. ' .. . . . . W . . , * - : 1 + r - I OFT ORNL P 2437 . I in 37 # U i * 1 . I hope . L . . by 96 este 12 1.4 1.6 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS -1963 ORNL -P-2437 S CONF-660906-22 FORM FACTORS FOR DWBA CALCULATIONS OF THE 34,52, 50cr lºve.cf . : ÜRNI - AEC - OFFICIAL SEP 2 2 1966 REACTIONS LEADING TO ISOBARIC ANALOG STATES" VA ORNL - AEC - OFFICIAL MPIEN CFSTI PRICE by HC $ 1,0-7, MA SL R.Stock, R.Bock, P.vonBrentano, H.H. Duhm Max-Planck Institut für Kernphysik, Heidelberg and T.Tamura, Oak Ridge National Laboratory, Oak Ridge, Tenn. * Y* ** " . .. abstract 54, 52, 50 cr (He,') reactions for 18 Mev 'He was analyzed by DWRA. It was found that, if proper account of the (t.T) interaction is taken in computing the wave func- tion of the picked-up neutrons to be used as form factors, all the derived spectroscopic factors to both Ty and Te states are in good accord with the French- MacFarlane sum rule. Research sponsored joiatly by the U. . Atomic Energy Commission under contract with the Union Carbide Corporation, and by the Max Planck Institut für Kernphysik, Heidelberg, Germany. ORNI - AEC - OFFICIAL RELEASED FOR ANNOUNCEMENT LEGAL NOTICE This ssport mo prepared us an account of Government sponsored work. Neither the Valled Statos, nor the Commission, nor any person acting on beball of obe Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accu- racy, completeness, or usefulness of the information coolained in this report, or what the use of way Information, apparatus, method, or proces disclosed in this report may not infringe privately owed righto; or B. Asames Any lumiliuos wild respect to the use of, or for damages resalung from the un of any information, apparatus, method, or grocess disclosed in a report. As used in the above, "person acting on behalf of the Commission" includes any em- ployse or coolructor of the Comtalsslon, or employee of such contractor, to the extent that such employee or concractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, way Information purrual to Ho employment or contract with the Commission, or his employment with such contractor. ORNL - AEC - OFFICIAL IX NUCLEAR SCIENCE ABSTRACTS . ORNI - AEC - OFFICIAL .ORNL - REC - OFFICIAL FORM FACTORS FOR DWBA CALCULATIONS OF THE 54,52,50ct (ºhe, a) REACTIONS * LEADING TO ISOBARIC ANALOGUE STATES by R. Stock, R. Bock, P. V. Brentano, H. H. Duhm Max Planck Institut fội Kernphysik, Heidelberg and T. Tamura, Oak Ridge National Laboratory, Oak Ridge, Tennessee.- - - . - . . Neutron pickup reactions excite levels with two isoepins in the final nucleus. Starting with a target ground state | T, T_) where I = T, = T. + 1/2 one gets the low lying levels | T-1/2, T, - 1/2) as well as states | T + 1/2, T, - 1/2) which are the isobaric analogues of the low lying levels in the (target minus proton) -system. I E . . . The sum rule limits for the spectroscopic factors are pre- . dicted as 1) ...- + : (1) solo velsi - pols 5/(27 + 1)., sem pols 1/(27 + 1) OFFICIAL "Research sponsored jointly by the U. S. Atomic Baergy Commission under contract ORNI - AEC - OFFICIAL with the Union Carbide Corporation, and by the Max Planck Institut für Keraphysik Heidelberg, Germany. NUO mamma sowie Toyota . .ORNL - KEC - OFFICIAL where T,- T - 1/2 = TG, T, - T + 1/2 - T. + 1 and Wh,) and Tokios are the numbers of neutrons and protons in the orbit b,j of tiie target nucleus. In (p,d) reactions), the values ORNI - AEC - OFFICIAL ....... ....... - - . . tion binding energy is chosen for the bound state. We find the same behaviour for the analogue states excited in f/2 pickup in the 54,52,50cr (He, a) reactions') at Eg = 18 Mev. The spectroscopic factors are shown in Tab. l; the values of .o. He Sme exceed the prediction of : (1) by factors of 1.5 to 3, de- panding on the target isospin. This failure of ordinary DWBA analysis cannot be avoided by inclusion of finite range and nonlocality corrections. A possible solution of this difficulty is given by consideration of the bound state functions to be used as for factors in the DWBA calculations for the T, and T, transitions. Decomposing the target ground state into single nucleon and core configurations with specified isospin, we write .. .. .. .. ... (2). 4. 20 ore de la Termen de * Bras o • Nd/21 .*+2 TRA +Yao1/ CT 'pe -1/2 onde ace TA OPNI - AEC - OFFICIAL ORNI - AEC - OFFICIAL - 3 - ORNI - AEC - OFFICIAL ORNI - AEC - OFFICIAL where c' and c denote respectively the ground states of the (target minus neutron) system and of the (target minus proton) system, while A = T.C is the analogue state of C: the P are the radial parts of the nucleon wave functions whereas n and p contain the spin, angle, and isosp;in parts. The differences of the y can be calculated from an 1sospin dependent optical potential as introduced by Lane), (3) V=V! - , + . + v, (t • ) and leads to the Lane equations * 1 1/2 (aa) { - h 2 + 0 + 0, - Ema}ilna-- 10240 1/2 2 .+ 1 1) U, vt U - 2m E OCJ PC Pos y pc = -1 For the radial part of the neutron configuration c'n Lorry no coupling due to the t • T term occurs and we obtain the usual equation which, however, contains a 180: 20 (ac {- filmy 2 + 0 - Boch - o. The energies are related by BA Bpc - 48. + M M - Bico- - AB - QP,n) where se, is the coulomb displacement energy ORNI - AEC - OFFICIAL ORNI – AEC - OFFICIAL L. ORNI – AEC - OFFICIAL ---ORNL. - AEC - OFFICIAL and Qlp,n) denotes the Q value of the c'(P, n)c reaction. In the DWBA calculation, one has to use or obtained from equation (4a, b) for proton pickup and Yna and Ync, from equation (4a,b,c) for neutzon pickup to t, and T, levels. These form factors replace the separation energy form factors calculated from . ... x2 (5) -5 02 + U - Ep.48.B. - 0 For . For 1-500, all equations (4) have the form 52 - B}Y= 0, and thus the experimentally known separation energy in each channel determines the slope of the radial part in the ex- ternal region. (So one avoids any use of effective binding energy prescriptions) which are wrong asymptotically''). The two prescriptions" given above yield different shapes in the interior and surface region. In the external region they give motor different amplitudes but with the same slopes. In the numerical calculations', we used a volume Woods- Saxon v potential (+ derivative spin-orbit term) and a posi- tive 0- 108AE (r) with both volume and surface derivative forms. The results are entirely different for the wo choices. ORNI - AEC - OFFICIAL ORNL - AEC - OFFICIAL - 5 - ORNL - AEC-OF.CIAL With the volume U,, the solution 4 of (4a,b) and the equations (4c) and (5) are identical because the ordinary shell model volume potential u contains the symmetry term® For the surface potential uze Pra as obtained from (4a,b) is increased in the external region (r) 6fm) by some 2.0-20%, depending on the target isospin. At the same time, the solution of (4c) for the T, bound state differs from that of (5). The adàition of a surface potential corresponds to a change in radius”, as it is seen by the Taylor expansion y f(r=RAR) = V. (r-R) + ARVEOR F(r=R) + ... from which one obtains (6) AR = 4av, F. (V 2A) - = -0.02, - 0.07, - 0.12 for 49,51,53cm. where a is the diffusensess. This T, deper dent reduction in radius leads to a decrease of the form factor in the external region and to a corresponding decrease of the DWBA cross section for the T, states?). In Fig. 1, the solutions of (4a,b,c) are compared with those of (5) for the target nucleus "cr. Since it is really 25 . I the ratio S/So, which comes out too large in the separation energy procedure, the increase of La against 4 mile and the decrease of Unco compared with 4 inches work together to give the desired reduction. The resulting spectroscopic factors are given in Tab. 1; they are rather close to the sum rule ORNI – AEC - OFFICIAL ORNI - AEC - OFFICIAL - mu 9 ORNL - AEC - OFFICIAL ORNI - AEC - OFFICIAL limit. "The preference for a surface isospin potential U, agrees with the results of the DWBA analysis of (p,n) reac- tions between isobaric analogue states). . 1 LL ORNL - AEC - OFFICIAL ORNI – AEC - OFFICIAL LA transport UN : ORNI - AEC - OFFICIAL ORNI - AEG - OFFICIAL wwwo powania References 1. J. B. French and M. H. Macfarlane, Nucl. Phys. 26, 168 (1961). .. ... ... 2. R. Sherr, B. F. Bayman, E. Rost, M. E. Rickey, and C. G. Hoot, Phys. Rev. 139, B1272 (1965). .. on--.. tore in cimethicsson-.. R. Bock, P. David, K. H. Duhm, v. Lynen, and R. Stock, . to be published . • ---- mieli *thay. The inclusion of nonlocality and finite range effects in the S.E. DWBA may reduce the So by about 20 ; see Ref. 3. dovno.. 5. ditints ide R. Bock, P. V. Brentano, A. H. Duhm, and R. Stock, Bull. Am. Phys. Soc. ser. li, li, 625 (1966). tv 6. A. M. Lane, Nucl. Phys. 35, 676 (1962). 7. W. T. Pinkston and G. R. Satchler, Nucl. Phys. 72, 641 (1965). Tema memahami - ...-. r-... -- 8. R. Stock and T. Tamura, to be published in Phys. Lett. (Aug. 1, 1966). 9. F. G. Perey, Phys. Rev. 131, 745 (1963). .-.. .- 10. The decrease of the T, DWBA cross section leads to a T dependent increase of the normalization constant. Alterr.atively; one could fix the T, bound state radius and increase the analogue state radius according to (6). -. ----- . ... 11. G. R. Satchler, R. M. Drisko, and R. H. Bassel, Phys. Rev. 136, B673 (1964). ANTE w -- - - - . E M 4 - ORNL - AEC - OFFICIAL URNI - ABC - OFFICIAL . . i . W 2. - ORNL – AEC-OFFICIAL CRNI - AEC - OFFICIAL Final nucleus (MeV) T 88.e: C.C. exp 8 sum rules . . .. ..-.. - 49 CE 1/2 4.1 - 0.27 3.24 3.51 0.25 *. 4.1 0.24 0.67 5.0 0.68 5.0 4.66 dem , von 4.76 19 1.3 1.33 armen C 51 cm 0.00 2.32 6.6 1.6 7.2def. 7.2 6.60 1.9 0.60 0.8 · 53 cm 9 1.28 1.54 3.36 3.44 3.72 4.54. 5.54 0.5 3.2 1.0 0.37 0.18 0.16 0.18 5.6 0.4 3.1 1.1 0.39 0.2 0.18 0.2 " - - , £ 5.6 7.43 - 10.65 772 1.3 0.44 0.57 Tab. 1 Spectroscopic factors for fq/ neutron pickup in the "50290*cr (Pue, a) reactions. The third column shows the values obtained in the separation energy procedure. The sum rule limit for the T, strength in 51Cr was chosen to normalize the DWBA Column 4 gives the results of the coupled channel calculation. 7 ORNL - AEC - OFFICIAL ORNI - AEC - OFFICIAL e c o ntinuamente podpo ra FIGURE CAPTION Figure 1. Comparison of the form factors obtained for 17/2 neutrous in "cr by separation energy and coupled channel calculations. ORNI - AEC - OFFICIAL 27 ORNL - AEC - OFFICIAL URY POTTITITTTTT faiz neutron in 52 cm ----SE:} for Ty state -.-.-.S.E.,Po-1.25 for Ts --S.E.,ro=1.18/ ground- - 3 . state 102H ON es S SS S= : :------------------------- * - *V2 - - to 2 4 6 8 10 12 14 r (fm) . as . ORNI - AEC - OFFICIAL . . . END DATE FILMED 10/21 / 66 - -. - - -- - - - -- MT FI