1 3U2U6 1 -p (9) k —2/? k c where A k =v k (*/a) =V.(l.l3aZ ' ) and a is the Stobbe formula. Comparisons of our analytic results with exact numerical screened calculations for the nonrelativistic dipole cross section and also with the full numerical relativistic multipole calculations are given for the K shell of several elements in the following table. Table I. Comparison of our analytic results for the K shell, a. , with exact numerical values of the K shell nonrelativistic dipole cross section, Cm,—.* and with the full relativistic results of Scofield, 4f transitions is a very particular case where the observed discrete transitions are similar to the ones observed in free atoms . It is now clear that this is due to several facts. In rare earths the 4f shell is incomplete and well localized. This shell is also closer to the nucleus than other more outer shell filled before in lighter elements, in particular 5s and 5p subshells. The f-electrons are embedded and do not participate to the chemical bonding as manifes ted by the well known chemical identity between all rare earths. For these reasons 4f configuration in rare earths, where N varies from for La to 1 3 for Yb, present the same behaviour and keep then atomic character independently of the phase. In this case the 4f states do not contribute to the conduction band and are well localized below the Fermi level in the ground state (1) In 1967, in a systematic study of rare earths absorption in the 50-500 eV region with thin films, Zimkina et al (2) were the first to observe a large absorption feature due to the excitation of the 4d- electrons. Haensel et al (3) then, with a better resolution, studied Ce, Pr, Nd, Sm and gave the first absolute values for the absorption coefficient. Explanation for presence of peaks in the absorption curve was given in 1972 by Sugar (4). Calculations for transitions of the type 4d 4f — ^ 4d 4f were performed with radial integral considered as adjustable parameters and fitted to the observed resonances. The lines observed were supposed to arise from triply ionized atoms, which explained all structures spread over lOeV and the large peak by transitions on 4d 4f , corroborating the assumption made. We present here experimental results obtained with synchro- tron light and a s pe ctromonoch r omato r described elsewhere (5, 6). In this case the system was used in the one grating mode with a 576 gr/ mm-l° blaze angle grating. Grazing incidence angle of 7° 5 was used to increase the intensity in the wavelength range of interest in the first positive order and without orders over lapping. Continuous electron multiplier was fixed directly behing the exit slit. Solid thin samples hav.e been prepared under good vacuum and then transfered in the experimental chamber. 321 -100 yj DC 50 o» Fig. 1: Comparison of |jlx absorption coefficient for gadolinium, with the calcu- lated oscillator_strength in 7 a & gf of the 4d 1U 4f S , — *4d 9 4f 8 from ref. \4). The three gf values out of scale are given between parenthesis. PHOTON ENERGY (eV) _Figure 1, shows the relative absorption coefficient ux obtained with unbacked gadolinium thin film at energies lower than the energy of the large peak. Each point corresponds to one measurement for direct and absorbed light. Relative oscillator strength gf from ref(4) was drawn. The relative intensities experimentally observed are not in as good agreement with the calculated values in the case of Gd as for Ce, Pr and Er (4). This is particulary evident when the intensities of the peak around 140 and 145eV are compared . After the measurements the free film was oxydized but new measurement did not give any shift or change in intensities. Other measurements with Gd backed on aluminium or carbon gave the same result. Figure 2 shows the case of Dysprosium over a larger energy range. For this element a thin film -was evaporated on carbon and the measurement of the thickness allowed to deduce absolute values for the absorption coefficients. Curve in figure 2 compared with relative values obtained by Zimkina (2) shows more details in fine structures because of our better resolution. Unfortunatly, oscillator strengths do not exist for Dy, as for Gd and only Bearden values (7) for the N threshold can be indicated. We have not tested the oxydation effect on Dy sample as in the Gd samples and nothing can be inferred from the insensitivity observed with Gd. Oxydation effects have been observed resulting in a change of intensities of small peaks and a shift for the large maximum for Ce and CeO by Haensel(3). Suzuki et al(5) reported also small differences in these features for La and Ce when combined with halides. Recently Dufour et al (9) have observed the X-Ray photoemission spectra from the 4d levels for Gd and Dy in metal and oxyde showing that only broadening appears in Gd but broadening and shift occur in Dy. In fact, 322 spectras obtained by XPS or UPS, X-ray emission and photoabsorption are not directly comparable because of differences in selection rules and final state involved ; however such a comparison can bring valuable informations to understand more deeply the very particular situation occuring in rare earths 4f shell. As a general rule more direct compa- risons can be done between photoabsorption and electron energy loss spectra (10) or with yield spectra as demonstrated for N excitation in metallic cesium obtained with synchrotron light (11). Fig. 2:Absolute photon absorption coefficient (jl measured for dysprosium in the region of N threshold. * *, * L i — i 1 . Dy - 0* V \ - t *•* . Jl/ o ^^ m a. r L' *w 1 ' 1 i i — i 1 — i — i i— . — L-T— «o 160 T70 PHOTON ENERGY (eV) 180 The authors wish thank P. Marin for his help in the use of the ACO storage ring , M. Berland for his contribution to the measure ments and M. Gasnier for the preparation of Gd sample. + Work carried out in Orsay at LURE, Laboratory jointly created by the C. N. R. S. and the University Paris Sud. 1)Y. Baer, G. Busch-J. of Electron Spectroscopy 5, 611(1974). 2)T.M. Zimkina, V. A. Fomichev, S. A. Gribovskii, I. I. Zhukova Soviet Phys. -Solid State 9, 1128 and 1163(1967). 3)R. Haensel, P. Rabe, B. Sonntag-Solid State Com. 8, 1 845(1970). 4) J. Sugar-Phys. Rev. B5, 1785(1972). 5)P. Jaegle, P. Dhez, F. Wuilleumier-IV^ 1 Conference on Vacuum U. V. Rad. Phys. (Hambourg 1974)Ed. E. Koch et al. p. 788 6)P. Jaegle, P. Dhez, F. Wuilleumier-Rev. Sci. Inst, (to be published) 7)J. A. Bearden, A. F. Burr-Rev. Mod. Phys. 39, 125(1967). 8)S. Suzuki, T. Ishll, T. Sagawa-J. Phys. Soc. Japan, 38, 156(1975). 9)G. Dufour-These d'Etat (to be published) 10)M. Cukier, P. Dhez, P. Jaegle, F. Combet Farnoux -Phys. Let. 51,173 , (1975). (11)H. Petersen-Phys. Stat . Sol. B72, 591(1975). 323 EXACT NUMERICAL CALCULATION OF RAYLEIGH SCATTERING Lynn Kissel and R.H. Pratt Department of Physics and Astronomy University of Pittsburgh Pittsburgh, Pennsylvania 15260 Using the numerical partial wave method developed by G.E. Brown [1] and extended by W.R, Johnson [2], we are continuing the study of elastic scattering of photons from isolated atoms. The method is exact for the scattering from each atomic electron, described by a single-electron wave function in a screened static central potential. We identify the individual contributions to the total scattering amplitude made by each atomic orbital and contributions due to specific electric and magnetic multipole transitions. Sensitivity of the result to the choice of potential can be explored; we have primarily used self-consistant fields of the Hartree-Fock-Slater type. These results permit a systematic comparison with experimental observations. We will first give a brief survey of the current status of theory and experiment. Since most previous theoretical work has been based on the simpler form factor approximation, with emphasis placed on the choice of wave functions within that approximation rather than on the validity of the form factor itself, we will then present results of a detailed comparison of the form factor with exact numerical results for the K-shell. Preliminary results of a similar survey for higher shells will be presented. Our discussion will reflect two different interests in Rayleigh scattering; its role in elastic scattering and its contribution to total photon attenuation . Previous work of this type has focused either on the zero frequency limit or on the energy range 100-1000 keV. The work and some of the motives for interest in the process are summarized in the accompanying table. In the zero frequency limit, Rayleigh scattering is related to the electromagnetic susceptibility of the atom. Johnson and Feiock [2] used this method to calculate electric and magnetic dipole susceptibilities of the noble gases. They found good agreement with experimental values only for magnetic susceptibilities. For the electric susceptibilities, the numerical calculation, while agreeing with previous nonrelativistic calculations, seriously over estimated the experimental values. 324 ENERGY PREVIOUS WORK INTEREST IN RAYLEIGH Threshold Johnson [2] electromagnetic susceptibilities dominates total attenuation Threshold to K-edge K-edge to 1000 keV > 1000 keV none Johnson [3] Brown [1] Brown [4] Cornille [5] apparent singularities in amplitudes contribution to total attenuation dominates elastic scattering needed to detect Delbruck scatter ing The original work of Brown, et. al. [1] focused on the K-shell of mercury over the energy range 164-1130 keV using the point Coulomb potential. Johnson and Cheng [3] have calculated exact Rayleigh scattering amplitudes for atomic numbers in the range 30-82, for photon energies on the range 100-1000 keV using self-consistant fields. They compared this data with experiments at angles 30-150 degrees. On the average, agreement of 5% to 20% was found. While such data is probably sufficient for prediction of elastic differential cross sections for angles in the region 30-150 degrees, it is quite inadequate for calculation of total elastic cross sections since Rayleigh scattering is becoming increasingly forward peaked with increasing energy. For still higher photon energies, other elastic scattering processes begin to become important. Interest in measurement of the real part of the Delbruck scattering amplitude requires the accurate theoretical prediction of the Rayleigh amplitude. Only two exact numerical calculations have been reported above 1 MeV. Considering the K-shell of mercury, Brown [4] preformed a calculation at 1.13 MeV while Cornille and Chapdelaine [5] calculated scattering at 2.615 MeV. Above several MeV, Rayleigh scattering becomes extremely forward peaked and is vanishingly small at ordinary angles. All present tabulations of elastic scattering cross sections by bound electrons and tables of attenuation coefficients for photons in matter have been based on the form factor approximation. Relativistic derivations of the form factor have generally required some nonrelativistic assumptions, suggesting that its validity should be restricted to low energies. However recently Gavrila and 325 Florescu 18] studied for the point Coulomb case elastic scattering of photons by K-shell electrons at high energies and found that neglecting terms of order (Za) 2 , the form factor approximation in fact becomes exact in the high energy limit and so should be expected to improve with increasing energy. We have made a systematic and detailed study of Rayleigh scattering amplitudes for K-shell electrons over a wide range of atomic numbers and for photon energies 1-1000 keV. Comparison of the exact amplitudes with those predicted by the form factor have been made. It has been found that for momentum transfers of 0-5 (inverse Angstroms), the form factor differs from exact calculations by a constant multiple, depending upon the incident photon energy. This range of momentum transfers represents the angles through which more than 75% of the scattered photons pass and provides the dominant contribution to the total Rayleigh scattering cross section. In most cases, these are angles considerably less than 30 degrees. Over this energy range the form factor prediction for high Z elements deteriorates with increasing energy, while for low Z elements the prediction improves with increasing energy. At larger angles, the form factor gives poor predictions for elastic scattering, often wrong by a factor of two from the exact results. A similar study of validity of the form factor is currently being completed for higher shells. Sample comparisons for the L-shell will be presented. References: [1] G.E. Brown, R.E. Peierls, J.B. Woodward, Proc. Roy. Soc. A227 , 51-58 (1955) [2] W.R. Johnson, F.D, Feiock, Phys. Rev. 168, 22-31 (1968) [3] W.R. Johnson, K. Cheng, Phys. Rev. A13, 692-698 (1976) [4] G.E. Brown, D.F. Mayers, Proc. Roy. Soc. A242 , 89-95 (1957) [5] H. Cornille, M. Chapdelaine, Nuovo Cimento 1A, 1386 (1959) [6] V. Florescu, M. Gavrila, "Elastic Scattering of Photons by K-shell Electrons at High Energies", Phys. Rev. (to be published) 326 ANGULAR CORRELATION BETWEEN K AND L X RAYS IN PLATINUM A. L. CATZ Department of Physics, University of Massachusetts at Boston Boston, Mass. 02116 During the past several years angular correlations between K and L x rays were measured in a number of elements [l] to test the accuracy of the theoretically predicted [2] admixtures to the x-ray transitions of mag- netic quadrupole (M2) radiation, admixtures, which were shown to affect the angular correlation functions [3]. The expected effects of the M2 admixtures are small however and their quantitative determination imposes stringent requirements on the experimental system regarding stability and absence of spurious anisotropics. Unfortunately the extent to which the system meets such requirements is difficult to ascertain for lack of easily accessible cascades of known anisotropies and in the energy range of interest, which could serve for comparison purposes. In the present experiment aimed at determining the angular correlation between Kal and L x rays in Platinum an improved experimental system was employed which allowed the simultaneous recording of all K-L x-ray coincidences and use of the known isotropic K-L x-ray cascades as internal standards relative to which the anisotropies of the other cascades could be accurately determined. THE X-RAY SOURCE . Platinum x rays were obtained from a radioactive source of Au 195. The x rays are emitted from the Au 195 source, in part, as a result of the Au 195 decay by electron capture to Pt 195 and, in part, following the deexcitation by K electron internal conversion of several excited states of Pt 195 populated in the Au 195 decay. A source of approximately kO uCi intensity was prepared by evaporating a small droplet of Au 195 chloride in HC1 solution on a thin (0.84 mg/cm 2 ) Mylar sheet . X-RAY DETECTORS AND DATA ACQUISITION SYSTEM . The K x rays were detected with a cooled Intrinsic Germanium detector 10 mm in diameter and 5 mm thick the energy resolution of which was sufficient to completely resolve the Pt Kal from the Ka2 x rays. The L x rays were detected with a cooled Si (Li) detector h mm in diameter and 3 mm thick. The LI, La, Lr), L$ and Ly* peaks were well resolved. Spectra of coincident K and L x rays were accumulated using a system which combined a time-to-amplitude converter (TAC) and a computer-based multichannel analyzer capable of storing on magnetic tape for each coincidence K-L x-ray event the following three parameters: the energies of the coincident K and L x rays and the time interval between their detection as measured by the TAC. This last parameter allowed the separation of the true coincidences from the random ones. Measurements were performed using a standard angular correlation table at relative angles between the two detectors ranging from 90 to 270 degrees in steps of 30 degrees; angles were interchanged at random at measured time intervals. 327 DATA ANALYSIS AND RESULTS . The data accumulated in each individual measurement were analyzed as follows: l) For all K-L x-ray cascades the number of true, random and net-true coincidences recorded were determined; in the process, background contributions to both K and L x-ray peaks due to higher energy radiations were subtracted. 2) For all Kal and Ka2-L x-ray cascades contributions due to Ka-L x-ray coincidence events in- volving "unrelated" Ka and L x rays i.e. Ka and L x rays emmitted in different cascades which occur in the same atom in quick succession (See Ref [h] p 638) were subtracted. In the present experiment the number of such coincidences is determined with high accuracy from the measured numbers of K3-L x-ray coincidences, all of which are of this nature, [5]» [6], and the simultaneously measured ratios of intensities of Ka to K$ x rays. 3) Following the above two steps, for all Kal-L x-ray cascades the numbers of net, coincidence events involving "related" K and L x rays recorded during the measurements were normalized relative to one of the following quantities: the number of random coincidence events recorded for the given cascade in the measurement (with proper correction for radioactive source decay), or the numbers of K$-La, K$-L$, or Ka2-L$ true coincidences recorded. Each of these quantities is expected to be independent of the angle of measurement , thus providing the internal standard of normalization desired, relative to which the anisotropies of the Kal-L x-ray cascades could be determined. The results obtained using the different normalization procedures were in close agreement with each other. In the final stage of analysis the normalized values of the numbers of coincidences recorded for each cascade in all measurements performed at a given angle were properly averaged and the resulting weighted averages N(0) were fitted by a weighted least square procedure to functions of the form N(8) = N(0) + N(2) P(2) (cos 0). From these, the angular correlation coefficients A22 = N(2)/N(0) were then determined (See Ref. [h]). The following results were obtained for the coefficients A22 from data analyzed thus far: 0.236 + 0.027 for the Kal-Ll cascade; 0.021+ + 0.006 for the Kal-La cascade and 0.021 +_ 0.017 for the Kal-L$ cascade. These results are slightly lower than the values of 0.2983, 0.03^8 and 0.0535 theoretically predicted [2] for these three cascades, respectively. The experiment is still in progress and results of higher precision are ex- pected to be available for presentation at the conference. Possible causes for deviation from theoretical predictions will also be discussed. REFERENCES [1] M. R. Zalutsky, E. S. Macias and A. L. Catz Phys. Rev. A 11, 75 (1975). This work contains references to most previous works on the subject. [2] J. H. Scofield, U CRL Report No. 51232, 1972 (unpublished). [3] A. L. Catz Phys. Rev. Letters 24, 127 (1970) [k] A. L. Catz Phys. Rev. A 2, 63 1 +"Tl970) [5] A. L. Catz and E. S. Macias Phys. Rev. A 9, 87 (197*0 [6] E. S. Macias and M. R. Zalutsky Phys. Rev. A £, 2306 (197*0 328 SOFT X-RAY PHOTOIONIZATION OF XENON BY PHOTOELECTRON SPECTROMETRY WITH SYNCHROTRON RADIATION * + F. Wuilleumier , M.Y. Adam E.R. "Spectroscopic Atomique et Ionique" n° 184 du CNRS Universite Paris Sud, BSt.350, 914-05-Orsay, France and V. Schmidt, N. Sandner, W. Mehlhorn Fakultat fur Physik der UniversitSt Freiburg, Freiburg i.B. D-7800 - Germany Photoelectron spectrometry is an unique method to delineate the electronic structure and dynamics of atoms. In particular, electron correlations can be investigated with accuracy, indirectly through their influence on single electron properties, and directly through the exis- tence and intensity of multiple ionization or excitation processes (1). Up to recently the number of photon sources supplying a photon beam of well defined energy and high intensity was very limited. Most of the electron spectrometry experiments have been carried out either with UV resonance lines of low energy or with the MgKol and AlKcC lines. In the last few years, the use of soft X ray emission lines brou- ght new informations about the energy dependence of various atomic properties in He (2) and Ne (3). These first energy analysis revealed clearly the interest to use a continuous photon source such as synchro- tron radiation to investigate, as a function of the photon energy, the atomic subshell properties by photoelectron spectrometry ; in addition, many interesting processes can only be studied with a continuously adjustable photon energy. Up to now only one group had obtained some results in the study of gaseous species by electron spectrometry with synchrotron radiation. Using the Daresbury synchrotron, single subshell cross sections and angular distributions of photoelectrons have thus been measured in neon (40, argon (5) and xenon (6). However, in these experiments, the band pass of the monochromator had to be set at 3 to 7 eV in the 100 eV re- gion. Only the gross features of single photoionization processes have been observed and neither the fine structure of the photoelectron and Auger lines nor the multiple excitation processes could be studied. We present here the first results of an experimental program devo- ted to the study of atomic subshell properties (3) and Auger processes (7) by electron spectrometry with the synchrotron radiation emitted by the ACO storage ring in Orsay (8). The electron produced are energy analyzed with a cylindrical mirror analyzer with the cylinder axis pa- rallel to the incident radiation. The acceptance of a 2n azimutal angle 329 around the incoming photon beam is the only experimental set up giving independence from the state of polarization of the incident radiation (9). In these first experiments, the analyzer accepted electrons about the magic angle of 54-°44' which makes the results independent of the angu- lar distribution effects . The apparatus has been designed to work in the first order focusing mode with intermediate focus point (10). A detailed description of this spectrometer and of the operating procedure will be given elsewhere (11). We just mention here that the residual magnetic field is less than 2 milligauss and that the resolution (FWHM) can be va- ried from about 0.2% to 1.5%, except at very low kinetic energy, where the limit is aroud 30 meV. In the first experiments with ACO, this reso- lution was set at 0.9 %. Continuum radiation from ACO operated at 54-0 meV-100 mA, was monochromatized with the lm grazing incidence monochromator specially designed for the laboratory LURE (12). In the experiments presented here, the apparatus has been used in the one grating mode with a fixed exit slit between 60 and 150 eV with a band pass of 0.4- to 1 .5 eV. A gold foil-electrometer amplifier combination monitored the incident ra- diation. Photon flux of typically 10" photons /A /sec at 100 A in the sour- ce volume of the electron spectrometer were measured. In the first experiments , electrons ejected from xenon at various photon energies were analyzed. Spectroscopically pure xenon was in- troduced into the spectrometer via a multicapillary array at pressures varying in the source volume from 10"-* to 10"^" Torr. Figure 1 shows the electron spectrum following photoionization of 90 80 70 BINDING ENERGY (cV) 60 50 40 30 20 g 300 o C/1 200 o u T 10 — r~ Ad 3/2 5/2 » I Xe hi) =93.2 eV Monochromator bond pass = 1eV Auger lines N-00 Auger lines N-00 Shake up V2 3/2 u i V VS«»w , »j'>i »■ ■ i V »■ 40 50 60 KINETIC ENERGY (eV) Fig. 1 - Electron spectrum of Xe after photoionization. "Shake up" indicates both true shake up and configuration interaction processes. Xe with 93.2 eV photon energy and a monochromator band pass of 1 eV. All main features of the photoelectron and Auger spectra can be distinc- tly seen. The spin -orbit splitting of the 4d and 5p subshells is well re- 330 solved, the Auger lines previously observed after electron impact (13) are clearly resolved and identified, and, in the 60-70 eV kinetic ener- gy region, some processes corresponding to the simultaneous excitation of a 5p electron accompanying the ionization of another 5p electron are clearly observable. The width of the Auger lines shows that the experi- mental resolution of the electron spectrometer is about 0.9 % and thus equal to the calculated one . The width of the 4d peaks , about 1 eV , is mainlv due to the monochromator band pass. One can also note the high peak to background ratio at the 4-d peaks C^i/30). The detailed study of all the features observed in this spectrum is now undertaken as a function of the photon energy. Preliminary results have already been obtained showing that the energy and width of the Auger lines increases with decreasing photon energy near threshold. This demonstrates that post collision effects occur also in the Auger decay of atoms following photoionization, as can be expected from the investigation of Auger spectra after electron impact (14) or in the ion charge distribution after quasi-photon ionization (15). The authors gratefully acknowledge the contribution of Dr P.Dhez to the success of these experiments by setting the monochromator. They would like also to thank Dr P.Jaegle for his constant support and Dr P.Marin for his help in operating the storage ring. v/ork carried out in Orsay at LURE, laboratory jointly created by the C.N.R.S. and the Universite Paris -Sud. Research supported by the Centre National de la Recherche Scientifi- que, France, and the Deutsche Forschungsgemeinschaft , Germany. (1) M.O.Krause, "Photoionization and Other Probes of Many-Electron Interactions" ,ed.F .Wuilleumier , Plenum Press (1976), p. 133. (2) M.O.Krause and F. Wuilleumier , J. Phys . B., 5,L143 (1972) (3) F. Wuilleumier and M.O.Krause, Phys. Rev. A 10, 242 (1974) (4) K. Codling et al. , J. Phys. B, 9, L83 (1976) (5) R.G.Houlgate et al. , J. Phys. B, 7, L 470 (1974) (6) J. B. West et al., J. Phys. B, 9, 407 (1976) (7) S.Flugge, W.Mehlhorn and V.Schmidt, Phys .Rev. Lett. 29, 7 (1972) (8) F. Wuilleumier, LURE Report 74/03, Orsay (1974) (9) V. Schmidt, Phys. Lett. 4SA, 63 (1973) (10) J.S.Riesley, Rev. Sci. Instrum., 43, 95 (1972) (11) M.Y.Adam, F. Wuilleumier and N.Sandner, V.Schmidt, W.Mehl- horn (to be published) (12) P.Jaegle, P.Dhez and F. Wuilleumier, Rev. Sci. Instrum (to be pub.) (13) L.Werme,T.Bergmark and K .Siegbahn, Phys .Scrip. ,6,141 (1972) (14) S.Ohtani et al. , Phys .Rev. Lett. , 36, 863 (1976) (15) M.Van der Wiel, G.R.Wight and R.R.Tol, J. Phys .B, 9, L5 (1976) 331 ABOUT THE Ltf SATELLITE SPECTRUM CAN Lq( DIAGRAM LINES BE OBSERVED ? J. P. Briand, M. Frilley, P. Chevallier, A. Chetioui, A. Touati, M. Ta vernier and J. P. Rozet Institut du Radium and Universite Pierre et Marie Curie 11, rue P & M Curie, 75231 Paris Cedex 05, France. The LX ray spectra exhibit a large amount of satellite lines which are gene- rally not well identified namely in the case of heavy elements. For heavy ele- ments most of the double vacancy production in photo or electron ionization is due to Auger ( KLX ) or Coster-Kronig transitions, direct multiple ionization by shake-off ( + up ) processes having a probability which is some orders of magnitude lower. In this paper, we intend to present experiments in which di- rect identification of LX ray satellites is performed and to give the interpreta- tion of an old experiment, done by M. Frilley (1), and the results of which were never explained. It can also be pointed out how important may be the contami- nation of XL diagram lines by satellites, the energy shift of which is lower than the natural width of mono ionization rays. Let us first present the main features of the Frilley' s experiment. Frilley studied with a curved mica crystal spectrograph, the L spectrum of bismuth, and namely the Lo<^ spectra observed in two different modes of excitation : - the usual electron bombardment in a conventional X ray tube with a bis- muth anode. In this case, the approximate ratio of direct ionization for the L subshells is 22/23/55 for Lj/Ljj/Ljjj. - the internal conversion of the 46, 5 keV nuclear energy level of Ra D. The 210 Pb ( Ra D ) ft decay leads to the 46,5 keV nuclear energy level of 210 Bi which can only be converted into L subshells. In this case, the Li/Ljj/Ljjj di- rect ionization ratio is very different from the previous one and equal to 92/5/3. Then, we can say that in this case, the direct ionization roughly occurs only in the Lj shell. In the first case, he observed the conventional Lo^ spectrum which is characterized by the appearance, near the diagram line, of a main satellite which is situated at 34 eV with respect to the Le 2p Coster-Kronig transitions when the atom is ionized in the Is shell. The study of K^ satellites emitted in electron capture decay which is characteristic of the (Is) (2s) ionized states can then give us valuable infor- mation on the validity of the assignments of these particular lines ( which is still an open problem ). References (1) L.G. Parratt.Phys. Rev. 50 ( 1936 ) 1. (2) T. Mukoyama and S. Shimizu. Phys. Rev. C9 ( 1974 ) 2300. (3) T.A. Carlson, C.W. Nestor and J. C. Tucker. Phys. Rev. 169 ( 1968 ) 168. (4) T.A. Carlson and C.W. Nestor Jr. Phys. Rev. A8 ( 1973 ) 2887. 337 RIGOROUS SCREENING AND EFFECTIVE PRINCIPAL QUANTUM NUMBERS Z.J. Horak, x) M.N. Lewis, +) H. £ihov£ x) x) Institute of Solid State Physics, Czechosl.Acad.Sci. , Cukrovarnicka 10, 162 53 Praha 6, Czechoslovakia + ) Center for Astrophysics, Harvard Coll. Observatory 60 Garden St .Cambridge . Mass. 02138 A common drawback of the atomic screening theories is that they are either semiempirical or introduce nonorthog- onal orbitals [l] inconvenient for refined calculations. In this contribution we obtain an ab initio and rigorous scheme of screening constants and principal quantum numbers by means of the perturbation theory . The quality of our wave functions is tested by a calculation of the dipole transition probability K -.> L in neon; K= Is (2sf (2p) , L , (14 2 (2sf (2P) 5 . The proposed perturbation scheme is defined by writing the atomic Hamiltonian N N H = - Z|l/2Z\. + Z(r. )" 1 J+ Id*,,)' 1 as H = Z^H + Z V 00 o N I where H = - / fl/2 A . + (f . )" 1 + B(r- )~ 2 1 o ^~: l 1 1 1 J N V = l(f i ,)~ 1 * li-^ir,)- 1 * p(r.) r 2 J r^f.^r 1 , 2. =^(Z )- 2 , Z = Z-^, p=Z B 338 and c , p are arbitrary Z - independent constants. The un- perturbed problem (H - E ^ o = ^ can ^ e s °l ve< ^ ^ n closed form [2] : 2E Q = - £ (n^)" 2 ; n* = n - An ; /In = ( I + 1/2 )x x{l - [l - 8B(2f ♦I)"" 2 /*]. We find L we computed first two terms of the exact Z-ex- -1 -2 pansion I = I Z + I-, Z + . . . The zero order of our gen- eralized perturbation scheme gives I = I (B)Z~ = I Q Z~ + + (I <3- + IqP)Z" 2 , where I Q (0) = I Q ; 1^(0) = 1^. We took f> = j^vc or = J L and adjusted cr such that Iff + 1*6 = I-, . The results for the emission rate (in units eV/h) are 0.0041 (f =f* ) and 0.0045 ( P = f> L ) in agreement with the Hartree Fock 0.0044 [5] . References: [l] D. Layzer: Ann. Phys. (N.Y.) 8 271 (1959) [2] S. Fliigge: Practical Quantum Mechanics I (Springer 1971 ) Problem 69 [3] E.P. Ivanova, U.I. Safronova: J. Phys. B 8 1591 (1975); U.I. Safronova, A.N. Ivanova, N.V. Rabinkina, V.N. Kharitonova: Optika i Spektroskopiya ^8 841 (1970) 339 [4] C. Laughlin, M.N. Lewis, Z.J. Hor&k: J. Phys. B 6 1953 (1973) Eq. (4) [5] J.H. Scofield: Phys. Rev. A J, 1041 (1974) 340 CONTRIBUTION OF RADIATIVE AND AUGER TRANSITION ON Kg' SATELLITE OF TRANSITION ELEMENTS Takeshi Watanabe and Chuji Horie Department of Applied Physics Tohoku University, Sendai 9 80, Japan There have been several experimental studies on the K3 emission spectra of transition elements in pure and compound materials. In comparison to the parent line the K3 * satell- ite is characterized by (1) a broad band spectrum locating in the lower energy side of the parent line, (2) a large amount of the integrated intensity which is far greater than other satellite lines, and (3) a spectral intensity highly dependent on the bonding nature of electrons. Interpretations of this satellite have been also carri- ed out along with experiments. In the analyses based on the electrostatic interaction of p-d electrons [1~3] the energy spread of the satellite is attributed to the energy split of multiplets created by p-d n electron interactions and the intensity distribution is given by the envelope of these multiplets weighted by their multiplicity. Tsutsumi propos- ed that the total spin of unpaired 3d electrons plays an essential role and the satellite structure is produced as a result of difference in the spin state of a 3p hole relative to that of 3d e le ct rons [ 4 ] . However, in these analyses the line width of the observed spectrum was assumed to consist of the life-time broadening of a K hole and the instrumental broadening, and when the theoretical result is compared with observed spectra a smearing function with an empirically determined width is convoluted to the discrete spe c trum. He re the line width is assumed to be constant for all multiplets, and a broad nature of the Kg' line is not fully explain- ed. Also, other proposals such as by Parratt[5] and Sawada [6] are too far qualitative and no positive interpretation seems to be deduced from them. In the present work we restrict ourselves to the K$ ' satellite of transition metal compounds such as MnO and Mn02 Noticing that a large member of these compounds are anti- ferromagnetic we consider, like Tsutsumi, that unpaired 3d spins give rise to significant effects on the state of a 3p hole. In contrast to the previous works we take into ac- count effects of Auger transitions on a 3p hole which occur among 3p , 3d and continuum levels. As shown by McGuire[7] for the phot oe lect ron spectrum of pure elements the Auger width is expected to be different for each multiplet also in the present case. Moreover, because of absence of screening 341 due to 4s electron width of p-d n conf to pure metallic e in the Auger width the K^ 1 satellite. It is assumed is given by the co interactions betwe Auger transition a order diagrams of contribute only to gives rise to non- spin orientation o 3d electron. An e p-d configuration in the above examp vanishes because t Since we are inter the imaginary part The Auger con s in the compounds considered the Auger igurations should be larger in comparison lements. We show that this difference of each multiplet causes a broadening of that the self-en ntribution of dir en 3p hole and 3d ssociated with 3d electrostatic int Re E ( 3p) , while zero contribution f a 3p hole is an xample of this ca . In the opposite le , the Auger con he spin conservat ested in the broa of the self-ener stibution to Im E ergy E(3p e ct Coulo e lee t ron e le c t ron e ractions the Auger to Im E ( tiparalle se is the case , e . g tribution ion canno dening of gy is mai (3p) can ) of a 3p mb and ex s and of s . Th e f (Hart ree- t ran si ti 3p) when 1 to that 5 P state . , the 7 P to Im E( t be sati the spec nly discu be expres hole change the irs t Fock) on the of a of a state 3p) s f ied . trum, ssed. sed as 6 (^3 p +e - 2w 3d ) Im E(3p) = ir E |<3p kl| (1/r-, o) I 3d 3d>| 1 where 0O3 is the renormalized energy of a 3p hole and £ is the energy of an Auger excited electron. Other quantities have the conventional meaning. Although the wave number k (e=k /2) or the energy e of the continuum should be deter- mined se lf-cons is ten t ly , they are approximated by using the experimentally measured binding energies of 3p and 3d states 3p* The value of k used is [8], where 103 is replaced by to 1.75(in a.u.) for Mn . In evaluation of the matrix element we have used hydrogenic wavef unctions with Slater's screening constants for the 3p and 3d states of Mn , and a spherical Bessel function for the continuum state. For calculation of the angular parts McGuire's table[7] was used. Because of the chi.ee of wave fun ctions the matrix elements can be calculated analytically and it is found that the f-continuum state con- tributes to the matrix element one order of magnitude small- er than the p-continuum state in the present case. There- fore, we consider the contribution from the p-continuum state only. Putting the renormalizat ion constant for a 3p hole to unity, we obtain the Auger line width as 21m E(3p). In Table are shown non-vanishing Auger widths and the effec- tive charges used for the calculation along with the electron configurations and spectral terms for some of manganese ions. The present calculation indicates that the Auger width of a 3p hole T(3p) of some manganese ions is much larger than the K width T (K) of a manganese atom which is estimated to be about one eV[9]. Therefore, according to our assign- 342 ment of the Kg' by T(3p)+r(K) an or of r(K)/(T(3p spin multiplicit ed the expected line. These rat of MnO and Mn0 2 [ teraction splits should be applie least with these ory. One thing width smears bot present argument In concluti rise to signific tion metal compo chromium ions, elusion of - 4s el satellite , d its peak )+r(K)) fr y. Puttin peak inten io6 are co 10] in Tab the spin d to each e lemen ts , to be ment h lines eq the line widt intensity is om what to be g T(K) to be 1 sity ratios of mpared with th le . When the multiplet, the mult ip le t . As agreements ar ioned is that ually and does h should be given reduced by a fact- expected from the .1 eV, we calculat- the K3' to K 3lf3 e observed values electrostatic in- present analysis shown in Table, at e quite satisfact- the instrumental not affect the on it is shown that the Auger width gives ant effect on the Kg' satellite of transi- unds. A similar analysis is being made for Use of better wavef unctions as well as in- ectrons in the formalism is for future work Table: Auger widths, effective charges, and calculated and observed intensity ratios of the K^' satellite to the parent line. Multiplet Z <5 3p Z 3d r(3 P ) V/I$i,3 MnO (pd 5 ) 5 p 13.75 6.6 1.8eV cal . 0.26 obs . 0.19 Mn0 2 (pd 3 ) 3 F 3 D 13.75 13.75 7.3 7.3 1.1 0.8 0.30 0.35 0. 14 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 REFERENCES B. Ekstig, E. Kallne, E. Noreland, R. Manne , Phys. Scr. 2 38 (1970) . R. P. Gupta and S. K. Sen, Phys. Rev. B10 71 (1974). Asada, C. Satoko and S. Sugano, J. Phys. Soc. Japan 855 (1975). Phys. Soc. Japan 14. 1696 (1959) and S. 18 K. 25 L. M. E. A. V. Tsutsumi, J 1418 (1068) G. Parratt, Sawada, Sci Rev. Mod. Phys. 31 352 (1959). Mem. Kyoto Imper. Univ. A15 43 (1932). McGuire, Phys. Rev. A10 32 (1974). Bearden and A. F. Burr, Rev. Mod. Phys. .39 125 (1969) 0. Kostroun, M. H. Chen and B. Crasemann, phys. Rev. A3 533 (1971). ] K. Tsutsumi, H. Nakamori and K. Ichikawa, Phys. Rev. B13 929 (1976) 343 THEORETICAL X-RAY SPECTRUM FOR DOUBLE VACANCY IN 2p SHELL OF ARGON* C.P. Bhalla Kansas State University, Department of Physics Manhattan, Kansas 66506 U.S.A. Measurements of L x-rays from ion-argon collisions show the production of double-hole (2p) states in addition to single 2p vacancy configurations with different degrees of multiple ionization in the M shell. The cascade of the double-hole states leads to a nonstatistical distribution of the terms. We present the theoretical results for argon. The Auger rate is given by r A (a i S i L i * a f S f L f } = 2ir INfl I Cl/^.)^ >| i 1 P 247.34eV 1.65 10" 4 3 3 10~ 4 P-* P 241. 5eV 1.54 u X dA 235. 5eV 1.43 10" 4 345 Table 2 4 Auger rates x 10 in a.u. for the^2p ■= 3p,3p transition from the three initial terms of the Is 2s 2p 3s 3p configuration of^argon leading to the various final states of the Is 2s 2p 3s 3p configuration. Initial States Final Term \ h 18.9 2 p 0.88 2 p 5.51 \ 33.5 h 1.05 2 F 32.5 2 s 0.0 4 S 0.0 4 D 0.0 4 P 0.0 X S 2, ,14 89. ,9 5. ,93 0, ,0 0, ,0 3, ,87 0. ,0 0. ,0 0. ,0 0. ,0 3 P 16, ,7 2, .20 3, .09 26, ,2 5, ,56 2, ,58 1. ,82 14, .5 18, ,2 10, ,9 References *Work supported by the U.S. Army Research Office, Durham, North Carolina. [1] U. Fano, Phys. Rev. 140, A67(1965). [2] C. P. Bhalla, Phys. Rev. A 12, 122(1975). [3] C. P. Bhalla, N. 0. Folland and M. A. Hein, Phys. Rev. A 8^, 649(1973). 346 SYSTEMATIC S OF X RAY SATELLITES Sidheshwar Rai Physics Department,Lucknow Univer si ty,Lucknow-226007, India* 1. INTRODUCTION The problem of the origin of x ray satellites has been a subject of interesting debate among x ray researchers all over the world. The construction of their energy level diagrams is still an open question. The challenge in this field has been to select the fundamentally new and interesting phenomena and to relate these to various probable satellite generation processes. The interpretations offered 90 far to explain the physics of the so-called x ray non-diagram(satellite)lines have, in a few outstanding instances, been remarkably fruitful but many have ended in frustration. A possible reason for this seems to be the lack of research on systematics of these lines* However, a consid- erable amount of work on this aspect has recently been done in India* The aim of the present paper is to review this work. The results are being discussed in the following sections. 2. SCREENING AND SPIN DOUBLET K)RMATI0N Spectroscopic analysis has led[l]to the establishment of two types of doublets in x ray satellite spectra, viz., (a) screening doublets and (b) spin doublets • Screening doublets are characterized [2-4] by the relation A(WR) 1 ' 2 » ( ACTf / n) « C (1) where C is not an absolute constant but increases very slowly with increasing Z • A critical study [4] of the data for x ray satellites on the basis of equation (1) has led to the discovery of the following pairs of screening doublets : 2-1 The K Region t c^ a (z - 16-28), oc^ a (Z .14-33), a a, ,a 0^? 11 1 1 1 , . , ..1 » t . x a 03 , a a (z - l4-29),a 5 ou(z -11 -14), a « 3 ,a 0^ toyx^ (Z -11 - 40), 1 , itt it tit OcO^Cz .11-17), 03^3(2 -14-40), 03 03 ,03 0C4 ,03 a (z -19-28) , a^Z -11-19), p tM ^(z»l5-30),p 3 p ,, (z -20-27), %% ffyfyt^Pfrf H&I .%% ^^e » ^6°^ ( z » 4 1-56),a 5 a 7 ,0^0^ ,0^0^(7 -46-5l),c?a x ,/« x / * iv , t t 1 t 1 1 »vl, (Z =73-82), a a a (z -73-92), c^a »cyxg ,oyju ,0^0, »oyx (z »42-48> cy^ »a 5 o 6 (z =37-49),cuOq(z -41-49), a a'"(Z -27-53), a ix cc x 3^7 ^V/(Z .75-90), $&\ ^(Z .73-90),^^ .{^.f^, ^ X ^(Z =78-90), ^ n ^ V (z -74-90),p I 1 I V 1 V (z -42-49), iy£ >&$2 (Z .40-50), p^2 »^2 (Z .42-50), ^'^(Z -39-51),^" (z -26-50), P^V -40 - 53), P^\z -78-88),^ ,pg£ (z -44- 53),p^ »^ P 2 (Z -44-50), ^'(z -72-82)^^2 'V^t 2 -73-83), /^(z =58-69). 2*3 The M Region t oFoc 17 , a 11 ©? 7 (z - 71-92), a a" (z -72-83) .P^j* &EI&EII (Z " 72 ~ 92 ) ♦ ^1 < Z -73-83). On the other hand spin doublets of x ray satellites are characte- rized[5,6J by the relation, (A^/R ) 1 ' 4 = Tj Z + y (2) where ^ - if- ( -f- - j*— ) l/4 and Y - ^ .Y[ The x ray satellite data have been critically analysed[6] on the basis of equation (2) • As a result following spin doublets are found out : 2.4 The K Region , ^ , p^ ^hv^hl^ohvh^ 7, - 33 ~ 44 )' 2.5 The L Region 1 ol q 2 t^V, (Z -73-83), f^ (Z -42-83) , p£y' (Z = 41-82). 2.6 The M Region » aFp^. , c? 1 ^ (z-71-92) , aFf^ »aFp III tO? 1 ^ » a 11 ^, oF V ^ (z -72-92), a 17 ^ ,0^ ^ n (z » 70-92). A ooupling of the knowledge of the screening and spin doublets in x ray satellite spectra is expected to be helpful in solving the problem of the formation of energy level diagrams for the so-called x ray non-diagram lines (satellites). 3. HEW LINEAR LAW It has been found that the empirical linear law[7],in its general form, (^/R) z+1 - UVR) Z - a( Z - n) ... ... (3) is equally valid for all the high-frequency (HP) satellites in the K, L and M regions as well as for the K and L low- frequency (LP) satellites [8-10] • On the basis of these studies Deodhar[ll] has concluded that 348 the LF satellites arise in the same way as the HF ones by single electron jump in the multiply ionized atoms supporting the basic idea of Went zel-Druy vest eyn theory [121 . It is interesting to note that this empirical linear law also plays two subsidiary roles ,viz. , (a) it enables one to check the accuracy of the measurement of a particular satellite for a given element and also to ascertain its correct assignment and (b)it can be readily applied for predicting a satellite for an element which has been left uninvestigated. 4. DIAGRAM LINE ASSOCIATES (PARENT LINES) The diagram line associates of almost all the HF satellites have been determined [l3j on the basis of the following criteria : (a) semi-Moseley diagram based on double jump hypothesis of Richtmyer stating that |*(^7R) - (^7 R) 1 1/2 holds a linear relation with Z r 1 / 2 and (b) 'new criterion 1 proposed by Deodhar [2] stating that (^/R) — 1 /2 T ■ s (V/R) J holds a linear relation with Z. As a result it has been P i i found that the satellites a , oc~ , «/ * Oc^ , ot and oc^ in the K series are associated with Ka. whereas a , cu' that with Kou «In the L series the satellites ou » ou » ou » oc^ , ou , ot »ou , ou , a' , o*- x , oc x and a are associated with Lou whereas ou that with L« 1 »0ur results for Lp and LY satellites agree with those of Cauchois and Hulubei [l4] «In the M series the satellites o? * or and o? v are associated with Mou whereas oe^ that with Ma .The diagram line associate of all the M£ satellites is M__N-_({3) line whereas that of the satellite MY is M N« 5. SEMI- EMPIRICAL ENERGY LEVEL DIAGRAM : Recently, it has been found [1 5] that a pair of common x ray terms (Ls »Ls' ) is involved in the emission of L satellite spin doublets (P , a,) and (p , ou) .The energy of the satellite Lg is given [l J * Z = ( \s>Z _ -C ( A ^ /R ) LS LB-} Z (6 > If F and Fp are, respectively, the final terms for the emission of spin doublets (#| , 0C4 ) and (f£ , . t » OU ) then, ^z e { \i z+ ( \ V ^ 1 (7) "* { \h ' l\s'z- (V ^' (8) d r 1 349 Knowing the energy values for Ls , Ls 1 , F and F p from equations (5)- (8) we can construct energy level diagram as shown in Pig. 1 (not drawn to the scale). In conclusion, this report is thought to be useful in unifying the majority of x ray satellites specially those which have been thought to be emitted by Wentzel-Druyvesteyn process (WDP) • 1 1 1 - L Ld *1 Pig* 1. Energy level diagram for the L satellites (3 a, 1 1 1 ,8 and 1 '-4 -'1 ~ *7 ' ACKNOWLEDGMENTS t The author is grateful to Professor B.G.Gokhale, Head of the Physics Department jLucknow University; for useful discussions 7 interest in the work and encouragement. The financial assistance of the Department of Atomic Energy, Government of India, is also thankfully acknowledged. REFERENCES : r-ii tai M eg C6j 17] L8j H [10J [iij [121 [i3j M Deodhar,G.B* Deodhar, G.B. Deodhar, G.B. Deodhar,G.B. Rai,S« i D. Phil. Thesis , University of Allahabad , India (1972). Deodhar, G.B. ,Proc. Roy. Soc. A131 ( 1931)476. Deodhar,G.B.,and Padalia, B.D.,Z.Phyk. 172(1963)490« and Rai, S» , J.Phys. B 5 ( 1972)418. and Rai, S. , Nature 222(1969)661. and Rai, S. , J. Phys. B 2( 1969) 1402. and Abidi,S*T.B., Naturwies. 42.(1960)319. Deodhar, G.B. ,and Padalia,B.£. ,Ind. Jour. Pure Appl. Phys* 21B ( 1962)4 Singh, R.B. , Ind. Jour. Pure Appl. Phys. 3( 1965)486. Singh, R.B. , D. Phil. The sis, University of Allahabad, India (1968). Deodhar, G.B. , Proc.Nat. Acad.Sci. A32 (1962) 320. Druyvesteyn, M.J., Z. Phyk. 43 ( 19277707* Deodhar,G.B., and Rai, S. , J.Phys. B 3 ( 1970) 1260. Cauchois,Y. ,and Hulubei,H. , Longueurs d' Onde des Emission X et des Discontinuites d' Absorption X (Paris t Hermann) ( 1947) • Rai,S. , Nature 243 ( 1973) 34 . 350 ON THE SATELLITES OF THE Ka-DOUBLET OF FLUORINE IN LITHIUM- FLUORIDE Y. Hayasi University of Munich, Department of Physics, Munich, West Germany and Tohoku University, Department of Applied Physics, Sendai, Japan The K-emission spectrum of fluorine in solid LiF (X=18.3 A) was studied using a focussing crystal spectrometer with a gas counter. If the spectrum is excited by radiation from either Cu, W or Co targets, satellites Ka3 and KCfy appear with considerable intensity. However, these satellites appear only faintly when radiation from an Fe target (hv of Fe La=705 eV) was used for excitation (Fig.l). The threshold energies for the K, KL2 3(^P) and KL2,3(^P) states of F" ion in LiF crystal lattice were calculated under several assumptions to be 693.07, 715.53 and 719.00 eV, respectively. These energy values were compared with present experimental observations and with our re- cent results for the K-absorption spectrum of fluorine in LiF (Fig. 2). This comparison indicates that: (i) The satellites KCC3 and Ka^ in the F K-spectrum of LiF correspond to transitions KL2 3— L2 3 of F" ion in LiF, which support the assignment made by Kennard and Ramberg. The weak maxima which appear at the sites of the satellites in the case where radiations from an Fe target (Fig. 3) was used for excitation may be caused by weak Fe LP radiation (hv=718.5 eV) or by bremsstrahlung. (ii) The second absorption edge ob- served in the fluorine K-absorption spectrum of LiF at 710-718 eV may be attributed to double electron exci- tation (KL2 3) of the F" ion in LiF. r - (iii) The markedly asymmetric pro- f file of the Kai 2 line of fluorine in LiF is not due to the overlapping of a satellite, but rather to the structure of the L band of fluorine in LiF. Fe 10 kv 105mA Vff%( 18 17.0 A 1 1 1 1 1 1 r •'„ * •. - 40.000 * 20.000 - V ■ s ,y .0" '• .'A. •- ,.-•* 1 1 1 — 1 — 1 ... 11,1,1, <*0 b90 700 710 720 730 740 750 ev Fig. 2. K-absorption spectrum of fluorine in LiF. ii J \ Fig.l. K-emission spectra of fluo- rine in LiF excited by radiation from Fe or Cu targets. Fig. 3. Intensity distribution I (E") of Fe L radiation from an Fe target (anode potential 10 kV) . 351 ELECTRON EXCITED K SERIES SPECTRA OF NEON GAS T.P. Tooman and R.J. Lief eld, New Mexico State University Las Cruces, New Mexico, 88003 A novel gas target x-ray tube has been used in conjunction with a vacuum two crystal spectrometer to obtain high resolution K series spec- tra of Neon [1]. The x-ray tube uses a microchannel plate nozzle to provide a neutral beam of gas. This gas beam is crossed by a monoener- getic electron beam and x-rays produced in the intersection region pass through a thin Formvar window into the spectrometer. There they are energy analyzed and detected by a two crystal (potassium acid phthalate) scanning monochromator and a flowing gas proportional counter. The gas beam density is regulated and the electron beam current is precisely integrated to permit counting for times corresponding to equal amounts of charge delivered to the gas beam. After passing through the x-ray tube the gas beam is scattered into the jets of a high speed diffusion pump, compressed, purified and returned to the microchannel plate to permit long term operation with small quantities of gas. A composite of eight spectra of the neon K series obtained with the new gas target tube has been subjected to appropriate smoothing and com- puter deconvolution of the spectral window of the monochromator. The resulting representation of the true spectrum is shown in Fig. 1. J6 6 Emission , 3KV 352 Careful analysis of the Ka^ o H ne reveals an essentially lorent- zian shape, a width for the ct^, 02 composite of 0.24 eV, and no detect- able separation larger than 0.05 eV. The satellite groups A, B and C are identified as Ka line transitions with, respectively, one, two and three spectator vacancies in the outer shell. Each group appears to have three components. Integrated intensity ratios are 3 3 4 A _ ^ 5 7 6 _ a l,2 °1,2 Both wide range and threshold region Kot^ 2 line excitation curves have been obtained but the threshold region excitation curves show no struc- tures such as are observed in photon absorption. [1] T.P. Tooman, Ph.D. Dissertation, New Mexico State University, 1975, 353 PLASMON SATELLITES IN AUGER SPECTRA OF METALS D. CHASTENET, Laboratoire de Chimie Physique, Universite de Paris VI, 11, rue P. et M. Curie, F-75231 Paris Cedex 05 , France P. LONGE, Institut de Physique, Universite de Liege, Sart Tilman, B-4000 Liege, Belgium The low energy satellites in Auger spectra of metals, due to bulk plasmon excitation, is investigated in the frame of the many body theory. The total intensity of these satellites is compared to the main band intensity. Attention is paid to two types of processes : the intrinsic plasmon production directly related to the core state transition and the extrinsic plasmon production by the Auger electron on its way to the detector. These two processes may present an important cancellation effect by quantum interference. We investigate the importance of this effect in the K; VV and L_ • W Auger spectra of various light metals. The plasmon satellites in Auger spectra are also compared to the same satellites appearing in the X-ray spectra, which present similar cancellation effects. 354 MULTIPLE PLASMON EXCITATION IN CHARACTERISTIC ENERGY LOSS SPECTRUM OF POLYCRYSTALLINE AL . By K.S.Srivastava, S.P.Singh, & R.L.Shrivastava Physics Department. K.N. Govt. P.G. College Gyanpur. Varanasi. (U.P.) India. Abstract: - Ashley and RitQhies ' theory for the mean free path for the second order process of double plasmon excitat- ion in a free electron gas has been extended to third order process. The relative intensities of double and triple plas- mon loss peaks of aluminum have been calculated. The calcul- ated results agree fairly well with the experimental value estimated from Henerich curve on the characteristic energy loss spectra of polycrystalline aluminum. Multiple plasmon peaks upto several orders have been observed in the characteristic energy loss spectra by Hen-jrich (1), in the Auger spectra by Jenkins et.al. (2), in SXAPS spectra by Br^adshaw & Menzel (3), and in the photo- emission spectra by Smith & Spicer (4). These multiple plas- monpeaks have, so far, been attributed as due to single plasmon-multiple scattering process. The contribution of multiple plasmon-single scattering process has not been taken into account. Few years ago, Ashley & Ritchie (5) have calculated the probability of the second order process of double plasmon- single scattering and found that for metals (e.g. Al) having r s a? 2, the probability is about 8 %. Later on Spence and Spargo (6), assuming that the above probability for the second order process is enough to be detected, performed an experiment on the characteristic energy loss spectrum of Al and found that at the double plasmon energy loss distance, both the processes!. e. double plasmon-single scattering and single plasmon-double scattering are contributing. Thus the loss at n^fr^ excitation energies may be due to two proce- sses namely (a) single plasmon-multiple scattering and (b) multiple plasmon- single scattering. The contribution of the first process will overlap with the contribution of the second process and due to this overlapping, we get an enhanced intensity of the peak at the same energy position. Therefore, we present here the calculation of the probability of exciting multiple plasmon peaks in Al upto third order et: andtheir relative intensities with respect to the main peak. The calculated results agree fairly well with the experimen- tal values estimated from Hen?rich curve (1) on characteris- tic b en«rgy loss spectrum of Al. Henerich (1) has recently reported plasmon peaks at 10 eV, 15 eV, 30 eV. and ^5 eV. in the characteristic energy 355 loss spectrum of aluminum. The peakSi^tiiOeV and 15 eV are due to surface and volume plasmon losses respectively. These losses have alrady been studied extensively by several work- ers (7-9). The other peaks at 2 fi ^ (30 eV) and 3 -fi^ (k5 eV) are due to double and triple plasmon losses respectively and is the subject of present study. Following Ashley and Ritchie \5) and Spence & Spargo v (6) the zeroth, first and second plasmon loss probabilities can be written as w. (t) = i*** 0) w, ( t) = C*/A,') e . O) Wi (t) = H^)\' VX -v 0>) e t/A Q) where 't 1 is the plasmon thickness of the material foil used, A is the effective mean free path and are connected to V and x^as _ v _ v and £ ^ o-o^v >-; CS3 In eqn. (3), the first term is the contribution of single plasmon- double scattering process and the second term represent the contribution due to double plasmon- single scattering process. Extending the work of Ashley and Ritchie (5) the probability for the energy loss of 3^ ^^ has been derived as , . ♦/% -% and X = *\ + *i A ^3 ^ 7J Equation (6) has been obtained by taking the contribution of the following three processes ( at the same energy position). (a) Single plasmon- triple scattering (b) triple plasmon- single scattering (c) Double plasmon- single scattering and single plasmon- single scattering event occuring simultaneously. From the above expressions faxxfchB for the probabilities of plasmon losses, one can also derive the expressions for the intensities ratios of the plasmon peaks (I w ) with respect to the main peak ( I ); At t= % , frqns.(l) and (2) can give % « ^ w 356 The value of I,/ I« can be estimated from Hentfrich curve (1). SsfeXKxixglxBSx&kcxxB The values of V s and the intensities K&fc ratios are given in tables 1 and 2 respectively. From table 2, it appears that the calculated values of intensities *«*I& ratios are in fair agreement with the estimated values from Henorich curve(l). Thus we can safely assign the peaks at 2-hoj, (i.e. 30 eV) and 3-h«o^ (i.e. 45 eV ) as due to double and triple plasmon excitations respectively. References : - 1. V.E. Henorich, Phys.Rev. B£, 3512 (1975) 2. L.H.Jenkins, D.M.Zehner & M.F.Chung, Surf .Sci. 38, 327 (I973) 3. A.M.Bradshaw & D.Menzel., Phys. Stat. Soli. (b) i|T 135(1973) 4. N.V.Smith & W.E.Spicer, Phys . Rev. Lett .2^, 769 (I969) 3. J.C.Ashley & R.H.ttifcchie. , Phys. Stat. Soli. 38, 425 (I970) 6. J.C.H.Spence &A.E.C.Spargo. , Phys .Rev. Lett. 267 895(1971) 7. C.V.Von Koch., Phys.Rev. Lett. 2£, 792 (1970T 8. W.Steinraann. , Phys. Stat. Soli. 2g7 437 (I968) 9. K.S.Srivastava, S.P.Singh & R.L.Shrivastava. , Phys. Lett. 47 A . 305 (1975) and Phys.Rev.r^, 3213 (1976) Table 1. S.N0.1 Mean free path 1 Value in Angstrom 1 *• ! 1 0.01422 x 10 5 ! 1 2. • A * 0.01490 x 10 S • 1 3. ! Ai 1 0.33853 x 10* 1 *. : ^3 • 3.6 x 10 s J Table 2:- Probabilities for energjr losses. ' ; — — -4 Energy Loss 1 Authors' Calculated 1 Estimated value from 1 Valste ' Henerich curve (1} 2 **> : o # 18 1 1 0.19 3 'n W|> 1 O.069 0.075 1 357 Review and Status of X-Ray Laser Research Ronald W. Waynant U. S. Naval Research Laboratory Washington, D. C. 20375 The possibility of developing lasers in the x-ray region of the spectrum has attracted serious attention over the past few years. This attention has occurred for several reasons: (1) the success of generat- ing vacuum ultraviolet laser wavelengths as short as 1100 A; (2) the suc- cess of nonlinear tripling and mixing processes to up-convert existing laser frequencies to attain wavelengths as short as 887 A; (3) the con- struction of extremely powerful laser systems to study laser fusion; and (4) the occurrence of results which have been attributed to stimulated emission from several x-ray experiments. Along with these developments numerous ideas for advancements have been made. This discussion collects the last results and proposals and places them within the framework of basic x-ray laser theory. Limitations of experimental technology and the lack of needed theoretical data are discussed. Construction of lasers below 1000 A is impeded by the lack of con- ventional optics. Window and reflector materials are used to make reso- nators in the visible, but below 1000 A no material transmits until the 10-50 A region is reached and the reflectance of metal coatings is usu- ally below 50%. It is possible to use Bragg reflectors, but these are very difficult to align in practice. Distributed feedback also would be a possibility for obtaining resonance in an x-ray oscillator, but the intense pump power required may destroy the delicate lattice spacing re- quired. Because of these practical limitations x-ray lasers are likely to resemble the single-pass, high-gain, mirrorless amplified spontaneous emission (ASE) lasers developed in the uv and vuv. Further study of the general properties of ASE lasers likely will indicate the operating char- acteristics of x-ray lasers. Single-pass lasers of length L have gain given by exp (ctL) where a, the small signal gain coefficient, is given by a X 5 AN 8jtA v Here X is the wavelength, Av is the linewidth in frequency units, A is the transition probability, and N is the inversion density. Substituting the wavelength dependency for Doppler broadening, the gain factor scales approximately as X 3 . The pumping power per unit volume (W-cm" 3 ) scales as X" 4 . Typical values for a - 5, L = 1 cm and particle velocity of 10 7 en/ sec are shown in Table I. This table shows the extremely high TABLE I X[A] 1 10 100 1000 2000 P[W-cm" 3 ] 10 19 10 15 10 11 10 7 10 s 358 power densities required in the 1-10 A wavelength region. At present only high-power focused lasers can approach this power density. The rate coefficients for energy transfer depend on the specific pumping process involved. Most of the excitation processes have rates which scale inversely with wavelength, the exception being resonance charge transfer. The use of metastable states to store excitation prior to rapid transfer to radiative states may alleviate the requirement for rapid excitation. Perhaps the most important pumping process is electron collisional excitation. All of the vacuum ultraviolet lasers generated have been excited by electron collision, primarily collisions with molecules. It does not seem likely that molecules can be used in this manner to produce wavelengths much below 600 A, however. Progress toward x-ray lasers will involve collisions with ions. One such proposal utilizes the electron- collision excitation process to invert the 3p-3s levels in ions. Since this transition has lifetimes connected with it that make lasing rather easy to produce in the visible and near uv, it may be possible to reach short wavelengths by following the isoelectronic ion sequence to higher stages of ionization. For example, the 3p-3s transition of U 8B gives a wavelength of 11 A. Various electron attachment processes can lead to population inver- sion. Three-body collisional recombination preferentially fills upper ion levels leading to population inversion with respect to the lower levels. This process is dependent on rather high densities to achieve a high pumping rate and may be best achieved in laser-produced plasmas. Some observations of population inversion in expanding laser plasmas have already been made. Dielectronic capture, where a free electron is captured and a second electron excited, is a possible means of creating a population inversion. Charge transfer interactions proceed as I z+ + A -♦ I (z - l)+ (n*) + A + + AE, where an ion, I , interacts with a neutral atom, A, reducing the ionic charge, z, by removing an electron from A and promoting the remaining ion to an excited level, n*. Charge transfer occurs spontaneously only when the defect energy, AE is exothermic. Stimulated charge transfer with the defect energy supplied by a laser also has been considered. Charge exchange experiments are presently underway. Photoabsorption has been considered for the production of a popula- tion inversion because of the possibility of tuning the pumping source to produce a specific innershell vacancy. Both Kcc and full-shell vacan- cies in alkalis have been studied. The alkalis have the advantage of only one outershell electron and therefore no Auger effects. The analy- sis of both the alkalis and the Ka laser proposals are positive provided photoionization losses of the laser frequency can be minimized and pro- vided a strong pumping source can be found. Such a source could come from a suitably tailored laser-produced plasma. 359 Other means of possible x-ray laser production include the use of nuclear transitions and the use of stimulated Compton scattering. Seri- ous consideration of nuclear transitions is definitely increasing and could produce an early breakthrough if methods are found to reduce the lifetime of long-lived isomers or if the shorter-lived excited nuclei can be rapidly assembled into a laser configuration. Stimulated Compton scattering has also received increased attention, but the attainment of wavelengths much below 200 A does not seem possible due to the present limitations of electron and photon beams. It must be pointed out that the verification of gain becomes very difficult in the far ultraviolet and soft x-ray regions. This is es- pecially true for the very small, single-pass lasers anticipated. Tech- niques for the verification of gain will likely require the ability to vary the length or other geometry of the gain region as well as the abil- ity to control the pumping intensity. Methods of examination for gain can follow those used for single-pass longer-wavelength vuv lasers, but it is essential that gain be measured to insure that laser action is present. Many of the above difficulties can be avoided by starting with a powerful infrared laser and using the nonlinear susceptibility of vapors to generate harmonic frequencies or to sum several frequencies. These techniques avoid the pumping intensities required at shorter wavelengths and transfer much of the high-quality spatial and temporal characteris- tics from the infrared to the far ultraviolet. The extremely low effi- ciencies associated with nonlinear processes have been improved greatly by using materials with resonances near the incoming laser frequencies or their harmonics. Wavelengths as short as 887 A have been generated, and mixing of tunable visible or near uv wavelengths has produced tunable vacuum uv in the 1000-2000 A region. Conversion efficiencies range from 10 3 to 10~ 7 for these processes. Some prospects exist for the genera- tion of shorter wavelengths via nonlinear processes employing higher- order harmonics in ionized vapors. It may also be possible to start with high-power vacuum-uv lasers rather than infrared lasers. Nonlinear pro- cesses will be available for mixing and tuning of x-ray laser wavelengths when these lasers are developed. While it is difficult to predict the impact that an x-ray laser is certain to have on future research, it is likely to be most valuable in materials research. Its coherence will be valuable in producing x-ray holograms having high resolution. Its temporal and spatial properties also will be quite valuable in many areas. It is likely that the most important applications have not been anticipated at this time. References R. W. Waynant and R. C. Elton, "Review of Short Wavelength Laser Research," Proc. IEEE , vol. 64, pp. 1059-1092 (July 1976) and the 268 references therein. 360 TIME-RESOLVED NEGATIVE ABSORPTION OF A LASER-PRODUCED PLASMA G. Jamelot, A. Carillon, P. Jaegle, A. Sureau Laboratoire de Speotroscopie Atomique et Ionique du C.N.H.S. Universite Paris-Sud, Centre d f Orsay, Bat. 350 91405, ORSAY, FRANCE We present new results on the observation of a negative absor- ption, in the soft X-ray range, in an aluminium laser— produced plas- ma. In our previous works, the absorption measurements were time integrated, due to the use of a slow proportional counter(l) or photographic technique (2) for detecting the X-ray radiation of the plasma. Here, the grazing incidence monochromator is equiped with a 11 ivt """' Te =70 «V Ni = 10 1 30 20 10 Ic H446 fl6,92 11741 01 02 03 0.4 *nn T c 0.5 X(A) 116.46 116.92 11741 XA Fig. I: I-c shows the intensity anomaly occuring in the dense part of a laser-produced plasma; on I— a are the relative intensities of the same lines in common situations; I-b gives calculated transition probabilities. Fig. 2 j For comparison with fig. I-c, spectrum calculated in assuming i) an absorbing external plasma shell, ii) the equalization of the upper level populations by collisions (L.TJ2. equilibrium); inset: ion and electron 'density distribution (cm-3) and temperature (ev) for which the calculation is made. The figure shows the transmission of the light through the plasma (dashed curves). I and T are the values corresponding to the continuous spectrum. Work supported by the D.G.R.S.T. under contract n° 75. 7.0812. 361 fast detection system, leading to a time-resolution of I nanoseconde. Pig. I shows the spectral features in the region under investi- gation. The surpri/singly high intensity of the 4d 3 ?i — >■ 2p 4 S fl line of the Al* 1 " ion, at 117 «4 A, is observed in several neon-like ions as Mg 2 *, at 171. 9 A, and Si 1 **, at 85.8 A. It occurs in the narrow plasma zone where the absorption of the very powerful impulse of the Nd-laser by the plasma initiates turbulences and particle velocity distributions turning away from the equilibrium. Since it was stated that the feature shown on fig. I-c should be due to the reabsorption in unhomogeneous plasma, without the necessity of invoking any upper level population anomaly, (3,4) we performed a detailed calculation of intensity and profile of the three 4d' f P 1 ,^D f ,^ — > 2p*S lines, as- suming the equalization of the upper level populations by collisions and a strong reabsorption in an external shell. Fig. 2 gives an ex- ample of result of these calculations for a plasma surrounded by a dense cold shell which absorbs the radiation emitted by the center of the plasma. It is obvious that these assumptions are quite inade- quate in interpreting the spectrum of fig. I-o. The absorption has been measured at the wawelength of the 3p^ line (117 • 4 A) an d in the continuous spectrum, at the wawelength of 118. 2 A, in using the two plasma technique described elsewhere. The absorption caused by the pure discrete transition is deduced from these two measurements. The time-resolved emission curves of each plasma and of both plasmas together have been averaged over 30 shoota Pig. 3* An example of time-resolved measure- ment of the plasma absor- ption . I - total absor- ption at 117. 4 A; II - continuous absorption measured at II8.2 1; III - absorption caused by the pure discrete tran- sition. On the left, emission of the "source" plasma, of the "sample" plasma, of both plasmas together, after averaging over 30 shoots. The lower curves, on the right, are the smoothed line emission curve ("sample" plasma) and continuum emission curve (118. 2 i,in the "sample" plasma). I A ( \ A%' 30 -30 1 I n _/ "^m t \ =117,4A A c =118,2 A t 362 Pig. 3 X =117.4 A Fig. 4 J Plasma absorption, a) total absorption at the wavelength of the line, b) absorption after taking off the continuous absorption. Smoothed emission curves of, I) the "souroe" plasma, II) the "sample" plasma, III) both plasmas together. In spite of the averaging, the cur- ves keep some irregularities and we smoothed them, by a last square po- lynomial regression, before the calculation of the resulting absorp- tion. This is shown on fig. 3 for the line "sample" emission curve. In the case represented on fig. 3, the line effects a negative ab- sorption, which is counterbalanced by the positive absorption of the continuum. Such a result is very sensitive to the exact position of the target with respect to the axis of observation (few tens of microns); this can slightly change, by mecha- nical inaccuracy and surface erosion, over a set of 90 shoots. With the most accurate sighting attainable in the present device, we achieved the measurement plotted on fig. 4, where the negative absorp- tion appears during a few nanosecon- des, without taking off the positive absorption of the continuum (curve a) Moreover, the absorption reaches a large negative value, when deduction of the continuum is made up. These results are to be added to the ones we reported recently(5) with a dis- cussion on population inversions. REFERENCES 1 - A. Carillon, P. Jaegle", G. Jame- lot, A. Sureau, P. Dhez, M. Cukier, Phys. Letters, 36A, 1971,167. 2 - P. Jaegle, G. Jamelot, A. Caril- lon, A. Sureau, P. Dhez, Phys. Rev. Letters, H, 1974, 64. 3 - J.P.J. Valero, Appl. Phys. Let- ters, 21,1974,64. 4 - W.T. Silfvast, J.M. Green, O.R. Wood, Phys. Rev. Letters, 35 , 1975, 435. 5 - P. Jaegl£, Report at the 2nd International Conference on Inner Shell Ionization Phenomena, Friburg, W. Germany, March 29 - April 2,1976, in the press. 363 POPULATION INVERSIONS AND THE MEASUREMENT OF GAIN IN HIGH DENSITY PLASMAS W.T. Silfvast, O.R. Wood and J.M. Green Bell Telephone Laboratories Holmdel , New Jersey 07733 Population inversions in high-density plasmas are considered and some general problems relating to the interpretation of gain measurements in such plasmas are described. General conditions will be discussed under which population inversions might occur between excited states and also with respect to ground states in these plasmas. Examples of possible inversions in He at 304A and also in some specific metal vapors will be included. In addition, it will be shown theoretically that population inversions with respect to the ground state are probably not possible in an adiabatically expanding plasma. Experimental evidence will be presented indicating that the measurement of gain in a laser-produced plasma using the so called "two-plasma technique" can be unreliable. Qualitative explanations for the origin of these measurement difficulties will be given. * Present address: Culham Laboratory, Abingdon, Oxfordshire, United Kingdom. 364 GAIN CALCULATIONS FOR ELECTRON COLLISION PUMPED X-RAY LASERS* L. J. Palumbo Naval Research Laboratory Washington, D.C. 20375 A steady-state computer model for estimating atomic level population densities and short-wave length laser gain has been developed and applied to electron-collisionally pumped, single-ion, quasi-cw lasing schemes in the carbon- like and helium-like isoelectronic sequences. The carbon-like scheme is an isoelectronic extrapolation to higher atomic number ions and shorter wavelengths of transitions observed [1] to lase in the near UV. The analysis described here is a detailed extension of previous analyti- cal estimates [2] for 3p -» 3s lasing following electron collisional pump- ing from a 2p ground- state reservoir; important refinements include the addition of ionization equilibrium and radiation trapping, extension to high densities [3] , the inclusion of more energy levels and more mixing transitions, and the solution for the relevant population densities by simultaneous rate equations. Because of the close similarity between the carbon-like scheme and another electron-collisional pumping scheme involving 3s -> 2p lasing (collisionally pumped Is -> 3s) in the 10-50 A range in moderate-Z helium- like ions, the computer code developed for the carbon-like ions was also used with minor modifications to model this two- electron scheme. In both of these schemes, the lower laser term is rapidly depleted by spontaneous dipole emission into the ground term, while the upper laser term can decay spontaneously only via the lasing transition and is pumped from the ground "reservoir." Such "single-ion" schemes in which the relevant levels are all the same ionization stage result in a main- tenance of population inversion independent of atomic lifetimes and ionic regeneration; thus, gain occurs for as long as appropriate plasma condi- tions can be maintained, and the population inversion is said to be quasi-cw. A set of steady-state rate equations, each of the form dN i V^ dt Zj k kj was solved for the population densities, N.s, of the levels considered in the present model. The W's in this equation represent the rates for appropriate atomic processes involving transitions between levels j and k and include electron collisional excitation and deexcitation, electron collisional ionization and (three-body) recombination, spontaneous photo- emission, photoabsorption (through an escape-factor treatment of radia- tion trapping [4] , and radiative recombination. Photoionization and transitions induced by ion collisions were negligible in all important cases considered here. In order to allow efficient computation, simple analytical estimates [5], [6] and semi-empirical fits [7] were used to 365 derive rates needed in the above level spacings and oscillator st tables [8] by scaling appropriat carbon- like and the helium- like solved for the population densit term (3d 3 D in C-like ions and 3 lisionally coupled to the upper dipole emission to the ground re lasing species, and the ground t 100 equations, and the necessary energy- rengths were extrapolated from published ely with atomic number. For both the schemes, a set of rate equations was ies of five levels which included the p 1 P in He- like ions) most strongly col- laser term and also strongly coupled by servoir term, the ground term of the erm of the next higher ionization stage. I 3p-^3s LASING IN CARBON-LIKE IONS kT e = kTj = y A LP. L = 10 d a: N e = 10 19 cm -3, d = 3.0 mm b: 10 20 , 1.0 c 10 21 , 0.1 d: 10 22 , 0.01 .01 10 L 1500 1000 700 500 WAVELENGTH (A) 400 350 15 25 30 ATOMIC NUMBER 35 40 FIGURE 1. Computed product of gain coefficient, a, times plasma length, L, versus atomic number for ions of the carbon isoelectronic sequence at a temperature of one-fourth the ionization potential (for most cases) . Solid curves are plotted for various practical electron density (N e )/ plasma diameter (d) combinations. The required plasma particle kinetic energy plus ionization energy is indicated for each curve. The dashed curve indicates the strong effect on curve (b) of varying the 3s - 3p collisionai mixing rate by decreasing the effective Gaunt factor from 0,75 to 0.2. Also, the effect of increasing the electron temperature by a factor of four while limiting the ionization rate to maintr.n an abun- dance of the carbon-like species equal to one-third the total ion densi- ty (as might be the case in a transient heating phase) is indicated for curve (a) by the dotted curve. 366 Computations were performed for a variety of electron densities and plasma diameters (the size alters the populations through optical depth effects) selected to model conditions presently attainable by plasma discharges or by high-power laser/target interaction. For most of the carbon-like runs, a temperature of one-fourth the ionization po- tential was selected to assure adequate abundance of the lasing species while still maintaining a high 2p -» 3p pumping rate. Some typical gains calculated for carbon-like ions in a cylindrical plasma of length ten times its diameter are shown in Fig. 1, where curves (a) and (b) repre- sent plasmas created in high-density discharge devices and curves (c) and (d) are typical of smaller high-density laser plasmas. Similar curves generated for helium-like ions under a variety of conditions exhibit population inversion on 3s -* 2p transitions yielding lasing in the 10-50 A range, but the computed gains in plasmas of reasonable length are two to three orders of magnitude less than those shown in Fig. 1. *Supported in part by the Defense Advanced Research Projects Agency, DARPA Order 2694. [1] Y. Hashino, et al., Jap. J. Appl. Phys. JUL, 907 (1972); 12, 470 (1973). [2] R. C. Elton, Appl. Opt. 14, 97 (1975). [3] R. C. Elton, in Progress in Lasers and Laser Fusion , eds., B. Kursunoglu, A. Perlmutter, and S. M. Widmayer (New York: Plenum Press, 1975). [4] T. Holstein, Phys. Rev. 72, 1212 (1947); 83, 1159 (1951). [5] R. C. Elton, in Methods of Experimental Physics, Volume 9 A, Plasma Physics , eds., H. R. Griem and R. H. Lovberg (New York: Academic Press, 1970) Chapter 4. [6] H. R. Griem, Plasma Spectroscopy , (New York: McGraw-Hill, 1964). [7] H. J. Kunze, Phys. Rev. A3, 937 (1971). [8] W. L. Wiese, et al., Atomic Transition Probabilities - Volume I; Hydrogen through Neon, NSRDS-NBS-35 (Washington, D.C.: U.S. Govern- ment Printing Office, 1971). 367 AUTHOR INDEX Aberg, T t , 35, 171 Adam, M.Y., 329 Agren, H. , 250 Ahmed, M., 46 Aita, 0., 220 Alperovich, G.I., 269 Andermann, G., 240 Avdeev, V.I., 53 Bachrach, R.Z., 245 Baer, Y., 29 Bagus, P.S. , 114 Baragiola, R. , 278 Barchewitz, R, , 81 Barrus, D.M., 263 Basilier, E., 119, 126 Benka, 0., 249 Bergknut, L., 240 Best, P.E. , 98 Bethge, K. , 287 Bhalla, C.P., 46, 344 Blake, R.L., 263 Blokhin, M.A., 145, 269 Blumberg, W.E. , 86 Bonne! le, C, 81 Briand, J. P. , 332, 335 Bristow, T.C., 300 Brown, G.S., 86, 88 Brytov, I. A., 248 Bunin, M.A., 269 Burek, A.J., 263 Burkhalter, P.G., 304 Burr, A.F., 95 Carillon, A., 361 Catz, A.L., 327 Cauchois, Y., 292 Caudano, R,, 119, 126 Chastenet, D., 354 Chetal, A.R., 163 Chetioui , A, , 332, 335 Chevallier, P., 332, 335 Chiao, T., 189 Chu, C,C, 98 Citrin, P.H., 29, 86 Combet Farnoux, F. , 310 Costa Lima, M.T. , 133 Crasemann, B., 1 Cukier, M., 321 Curelaru, I. , 102 Das Gupta, K. , 260 Dehmer, J .L. , 75 Delvaille, J. P., 245 den Boer, M.L., 105 Dhez, P., 321 Dietz, R.E., 217 Dijkstra, J.H., 245 Dill, D., 75 Dow, J.D. , 10, 111 Doyle, B.L., 177, 186 Dozier, CM., 304 Drahokoupil , J. , 154 Dufour, G,, 208 Eisenberger, P. , 86 Epstein, A. , 245 Fabian, D.J., 108, 205 Faesseler, A, , 60 Feldman, L.C., 284 Finster, J. , 214 Flynn, C.P., 26 Folkmann, F, , 275 Foil, H., 232 Fortner, R. , 183 Franschetti, D.R., 43 Franck, C.P., 319 Freeman, A.J. , 16 Frilley, M., 332 Fuggle, J .C. , 205 Fukuda, Y., 105 Gardner, R.K., 272 Gelius, U., 119, 126 Gel 'mukhanov, F.K. , 53 Genz, H., 256 Geretschlager, M. , 249 Gibbons, P.C., 23, 319 Gilberg, E., 229 Girvin, S.M., 13 Gohshi, Y., 168, 235 Goldstein, H.-E., 238 Gonzalez, L. , 40 Goscinski , 0. , 35 Graeffe, G., 157 Gray, T.J., 272 Green, J.M., 364 Greenberg, J.S. , 180 Gregory, T.K., 211 368 Griesehaber, G., 240 Groeneveld, K.-0., 275 Gupta, R.P., 16 Gupta, S.N. , 166 Gusatinski, A.N. , 269 Haensel, R. , 89 Hagstrom, S.B.M. , 122 Hague, C.F., 208 Hall, J.M., 272 Handel, S.K., 266 Hayasi , T. , 64 Hayasi, Y., 64, 241, 351 Haycock, D., 139 Hoffmann, D.H.H., 256 Hopfield, J.J., 13 Horak, Z.J. , 338 Horie, C, 341 Howat, G. ,- 35 Humberg, H. t 101 Ichikawa, K. , 220 Iguchi, Y., 130 Ishii, T., 116 Jaegle, P., 321, 361 Jacobs, W.W., 177, 186 Jamelot, G. , 361 Jamison, K.A., 272 Jenson, F.E., 189 Johansson, L.I. , 122 Jones, J.B. , 136 Joshi, S.K., 226 Juslen, H. , 157 Kallne, E., 205, 245 Kanski, J., 102 Karlsson, S.E., 122 Karnatak, R.C., 208 Karras, M., 240 Kashiwakura, J., 168, 235 Kasrai , M. , 136 Kauffman, R.L., 284 Keller, F., 310 Keller, J., 316 Kieser, J., 198 Kincaid, B.M., 86 Kirchmayr, H. , 238 Kissel, L., 324 Kiyono,^S.,^241 Klokocnfkova, H. , 154 Komyak, N.I., 248 Kondawar, V. , 148 Kondratenko, A.V. , 53 Kosakow, A. , 57 Kosuch, N. , 60 Krause, M.O., 32 Krieger, A.S., 293 Krishna, V., 151 Kropf, A., 249 Kunz, C. , 19 Kurmaev, E.Z. , 125 Lahdeniemi , M. , 142 Lang, W.C., 108 LaVilla, R.E., 243 Lee, CM., 281 Lee, T.N., 301 Leeper, A.K., 189 Leonhardt, G. , 57 Lewis, M.N., 338 Lichten, W. , 180 Lichtenberg, W, , 174 Lieber, A., 307 Liefeld, R.J., 95, 352 Lindau, I . , 78 Longe, P., 354 Low, W, 256 Lurio, A. , 316 Lytle, F.W., 84 Mahan, G.D., 7 Malmqvist, P.-S., 119, 126 Mande, C. , 148, 223 Mariot, J.-M., 208 Martens, G., 89 Matsukawa, T. , 168 Matthews, D., 183 Mazalov, L.N. , 53 Mehlhorn, W., 329 Meisel, A , 63, 214 Merz, H., 101 McEnnan, J. , 313 McRae, E.G., 217 Miller, D.L., 43, 111 Mokler, P., 275 Mstibovskaya, L.E., 248 Muller, P., 214 Muranaka, T., 241 Nagel, D.J., 304 Nakai, S., 168 Nicholls, C.J., 139 Nigam, H.L. , 151 369 Nilsson, P.O., 102 Nolte, G., 174 Nordgren, J. , 250 Nordling, C, 250 Norris, P.R., 108, 205 Obashi, M. , 168 Oh, S.D., 313 Okusawa, M. , 116 Orlova, E.G., 145 Padalia, B.D., 108 Palumbo, L.J, , 365 Papaconstantopoulos, D.A,, 192 Park, R.L., 105 Paul, H., 249 Pease, D.M., 211 Pendharkar, A.V., 223 Petersen, H. , 19 Petke, M., 57 Pfliegl, R., 238 Pianetta, P., 78 Pireaux, J.J., 119, 126 Platzman, P.M. , 67 Prasad, J. , 151 Pratt, R.H., 281, 313, 324 Presnyakov, L.P., 296 Rabe, P., 86 Rabinovitch, L.G., 248 Radler, K., 54 Rai, S., 347 Rao, P. V., 38 Reed, J., 86 Reed, W.A., 70 Reuter, W. , 316 Richard, P., 272 Richter, A., 256 Rihova, H., 338 Rozet, J, P., 332, 335 Sagawa, T., 116 Salem, S. I. , 160 Sandner, N., 329 Sarode, P.R., 163 Sauder, W.C., 243 Sayers, D.E., 84 Schader, J. , 275 Schliiter, M., 29 Schmidt, V., 329 Schmidt-Bocking, H Schnatterly, S.E. , , 174, 287, 23, 319 289 Schnopper, H.W., 245 Schuch, R., 174, 287 Schule, R., 174, 287, 289 Schwarz, W.H.E., 49 Schweizer, I.G., 145 Schwentner, N. , 89 Segall, B., 202 Senemaud, C. , 133 Sevier, K.D,, 275 Shafroth, S.M., 177, 186 Shrivastava, R.L., 355 Shulman, R.G., 86 Siegbahn, K. , 119, 126, 250 Silfvast, W.T., 364 Silverman, P.J., 284 Sim8nek, A., 154 Singh, S.P. , 355 Siota, Y., 253 Skibowski, M., 89 Slusky, S.G., 23 Sobelman, 1 .1 , , 299 Sommer, H. , 57 Sonntag, B., 19, 54 Sonobe, B.I., 189 Soong, S.C. , 46 Specht, H.J., 287 Spicer, W.E, , 78 Srivastava, K.S., 355 Srivastava, V. , 226 Stern, E.A., 84 Stiebing, K.E., 174 Stodiek, W. , 298 Stolterfoht, N., 278 Sugiura, C. , 168 Sundbom, B. , 266 Suoninen, E. , 142 Sureau, A. , 361 Sutphin, H.D., 307 Suzuki , I . , 235 Suzuki , T. , 72 Svensson, S. , 119, 126 Szargan, R. , 63 Szmulowicz, F. , 202 Tanis, J. A., 177, 186 Tavernier, M., 332, 335 Tegeler, E. , 60 Testardi, L., 88 Thiel, F., 214 Topol, I. A., 269 Tooman, T.P. , 352 Touati, A., 332, 335 370 Tserruya, I., 174, 287, 289 Tsutsumi , K. , 220 Ulmer, K. , 92 Urch, D.S., 136, 139 Vaiio, E., 40 Van Speybroeck, L.P., 245 Viinikka, E.-K., 114, 157 Vincent, P., 180 Vipayavargiya, V.P., 166 Waltner, A.W., 177 Watanabe, T., 341 Watson, L.M., 108, 205 Watson, R.L., 189 Waynant, R.W., 358 Webb, C.B., 307 Weber, W.M., 90 Werner, A. , 89 Wertheim, G.K., 29 Wiech, G., 60, 195 Wolff, H.W., 54 Wood, O.R., 364 Wuilleumier, F. , 329 Yokota, M., 253 Ziem, P., 278 371 ftU.S. GOVERNMENT PRINTING OFFICE:1976 210-801/364 1-3 PE .NN STATE .UNIVERSITY LIBRARIES ADDDD7DTDEm c ]