Glashausser, C.

Harvey, B.G.

Hendrie, D.L.

Mahoney, J.

McClatchie, E.A.

Saudinos, J.

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Lawrence Berkeley National LaboratoryRecent WorkTitleEXCITATION OF SINGLE NEUTRON HOLE STATES IN Pb207 BY INELASTIC PROTON SCATTERING AT 20.2 MeVPermalinkhttps://escholarship.org/uc/item/7qv8h49kAuthorsGlashausser, C.Harvey, B.G.Hendrie, D.L.et al.Publication Date1968-07-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaRECEIVED lAWRENCE RADIATION LABORATORY SEP 1 7 1968 LIBRARY AND DOCUMENTS SECTION UCR L-18376 . • University of California Ernest O. Radiation Lawrence Laboratory TWO-WEEK LOAN COpy This is a Library Circulating Copy which may be borrowed for two weeks. for a personal retention copy. call Tech. Info. Diuision. Ext. 5545 EXCITATION OF SINGLE NEUTRON HOLE STATES IN Pb207 BY INELASTIC PROTON SCATTERING AT 20.2 MeV C. Glashausser, B. G. Harvey, D. L. Hendrie, J. Mahoney, E. A. McClatchie, and J. Saudinos July 1968 . Berkeley: California .,.~ -,., ~ n ~ r-• -.... -q \At ~ ". DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of Califomia. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. ! . \ I "i·f ;\) Submi tted to Physical Revie'l-r Letters UNIVERSITY OF CALIFORNIA La'l-rrence Hadiation Laboratory . Berkeley, California AEC Contract No. vl-7405-eng-48 EXCITATION OF SINGLE NEUTRON HOLE STATES IN Pb207 BY INELASTIC PROTON SCATTERING AT 20.2 MeV .UCRL-18376 Pre print C. Glashausser, B. G. Harvey, D. L. Hendrie, J. Mahoney, E. A. McClatchie, and J. Saudinos July 1968 EXCrTATION OF SINGLE NEUTRON HOLE STATES IN Ph207 BY INELASTIC PROTON SCATTERING AT 20.2 MeV* C. Glashausser, B. G. Harvey, D. L. Hendr~, J. Mahoney, E. A. McClatchie, and J. Saudinost Lawrence Radiation Laboratory University of California Berkeley, California ABSTRACT UCRL-18372 Differential cross sections for the excitation of the 0.570, 0.894, 1.633, 2.33, and 2.74 MeV states in Ph207 have been measured in inelas-tic proton scattering at 20.2 MeV. Analysis via the microscopic model indicates that core poiarization is important in describing these pre-surned single particle transitions. Differential cross sections for the excitation of single-particle or single-hole states provide a direct test of the microscopic modell ,2 of inelastic pro-ton scattering. Few experimental data exist, however, since the cross sections are generally much smaller than the cross sections for the excitation of collec-tive states. Angular distributions are reported here ~or five such transitions in Pb207 at an incident proton energy of 20.2 MeV. The analysis of these data in terms of the microscopic model indicates that a large part of the observed . 208 cross section is due to excitation of the Ph core. *Work supported by the U.S. Atomic Energy Commission. +Present address: SPNME, CEN - Saclay, France. -2- UCRL-18376 The first five states in Pb207, at 0.0, 0.570, 0.894, 1.633, and 2.33 MeV, are considered to be single 3P1/2' 2f5/2' 3P3/2' li13/2' a~d 2f7/2 neutron holes, respectively, in a Pb208 c.ore. The 9/2+ state at 2.74 MeV has been identified as the [~g9/2,Pb206gs]9/2+ state in (d,p) reactions4 on Pb206 ; recent ana1YSis5 of reactions which proceed via the analog of this state indicates a 610 admixture of , Within the probable errors of analysis, I , the measured spectroscopic factors for excitation of the hole states in single-. nucleon transfer reactions are appropriate for pure si!lgle-hole configurations. Further, no definite evidence from such reactions has yet been found to indicate that the hole strength is split or that Pb208 is not a good closed shell. On the other hand, va1ues7 of B(E2) have been measured for the (2f5/ 2)-1 -(3P1/2)-1 and (3P3/2)-1 - (3P1/2)~1 transitions i~ Pb207 ; an effective charge close toone has been deduced. In addition, while the magnetic moment of the ground state of Pb207 is close to the Schmidt value, the magnetic moments of the 5/2- state8 in Pb207 and the ground state of Bi209 differ considerably fro~ the single-particle limits. Values of B(E2) derived from the measured quadrupole moment of Bi209 and from Coulomb excitation of the (2f7/2)1 proton state in Bi209 give an effective charge of the extra-core proton of about'two or even larger. Contrary to the evidence from transfer reactions, these data indicate there is considerable polarization of the Pb208 core. The present inelastic scattering data were taken with the 20.2 MeV proton beam of the Berkeley 88" cyclotron; no analog-state resonances have been found at this energy.9 Two 3-mm Si(Li) detectors were used; an overall resolution of of about 30 keV was maintained in each. A ratio of peak channel elastic counts to ~earby background of about 104 was obtained 'by careful beam prepar·ation and choice of counter collimators. Because of the small Pb207 cross sections, ./.;-.. ,1" , I '.i ...... .J , .I -3- UCRL-18376 light-element contaminantslO in the target were a major problem; at some angles, these contributed the largest components o~ the experimental error. Absolute cross sections correct to about ±5% were obtained by comparing the measured elas-tic cross sections with optical model predictions. The resulting di~~erential cross sections are shown. in Fig. 1, together with I theoretical curves describied below. Five sets o~ optical parameters were obtained which gave good ~its to the elastic scattering data; they are given in Table 1. The ,set used in calculating the curves illustrated is the ~irst set listed in the table. The microscopic-model calculations assumed a direct (D) projectile-target nucleus interaction o~ the standard ~orm: a Yukawa shape with range 1 F was chosen ~or g( Ir .. 1). The strength o~ the po-lJ tential VI' which allows trans~er o~ spin angular momentum (S) to the target, was set to Vo/3. A non-locality range o~ 0.85 F was assumed in the computation of bound-state wave fUnctions; the curves shown do not include non-locality in the distorted waves. The depth of the bound-state Woods-Saxon well was adjusted to give the correct binding energy; the radius was 1.20 Al/3 (F) and the diffuse-ness was 0.7 F. Antisymmetrization of the projectile with the target nucleons was not included. Predictionsll o~ this model are shown by the dashed curves in Fig. 1. The values of V obtained by normalizing these curves to give the best fit to the o experimental data are listed in Table II. (This is the normalization illustrated in Fig. lB.) Note that the strengths are much larger than the free proton-neutron interaction strength although they are comparable with the values found in other similar microscopic-model analyses in even-even nuclei. l ,12 -4- UCRL-183'76 In computing the (D) cross sections, 8=1 contributions were included only for the minimum orbital (L) and t~tal (J), angular momentum transfer allowed. These 8=1 contributions are substantial for all states except the 5/2- state, but 8=1 contributions for larger values of Land J are not significant. The values of V (D) in Table II are subject to some Uncertainty due to the poor ,0 . quality of the fits. Uncertainties arise also from ambiguities in the parameters ;\ of the optical and bound-state potentials and in the range of the force. However, .further calculations were performed with the four other optical potentialsj the range of the force was varied between 0.'7 and 1.4 F and the radius of the bound-state well was varied between 1.1 and 1.35 Al/3 (F). These calculations indicate that no reasonable change in these parameters will red~ce Vo (D) by more than about 30%. ; These strengths might be lowered significantly if the knockout-exchange amplitudes were included. Recent calculations by Atkinson and Madsen13 indicate that the exchange and direct amplitudes are closely in phase, that the relative cross section is affected mostly at large angles, and that the ratio of total cross sections a(exchange)/a(direct) increases rapidly with L. Assuming a 8er-ber exchange mixture .for a force of YUkawa shape, they have calculated this ratio for can the [(lg9/2)2 Jo+ - [(lg9/2 )2]2+ proton transitions in Zr90. Their results give a rough guide13 to the exchange contributions to the Pb20'7 transitions. They indicate that the values of V might all be reduced to about 100 MeV, . 0 is about tw'ice as large as the free nucleon-nucleon scattering strength. The fact that the values generally found for Vo are so large has led and 8atchler14 to develop a ,way of treating core polarization effects. In which Love their phenomenological model, which does not include exchange contributions, the effects of collective correlations neglected in the nuclear wave functions are included .-I .( / .. .. , . , ' J \' \ ~f -5- UCRL-18376 by coherently adding to the direct form factor a core polarization form factor (CP). The strength of the CP term is proportional to the value of B(EL). In transitions for which B(EL) has been previously determined, e.g. the (3Pl/2)-1-(3P3/2)-1 and (3Pl / 2 )-1 - (2f5/ 2)-1 transitions in Pb207, including theCP term does not add a free parameter to the calculation. For other transitions B(EL) can be determined from th~ inelastic scattering data provided V is fixed. o Calculations of this type for transitions with known ~(E2) are shown by the solid curves in Fig. lAo The quality of the fits to the shapes of the experi-mental distributions are generally improved, although it is interesting that the pure CP fits (the dotted curves) are better. The magnitudes of the cross sec-tions predicted by the microscopic model for these first two transitions are now in reasonable agreement with the data. to the free nucleon-nucleon interaction. The value of V is 60 MeV, which is close o Note that the cross section predicted with the CP term alone is almost everywhere larger than the cross section pre-dicted with the D term alone. The fact that the CP term alone is not suffici-ent, however, indicates that the B(EL) which would be derived from a purely collective-model analysis of these data (without exchange contributions) would not be consistent with the B(EL) derived from electromagnetic data. With Vo fixed at 60 MeV, (D+CP) calculations for the higher states (the solid curves of Fig. lB) determine B(EL) for these transitions; from B(EL), .~ values of the effective charge were deduced. The radial matrix elements (flrLI~ needed to determine eeff were evaluated with the same Woods-Saxon wave functions used in the scattering calculations. These values of (rL) (cf. Table II) are up to three times larger than those used in defining Weisskopf units. 15 For all these higher transitions the CP contribution is substantially larger than the D contribution, but the relative importance of the two terms could change -6- UCRL-18376 if exchange were included. The values of eeff calculated without exchange are shown in Table II. ./ .', -7- UCRL-18376 Table r. Parameters of the optical potential used in the present calculation. f· I V WD V r a rr a r r a 0 0 0 SO so so ~" (MeV) (F) (F) (MeV) (F) (F) (MeV) (F) (F) . 52.62 1.25 0.65 ' 9.69 1.25 0.76 6.38 1.25 0.65 57.24 1.184 0.74 i 8.'38 1.38 0~73 6.31 1.12 0.60 52.14 1.25 0.65 8.62 1.29 0.76 6.38 1.25 0.65 57.52 1.20 0.70 11.27 1.25 0·70 6.37 1.10 0.70 62.71 1.12 0.75 9.28 1.33 0.75 6.3 1.12 0·75 Table II. Strength Parameters. The values Vo(D) were derived without core polarization. -The parameters V 0 (:o+Cp), (rL)-, and eeff were used in the core polarization calculations. The _ p_ar~I?~ter I\~ is 1.2 A1/3 (F) • State L S J V (D) o V (D+CP) o (rII't{R- L "~--c eeff 5/2 - 2 0 2 160 MeV 60 MeV 0.62 1.0e 2 1 2 3/2 - 2 0 2 110 60 0.71 1.0 0 1 1 13/2 + 7 0 7 285 60 0.84 0.73 5 1 6 7/2 - 4 0 4 170 60 0.75 1.0 2 1 3 9/2 + 5 0 5 175 60 1.10 0.75 3 1 4 .' '- ./,-1 :~ -o~ I ()) I 8 ~ t-' I I-' ()) \.)J -J 0'\ -9- UCRL-18376 Figure Captions Fig. 1. (A). Measured cross sections and predictions of the microscopic model. The label D refers to the direct or single particle cross section alone; the label CP refers to the core polarization cross section alone. The (D+CP) calculations include the coherent contributions of each. The normalization of all curves assumes the (D:CP) values of Table II. (B). The solid curves are normalized as in Fig. lAo The normalizations of the D and CP curves are adjusted to give the best fit to the data. -10- UCRL-18376 References 1. N. K. Glendenning and M. Veneroni, Phys. Rev. 144, 839 (1966). 2. G. R. Satchler, Nuc1. Phys. 'lJ., 481 (1966); K. A. Amos, V. A. Madsen, and I. E. McCarthy, Nucl. Phys. Ag4, 103 (1967). 3. G~ Vallois, thesis, University of Paris (1967)~' unpublished; C. B. Fulmer, I! J. B. Ball, A. Scott, and, M. L. Whiten, Phys. ~tter~ 24B, 505 (1967); M. M. Stautberg, J. J. Kraushaar, and B. W. Ridley, Phys. Rev. 157, 977 (1967). 4. P. Mukherjee and B. L. Cohen, Phys. Rev. 127, 1284 (1962); W. Darcey, A. F. Jeans, and K. N. Jones, Phys. Lett. 25B, 599 (1967). 5. N. Auerbach and N. Stein, Phys. Lett. 27B, 122 (1968). 6. G. Muehllehner, A. S. Poltorak, w. C. Parkinson, and R. H. Bassel, Phys. Rev. ~ 1039(1967); W. C. Parkinson, D. L. Hendrie, H. H. Duhm, J. Mahoney, J. Saudinos, and G. R. Satchler, to be published. 7. Cf. o. NathanandS. G. Nilsson, Alpha-, Beta-, and Gamma-Ray Spectroscopy, ed. Kai Siegbahn, (North-Holland Publishing Company, Amsterdam, 1965), p. 601. 8. S. Gustaffson, K. Johannsson, E. Karlsson, and A. G. Svensson, Phys. Lett. 10, 191 (1964). 9. N. Stein, private communication. 10. The contaminants (Na, Si, Al, P, S, and Cl) appear to come from the commercial detergent Teepol that was used to facilitate stripping of the taI'get foils from the glass substrate on to which they were evaporated. .,- ,-' 11. We are grateful to A. D. Hill and P.D. Kunz for makingtneir computer codes available to us. 12. G. R. Satchler, Nucl. Phys. !22., 1 (1967). ., ,) '. -11- UCRL-18376 13. Jay Atkinson and V. A. Madsen, Phys. Rev. Lett. ~ 295 (1968), and V. A. Madsen, private communication. 14. W. G. Love and G. R. Satchler, Nucl. Phys. AlOl, 424 (1967). 15. J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley and Sons, New York, 1952) p. 626. -12-20 Ex=2.74MeV 40 80 120 8. (deg) c.m. Fig. 1 10 2 20 160 10 UCRL-18376 This report was prepared as an account of Government sponsored work. Neither the United States, nor the Com-mISSIon, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, appa-ratus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for Jamages resulting from the use of any infor-mation, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Com-mission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. 

EXCITATION OF SINGLE NEUTRON HOLE STATES IN Pb207 BY INELASTIC PROTON SCATTERING AT 20.2 MeV

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