| OF I 7 . • .. meting S i . . ORNL P 960 : - ! - _ — CO '. . er - . - HISO + 56 La 11:25 114 1.4 ) MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 . .. - - bityь -- 0 0 0 C LITE-P MASTER COPY FEB 1 1 1995 Optical Potentials and High-Energy Inelastic Proton Scattering* . PIAĽ R. M. Haybron Oak Ridge National Laboratory Oak Ridge, Tennessee and -LEGAL NOTICE The report we prepared an accow. of Coronna ponsored work. Nolther the Uulad Status, nor the Commission, nor may pornoo acung on bowall of the Counsalan: A. Makos my wraty armprimatothon, aproceed or lupud, me respect to the accu- rhoy, completeness, or wataloons of the laformasjon catalred in the report, or that the . al may taformation, appunta, method, or procou disclosed to the report was not latring privately owned rechtes or B. Asse ur but with respect to the wool, or for dumugo raculty from the ww of any Information, appunto, method, or poseu disclosed in this report. As wed in the above, parna octag on behall of the Conntastoo" tacludes way ea. ploge or contractor of the coulosban, or sployu ol rocha contractor, to the asteat 'hat' tool omployon or contractor of the Comalestan, or employee of much contractor prepares, dumbrates, or portions now to, u taformettaa parnunal to Ho saploymeal or contract wild the Connlaston, or Me employed with much contractor, This paper was submitted for publication in the opon literature at least months prior to the issuance date of this Micro- card. Since the 1.8.A.E.C. has no evi- dence that it has been published, the pa - per is being distributed in Microcard form as a preprint. Michigan State University East Lansing, Michigan SECA Distorted wave effects reduce inelastic proton cross-sections in the few-hundred MeV range by factors of two or more from the plane wave results. In addition the spin-orbit coupling in the optical potential produces non-negligible effects on the polarization of the scattered proton. The character and magnitude of these effects are determined by the optical potential which in turn is determined from the elastic scat- tering data. These data do not uniquely define the optical potential in general a given set of data can be reasonably well fit with several sets of parameters"). We wish to remark in this note on the sensitivity of the inelastic cross-section to the choice of optical potential. The inelastic cross-sections have been calculated in the distorted- wave impulse approximation as described in ref. 1. Since this requires a knowledge of the free two-nucleon scattering amplitude we have per- formed these calculations at 156 MeV where this quantity 18 readily available. In addition data is available on the inelastic scattering of. protons from 12c at this energy for comparison with our results. We ? .. *Research jointly sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation and by Michigan State University RELIASDD FOR ANNOUVET ginawe. Am . LI MUKHTAR SCIENCE ABSTRACTS E have considered excitation of the 2*, 4.43 MeV and 3, 9.6 MeV levels of 1. évi --. t . * n .- i ... . . . . . . . . * . . Cc. The nuclear matrix elements have been evaluated using the wave functions of Gillet and Vinh Mau" which seem to provide realistic tran- sition densities for inelastic electron scattering”. The cross-section and polarization results for the 2* and 3" levels are shown in figs. 1 and 2, respectively. The experimental errors on the cross-section data from ref. 3 have been taken as .] mb/ster. The curves are labeled by the optical potentials used to calculate the distorted waves. The parameters specifying these potentials are given in Table I. V is the potential obtained by Johansson, et al) from their data at 180 MeV: V19 and 517 are, respectively, volume and surface potentiels obtained in a more recent analysis of these data (rer. 2). The potential strengths at 180 MeV were extrapolated to 156 MeV as in ref. l. The total reaction cross-sectione calculated from the three optical potentials are given in Table II compared to the measured 180 MeV reaction cross- section. The differential cross-section plots in figs. 1 and 2 show that variation of the optical parameters has a rather complicated effect on the small angle scattering. However, from the region of the peak cross- section out to larger angles the major difference among the three com- puted curves is the degree of attenuation which is directly related to the size of the reaction cross-section, op: This result was anticipated in ref. 1 where it was shown that the imaginary portion of the optical potential produces most of the important distorted wave effects at high energies (excluding the forward direction). This requires the use of an optical potential which predicts or accurately. Since the experimental -3- reaction cross-section varies slowly with energy in this region the re- sults in Table II show that none of the potentials employed here are entirely satisfactory. The calculated peak cross-sections are of the correct order of magnitude relative to the data but the peak for both levels occurs at too large an angle. The angular position of the calculated peak is relatively insensitive to the optical potential. For a transition of a given multipolarity the position of the peak cross-section is determined by the effective radius of the nuclear transition density and (to a lesser extent) by the form of the two-nucleon transition amplitude. Comparison of the transition densities used here with inelastic electron data (ref. 5) does not seem to sindicate an incorrect effective radius for either level. This may mean that the Gammel-Thaler phase shifts used here are inadequate and should be repiaced by one of the more current sets which are available. The sensitivity of the inelastic cross-sections to the choice of two-nucleon phase shifts remains to be investigated. The polarization results indicate a relative independence of the optical potential used. This does not mean that tie distorted wave contributions to the polarization is correct here. None of these po- tentials provide a reasonable fit to the elastic polarization. In addition, the spin-orbit parameters which were obtained in fitting the elastic cross-section ar'; poorly determined. This situation will perhaps be improved by a simultaneous search on elastic cross-section and polarization which is being performed here. None of the optical potentials used here seem to be completely adequate for the analysis of the inelastic data. The inadequacies, 3 reflected in the predicted reaction cross-sections and elastic polari- zations, have probably been increased by extrapolation from 180 MeV where the elastic measurements were done to 156 MeV where the inelastic scattering was performer. More accurate analysis would seem to require elastic and inelastic measurements at the same energy, preferably at an energy where two-nucleon data is also available. + The author is indebted to G. R. Satrhler (ORNL) for helpful comments. : . ' . . /% * .. . "" !. . . . . . . - . 2 16 * -5- References 1) R. M. Haybron and H. McManus, Phys. Rev. (to be published). 2) G. R. Satchier and R. M. Haybron, Phys. Letts. 11 (1964) 313. 3) J. C. Jacmart, (thesis, Paris, 1963). 4) V. Gillet and N. Vinh Mau, Nucl. 5.38. 54 (1964) 321. 5) V. Gillet and M. A. Melkunofi, Phys. Rev. 133B (1964) 1190. 6) A. Johansson, U. Svanberg, and P. E. Hodgson, Arkiv Fysik 19 (1961) 541. - - - --r - - - ---- -- --- - ... . . . . . . Lodge Figure Captions Figure 1 - Cross-section and polarization for excitation of the first level of c. The data 18 from ref. 3. The dotted portion of the polarization between 0 and 5 degrees was estimated. . Figure 2 - Cross-section and polarization for excitation of the 9.6 MeV level of 12c. Table: Captions Table 1 - The parameters for the three optical potentials used. The form of the optical potential is given in ref. 2. Table 2 - Comparison of the calculated reaction cross-section for the three potentials to the experimental value measured et 180 MeV. .wer ** . .... . . . .. . . . Table I . - v19 $17 - - - - - - - 18.2 22.1 29.2 -- .902 .827 .452 .413 10.2 0. 15.9 0. 1.19 1.34 19.4 .656 .669 .556 2.62 4.31 4.31 3.51 -1.07 woll .490 1.26 1.33 2.33 Art Table II OB (mb) 199. v19 226. 263 s17 Experiment at 180 MeV 212. $ 5. . . .. - . UNCLASSIFIED ORNI,-- OWG 64-10898 2012, e92c* Eo = 456 MeV + 27, T= 0 AT 4.43 MeV V 19 517 -ned DIFFERENTIAL CROSS SECTION (Mb/steradian) POLARIZATION -0.4 - 0 10 20 30 40 50 0 10 20 CENTER - OR-MASS SCATTERING ANGLE (deg) 30 40 50 Fig. 1. . . UNCLASSIFIED ORNL-DWG 64 - 10897 3.0 9 12clp,pi) 12c* Eo=156 Mev — 3,1 = 0 AT 9.6 Mev V 19 - 517 ------ DIFFERENTIAL CROSS-SECTION (mb/steradian) POLARIZATION . 0 10 20 30 40 50 -0.6 30 40 50 0 10 20 CENTER-OF-- MASS SCATTERING ANGLE (deg) Fig. 2. DA**In ali moramo da 2a traill men inget for minden turibsa v mnoha od thing yu. internationalities END - -- DATE FILMED 2 / 15 /66 . 6 I