l-. .3... I r “v .- ' -..., -.. . ~.- 0 -‘ é.' -" h-._ ‘ t V‘-- -; _ -\ .-"“-‘- - ‘ ~ '-- -.-~‘-: .— -Q.-v‘. .-“_ ~ _ A ‘- . -\ ‘-‘ .--_‘ 11“ s..- . — V».-. . .i.~- y... _ .'--§v‘ ‘- “A o.~‘.- _v-“__‘ »-_.-. _ ‘-. ‘A -“ b A ~"- _ . A‘ 5‘. V.. - 11“-- “ v... u ‘ ‘A- '. w a.‘.. ‘__ . u y-A A --.h ‘ .- ‘V Id t; » ‘3 .K c ‘ ~' ”a J v... ' «.__ $."~ . .__ . ' I " \I. a L, . u‘ _. ‘ A" ‘3 5“ “. vu. ‘v \ ‘_. ‘0 -‘ ‘-‘ ‘ ‘ V ‘ ‘Jv .- A. ‘ ‘s— 5.. ~ \_ . y l" ‘1 fl.‘ .- O -A ., u‘$: ., "‘4 ‘\.l .‘ n." ‘- ‘ ‘t - AHA a ‘ \ i V'w v- V §‘. v. F. Jq\"‘h ‘V c..‘ ~ ABSTRACT A HIGH RESOLUTION STUDY OF PROTON INELASTIC SCATTERING 207 208 209 FROM Pb, Pb, and Bi By William Thomas Wagner 207 208 Angular distributions of states in Pb, Pb, and 2098i excited by 35 MeV protons have been measured with a resolution of 5 to 10 keV. Collective model calculations enabled the R-transfers of many transitions to be iden- tified. In 208 Pb, calculations for a number of the observed states were made with both phenomenologically determined and theoretically calculated wave functions. Both central and non-central two-body forces were used in the analysis and the effects of knock-on exchange were accounted for. The large number of observed unnatural parity states permitted the role of non-central forces in these inelastic transitions to be investigated. The states which are strongly populated in both the (p,p') and (e,e') reactions were analyzed in a microscopic theory using the electron scattering form factors. The possibility of excitation of giant magnetic dipole levels was also investigated. 207Pb and 209 In the nuclei Bi the transitions to the identified single particle levels were compared to calcula- tions involving valence orbitals with both central and non-central interactions. The effects of core polarization A, n p on v p‘ ‘T O . ... . .- - .. n... .u-. f/¢§} William Thomas Wagner 5; in excitation of these states were investigated with a microscopic model using an expanded shell model basis. In the framework of a weak coupling model, the transitions to many levels in these odd mass nuclei were compared to excitations in 208Pb. A HIGH RESOLUTION STUDY OF PROTON INELASTIC SCATTERING FROM 207Pb, 208Pb, and 20931 By William Thomas Wagner A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1974 . .<- .. _ 2‘ a v . . r. .3 T. .. .. .. .. . .1 a. C. a: a. . .. .t . ... .. . .2 . . . .. r. .1 . ..C .. ... L» .. .3 .u L y .u .. 2‘ . s u .1 .a .. ... . .. r. ~Z~ L ~ .. .‘ .—— u a .x. ...... s .n u‘.- .n V. Yd . s . .. .2 .: 2. .ng ;. A... . ..- ~ ~“ o n .. - «q‘ ‘n u .u. .‘ ~ ACKNOWLEDGMENTS I am indebted to Dr. G.M. Crawley for the assistance and guidance that he has given. His patience and under- standing have provided sources of inspiration and aspiration. I especially thank him for suggesting this thesis topic. I am also indebted to the entire staff and graduate student population of the Cyclotron Lab. I especially thank Julie K. Perkins for typing this thesis. The kind assistance of Mr. W.F. Steele and Mr. Joseph E. Finck in taking the data is also greatly appreciated. To my parents I owe a large debt of gratitude for the demonstration that satisfaction can be found in performing a job. I am also grateful for the understanding of my two daughters, Michelle and Danielle. I owe much to my wife, Barbara, for her incessant encouragement and understanding for lack of which this thesis would have suffered. Lastly, I acknowledge my debts to Him. ii u--. "-.— u-.. “--— .q‘.' g.-. cu.,. -a.o _ H. ‘ I. WI A v '0 .. ~I . .. I-“ . .1.- ‘ ‘t1. H‘ a. - _ ~_ -‘ in ~. b . A I hu. v. , ‘C "A ,\,A‘ VJ u wk. - "5 ~ 4.“ ‘Q ‘ \. “.‘ \“ — Q.\ “‘1' TABLE OF CONTENTS ACKNOWLEDGMENTS O O O C O O O O O O O I LIST OF TABLES . . . . . . . . . . . . LIST OF FIGURES 0 O O O O O O O O O O 0 INTRODUCTION. . . . . . . . . . . . . PART I. A__2 INTR 08Pb ODUCTION O O O O 0 O O O O O 0 II. EXPERIMENTAL PROCEDURE. . . . . . . . III. IV. PART I. II, DATA 0 I O O O O O O O O O I O O A. Excitation Energies . . . . . . B. Inelastic Angular Distributions . . C. Discussion of the Collective Model . . D. £- transfers and Deformation Parameters . l. The 1- states . . . . . . . . 2. Search for 1+ states . . . . . . 3. The 2+ states . . . . . . . . u. The 3: levels . . . . . . . . 5. The 4 levels . . . . . . . . 6. The 5' states . . . . . . . . 7. 6+ stateS. . . . . . . . . . 8. States with L37. . . . . . . . APPLICATIONS OF THE MICROSCOPIC MODEL. . . A. Comparison with (e,e') for the Strongly Excited States . . . . . . . . . B. Phenomenological Wave Functions . . . C. Theoretical Wave Functions . . . . . CONCLUSION. . . . . . . . . . . . B-—207Pb and 209Bi INTRODUCTION . . . . . . . . . . . EXPERIMENTAL PROCEDURE. . . . . . . . iii Page ii vi vii 11 ll 20 26 30 35 37 39 HO HO HO Ml #1 H2 H2 H8 55 65 68 69 I s A.» -u :5 \ . . ‘A,.& a... . uh A‘ ‘ ~| .Cpc ms 0 “q E E \ \ urn. \hcn “\V . N N s N .s \L x; x v 2.. a . o o a U... .1. kww III. DATA. 0 O O O O O O O O O O O 0 IV. A. U003 THE Excitation Energies . . . . . . Inelastic Angular Distributions . . Discussion of the Collective Model . . fi-transfers and Deformation Parameters for 207Pb. . . . . . . . . . . l. Quadrupole excitations 2. Octupole excitations . 3. States involving L=u . u. States with L=5. . . 5. States with L>6. . . z-trangfers and Deformation Parameters or 20 Bi. 0 O O O O O O O O O H') l. Quadrupole excitations 2. Octupole excitations . 3. Levels with Lzu. . . H. Transitions with L=5 . 5. States with L>6. . . O O O O O O O O O O O O O O O O O O O O 0 Summary of Collective Model Results . . WEAK COUPLING MODEL . . . . . . . Discussion . . . . . . . . . . 207Pb ReSUltS O O O O O O O O C . Coupling to the 3- core state . . . . Coupling to the Egng first 5‘ state. . Coupling to the Pb second 5' . . . Coupling to the 208Pb quadrupole excitation . . . . . . . . . 5. The unresolved multiplet at ”.313 MeV 6. Other possible weak coupling levels . 209 l 2 3 u Bi ReSUltS o o o o o o o o o l. Coupling to the 3- core state . . . 2. Coupling to the 208Pb first 6‘ state. 3. Coupling to the 208Pb second 5- state u. Other possible weak coupling levels . SINGLE PARTICLE STATES AND A MICROSCOPIC MODEL 0 o o o o O O o o o o O O A. B. The States in 207Pb . . . . . . . The States in 209Bi . . . . . . . iv Page 71 71 7a 92 99 99 100 101 101 102 103 103 10H 10” 105 105 106 106 106 116 116 118 118 119 120 120 121 121 122 125 125 126 126 137 Page VI. CONCLUSION. . . . . . . . . . . . . 1H2 APPENDICES . . . . . . . . . . . . . . 1H5 I. Optimum Target Thickness. . . . . . . . 1H5 II. Analysis of the Data . . . . . . . . . 1H9 III. 208Pb Angular Distributions. . . . . . . 152 IV. 207Pb Angular Distributions. . . . . . . 161 v. 20981 Angular Distributions. . . . . . . 171 REFERENCES 0 C I O C O O O O O O O O O 177 -n.-—— .. —. V.- n. . v. 2. r. .‘ ,.. ..., .t r. E v. i .1 I. .H i .H .2 E I... l\ _; C. .1 I. ...n ...n . . . . . . . . . . ... n- . . . . . . . . . . ..n . . . . ..- as T. u ‘e :4 us. 4.; ..~ ~ ‘ Y§ 2‘ Va 5» a.» a: a... \f 2» ”a TABLE II. III. IV. VI. VII. VIII. LIST OF TABLES Energy levels, £0 ransfers, and parameters for 2 Pb. . . . (p,p') collective model results Energy levels, l-transfers, and parameters for 207Pb. . . . Energy levels, fl-transfers, and parameters for 20981. . . . Weak coupling results for 207Pb Weak coupling results for 20981 Spin and parity assi nments for x 51 multiplet in 20 B1. . . Proton and neutron orbits used in the core polarization calculations. Lack of J sub- script indicates both j=£il/2 orbits were used . . . . . . . . . vi deformation deformation deformation the 9/2- Page 12 3M 75 81 112 113 123 136 . _ . .. _.. A; 1.. ~: ._b.. Zn A—. r. *. .H. u-\_ J. Lu ._.... —.. ox; ‘7‘... — . ~u. ~O. .. __ .p u. o 0 ~.. . u v. — — A... A: —~v .\ A Ah» .4.- ‘.:.- a» I: :1.‘ I X E C ax. Fk. .. m ‘ c I kn. ‘II‘ A.» K .6 b« a Q. L. 1.; ... .q .2 ‘ .. . 3 s T. I E .1 . . I: i T T E i C C. so 3. a... «4.0 as. . s P. .. I - T. 3 I Z I E E S .x. 3.1.. a I FIGURE 1. 2. LIST OF FIGURES Page ngical spectrum of protons scattered by 2 Pb. The resolution is about 6 keV . . . 9 Measured inelastic cross sections for 208Pb. The lines drawn through the points are merely to guide the eye and do not represent fits to the data. The excitation energy of the levels is given in MeV. . . . . . . 21 Same as Figure 2 . . . . . . . . . . 23 Same as Figure 2 . . . . . . . . . . 2n Same as Figure 2 . . . . . . . . . . 25 Comparison of the measured elastic angular distribution with calculations described in the text. . . . . . . . . . . . 28 Collective model fits for all identified states. Displayed with the fit is the excitation energy of the state and the deformation parameter, BL, corresponding to orbital angular momentum transfer L . . 31 Same as Figure 7 . . . . . . . . . . 33 Data for those states which have been previously identified as 1‘ levels . . . . 36 Angular distribution for the 6.233 MeV level. The solid lines correspond to calculations done with both central and non-central forces; the dashed curves show results with only a central force. The asterisks indicate calculations including exchange effects. The curves without the asterisks show the direct contribution to the cross section only . . . . . . . . 38 vii .‘4‘0 .. .. ._ ...m a V. .. .» ‘. . I .. .. o 1.1... 2. ..‘ “ma. “1.: .. .._ .. I . ... ._. i... n. .1. C C I... a. E .l I Z - .1 7.1.- an. a... 7. .. 9 I .. u. . a. u. .1 .. .m .. :. ..-.. n... a.” :2 ‘ a: i r .4 a. C... 7. 1... ..._ Ht“ L. a. L... A. L“ 2‘ L. “H .3 .3 .3 .n.. L. a: .1 1: H) .V‘ Y. A: a; A.» .—u NV U} a: ‘2 ‘2 I. 3.1!. a. ._ .. .. _ . ”A .m... x... :1 no a. .. a: C. Q. «A H... a: h.. C. a» $L 4‘ Q.» U.. Cy A\w h _ a m. .0. O O O O I O 0 0 O O O 0 . ... ... - ... ... a .n. s.. a . . x .14 ..u . . . . . . . . . a . . a. . a .4 n.« 2‘ «xx FIGURE Page 11. Results of calculations for the strongly excited states seen in both (p,p') and (e,e'). The lower and upper dashed curves correspond to calculations with and with- out the exchange approximation, respec- tively. The solid curve includes complex coupling effects as explained in the text. . H5 12. The calculations using phenomenological wave functions for the states shown. The meaning of the asterisks is the same as in Figure 10 . . . . . . . . . . . 51 13. Same as Figure 12. . . . . . . . . . 52 14. Same as Figure 12. . . . . . . . . . 53 15. Calculations for the indicated states using theoretical wave functions as cited in the text. The curves are labeled with asterisks as described in Figure 10 . . . . . . . 57 16. Same as Figure 15. . . . . . . . . . 60 17. Same as Figure 15. . . . . . . . . . 61 18. Same as Figure 15. . . . . . . . . . 63 207 208 209 19. Typical spectrum of Pb, Pb, and Bi. Multiplets built on strong levels in 208Pb are apparent in the other spectra . . . . 72 20. Measured inelastic cross sections in 207Pb for which collective model assignments could not be made. The lines drawn through the points are merely to guide the eye and do not represent fits to the data. The echfation energy of the levels is given in MeV O O O O C O O O O O O O O O 85 21. Same as Figure 20. . . . . . . . . . 87 22. Same as Figure 20. . . . . . . . . . 88 209 23. Same as Figure 20 but for Bi . . . . . 89 viii «- -OAuv-g- tout»- .H. .m I.“ 1‘ As» fix.» 0 O -—. n .a p . a.» v. :. v. .2 -». .: g . :: In. mac“ 1 . 5 b Au. l ‘ n“ 2‘ . L. ‘I . .. \ I: V + . v V. : E E x, H. wk . ‘ c. ; ._u v. a. nu .\ ‘ :\ 5.21:1? 2V. my 1 \ ».. .....l C 3 S T. ...s ‘ 1 s I s « I. v. a» T. 2 E x .. U Cx‘d ~‘\ ‘ t 3.; 1:...\.1...; Q. ~:\ its II\ vs : no 3 C FIGURE 29. 25. 26. 27. 28. 29. 30. 31. 32. Comparison of the measured elastic angular distributions with calculations described in the text. . . . . . . . . . . Collective model fits for all identified states in 207Pb. Displayed withe the fit is the excitation energy of the state and the deformation parameter, BL corresponding to orbital angular momentum transfer L. . Same as Figure 25. . . . . . . . . 209 Same as Figure 25 but for Bi . . . . Summary of the collective model results for the three nuclei. The deformation parameter, BL, is plotted against excitation energy for a number of R-transfers. . . Comparison of 208Pb angular distributions with cross sections for weak coupling multiplets in 207Pb built on the indicated 2 8Pb excitation. The curves resul from smooth interpolation through the 20 Pb data for the indicated level. . . . . . . game as Figure 29 but for multiplets in B1. 0 C O O O C O O C O O 0 Measured differential cross sections and valence orbital model predictions for single particle states in 20 Pb. (a) Predictions using a purely central force. The broken and solid curves give the direct (D) and direct-plus-exchange (DE) results, respec- tively. (b) DE results using the code DWBA70. The broken curve gives the predic- tions using a central force only. 'The solid line displays calculations including non-central interactions . . . . . . Measured differential cross sections and core polarization model predictions for single particle states in Pb. (a) The macroscopic core polarization prediction is given by the solid line; for comparison, the broken curve shows the DE valence model. (b) The DE microscopic core polarization results are given by the broken curve. The solid curve shows results using complex coupling. . . . . . . . . . . . ix Page 93 95 97 98 107 108 110 128 132 FIGURE 33. I-1. Page Calculations for the single particle states in 2 9Bi. The meaning of the curves is given in the text . . . . . . 139 The effects of target thickness on resolution . . . . . . . . . . . . 147 n~ :‘ .a. AV T: L. y. a. a»; at Q. to L .. .t ‘. ‘ s 2‘ a u \. ‘ . «x. ». INTRODUCTION The lead mass region has rightly been called an ideal testing ground for nuclear models. Experimentally, the isotopes in this region exhibit a wide range of nuclear behavior. For example, levels corresponding to single nucleon excitations have been identified; states which exhibit properties associated with collective nuclear motion have also been observed. Further, the doubly—closed shell in 208Pb is of such purity that low-lying levels in this nucleus are expected to have a simple theoretical descrip- tion. These facts make a study of these nuclei of great interest and importance. This mass region has been examined previously in a variety of ways. While each of the different reactions and methods used to study nuclei gives a particular kind of information, inelastic scattering probably is sensitive to the broadest range of nuclear properties. Inelastic scattering excites many different configurations including states seen in decay studies, transfer reactions and isobaric analog resonance work. Inelastic scattering can excite large nuclear collective excitations not seen in reactions involving nucleon transfer. Inelastic scattering can initiate large multipolarity transitions and hence I . . . _ . . 0 ‘. .~ .1 a. .fi ... .H. .2 ~. .. .. .2 ... \. rm __ E T. :1 V. Z. :1 .1 ._ ”n ‘. .- [.1\ A .y.. .. a» :. -“ NW .L- Y. L. a: V. 2. .v .. v. .u . . .u 3. s ‘ 1.‘ .. L. .. . s . :_ .... A.» .. .u .u A. v a. a ”A L. , . .. ... . . ... Wu complements electromagnetic processes which are involved primarily in dipole and quadrupole transitions. Experimentally, (p,p') seems an ideal mechanism to study the lead mass region. One search using 28.5 MeV 1’57’70 This study was performed protons has been done. with 25 keV resolution and at sufficiently high bombarding energy so that collective model comparisons could be made. Unfortunately, the theoretical tools for a microscopic analysis were not well developed at the time that data was taken. Theoretical analysis was limited to use of the collective model for identification of angular momentum transfer and to applications of the weak coupling model. 2,58,50,71372 have examined single Other (p,p') studies nuclei in this region and have been limited by resolution or low bombarding energy where compound and direct nuclear effects may be present and where angular distributions involving different angular momentum transfer may not have distinct shapes. Interest in proton inelastic scattering has been renewed by the numerous, recent experimental improvements. Primary among these is the development of ultra—high resolution 19’56 in particle reactions. Energy resolution techniques on the order of 1 part in 10000 has become possible and has opened a new chapter in experimental study. With this reso- lution, weakly excited states very close to other states may be cleanly separated thus permitting analysis without fear of anomalous contributions. Further, the availability of high . .H E .. . 2‘ s. g 0. .sn .. in s. .. . . ... a. u I. — n u Q ~ . .u . . .. .t .1 .1 .. .. V. v” u“ .- V. V. .1. . v Q .a .. ... ... . . y . u .x— o u .s. .: 2» n - A I «an. . s. I 4‘ 1; 1 f. .1 5. .2 a . 2» .2 3 K1 sw‘ .K u V . ‘5. a-v . c A A «c; r. .. I I. L... a... C» «I» ma! Lu T. a. 1 Vs ‘ u 7. \ . » Q. 1‘ an d ‘2‘ a.\ Q- o' ~ -\ :‘ .N» 45‘ :1— ‘ ~ ¥ ‘ nu A. c. s. Q» C v. .v. uh .\ x \ . «l» purity, isotopic material for targets, stable and large current accelerators, and particle detectors with high signal to background ratio strongly suggests that excep- tionally high quality (p,p') data can now be collected. While experimental techniques have improved, the solution to the nuclear problem has also progressed. The knowledge of the nucleon-nucleon forces, the proper models for structure calculations, and the theory of direct reac- tions has increased greatly. The success of structureSl—53 57,60,70,72 and scattering models in the lead mass region makes testing and extension of these methods intriguing. These facts have motivated an extensive study of inelastic proton scattering from the three nuclei: 207Pb, 208Pb, and 209Bi. Both macroscopic and microscopic models will be used in analyzing the data. Emphasis will be placed on analysis of the unnatural parity states. The study divides naturally into two sections: Part A, 208Pb, and Part B, dealing with the other two 208 dealing with nuclei. In the first section, the Pb nucleus is examined in the light of collective and shell models. Part B deals With the odd mass systems and the influence of the 208Pb mire upon the odd particle or hole. Both weak coupling and COPGLpolarization calculations will be presented. Five Appendices have been included. The first two deal with experimental problems and procedure. The last three contain lists of all the measured cross sections, glVen in the center-of-momentum coordinate system. PART A 208Pb . . . ... .. . . . . .1. .T . . ... ... . . .1. : .2 E P“ .. . . I. 2. —. A. . t ~ _ o. o. 2* u. I o 2‘ 2‘ —~‘ V. ~n A. .. . . .. v“ n._ ... H‘ A. .. ». ... .p. C. .~« no)" . . —.. :— 2. ... 2. v. I . . . u/ s . .,. us. . a. .1. V. V. .u h... by L. 2‘ Au. x. .p. ._ A. ”I. .. f. AV ~ . a L. 1. A. . . o. ‘ .hw C O. ‘ ax. ‘. Av ‘ ‘ u.h.. Aw *Q O F s . L. r. A. w.. r. C v. A. .4 to .Q v. a . CL C. A; C. ‘. .vlv. Pv u.. A» C» cs E 1.. ... c. . 1 S . . . .. . :. .. . c. n... . . Lu 2. ‘ J. .r... ... ‘ . s. . a. 1 u a . .. x . .3 a .. a. r. . . .2 h. .1: a. 2. ‘: .... A. 1.. .C C. L» 2‘ L. .lv‘ u: .m. Au» 2. 39 ‘ . N. .~.. .\ .I‘ A. .c. r . - A ¢ . . . . . . . n u g n .A‘ an 5 n u. A. g Y -. aux ~~ .l ‘ M \Yu. H v .su . . ~ .. .n c . ~ . u . . I. INTRODUCTION 208Pb have been l-l7 Nuclei in the mass region about extensively studied both experimentally and theo- retically51-55. Inelastic scatteringl"9 and Coulomb excitation10 have given information about the strongly populated states of many of these nuclei. Decay studies ll-13 and transfer reactions together with isobaric analog lH-l7 have provided information about resonance experiments the microscopic structure of many of the low-lying states. The level prOperties and the microscopic configurations have been intensively studied in nuclear structure calcula- tions. This mass region therefore provides an attractive place where recent developments in inelastic scattering can be applied. The microscopic description of nucleon-nucleus scatter- ing has progressed greatly. After the initial success of the collective model in fitting the angular distributions of the strongly excited states, inelastic scattering was used primarily to obtain Q-transfer information. More recently, since knock-on exchange and the central portion of the nucleon-nucleon interaction are better understood, microscopic inelastic reaction theory can more sensitively probe nuclear prOperties.18 Normal parity transitions permit the testing of wave functions and transition densities of the target nucleus since such transitions apparently depend little on the non-central two-body interactions. Non-normal parity transitions to levels with well determined wave functions allow the two-body Spin-orbit and tensor forces to be studied. Recently, experiments with charged particle reactions at energies of 30 to 50 MeV and resolution better than 10 keV have become possible. This permits the extraction of cross sections and excitation energies for weakly excited states which can be reliably compared with theoretical predictions. A (p,p') study of nuclei neighboring 208Pb allows examination of the nucleon-core interaction. For these nuclei, the effects of core polarization and the applica- bility of the weak coupling model can be determined only after study of 208 Pb has provided a basis for these models. A relatively high resolution proton inelastic scattering experiment1 has been performed at 24.5 MeV bombarding energy with energy resolution of :25 keV full-width-at-half-maximum (FWHM). Spin and parity assignments for the most strongly excited states below 4.7 MeV of excitation energy were made. Lately, analysis2 of the (p,p') reaction at 54 MeV has extended z-transfer assignments to states below about 7 MeV of excitation where 208Pb becomes particle unstable. The resolution was about as-uo keV FWHM. In both studies, experimental angular distributions were compared primarily with the collective model predictions. To date, these represent the most extensive and highest resolution (p,p') studies of 208Pb. ~ 0 ’- "--‘§~A-- o'--.-‘--—: . . . .. . . .2 r. V. I. L. .u .L a. 2. ../. .. .r L. .. ... .. .. .. o C. v. y.. L. CL ‘. ..\ o ¢ ._ .. A. r. . .2 C A. E 2. L. 3 ”A .t .2 a. a. ... :. :. ... c. MM N . . . ”m .. .. A. u.“ ‘. 1.. .1 v. a. h‘. M»: I. .. . .u 2. .2 .. a x . CC 2.. h. o m z. r. E H. a... . . .. :. . . .. .. .. a. c. .. 2. ... 2‘ I. A a .. .. ‘ . A . ‘1 “K. .2 . .. C. v . L. ... A . 2. . . NM. .;.. A u .n. n... W" .r ... «In. .J‘. v ...4.. J... HI...‘ .x. t. ..u. s .. 208Pb(p,p') This paper reports a high resolution study of performed at 35 MeV with energy resolution on the order of 1 part in 5000. Angular distributions at this bombarding energy have more distinguishing features than those at lower energies yet are not so forward-angle peaked as to make identification of small l—transfers difficult. About 150 states with excitation energies up to 7.5 MeV have been experimentally resolved and their angular distributions are presented. Determinations of Q—assignments and deformation parameters as well as comparison with previous measurements are made. Microscopic model inelastic scattering predictions are compared with the data for normal and non-normal parity excitations. The existence of magnetic dipole states is also discussed. II. EXPERIMENTAL PROCEDURE The experiment used the 35 MeV proton beam from the Michigan State University sector-focussed cyclotron and the scattered protons were detected using the Enge split-pole spectrometer. The high resolution data was recorded on Kodak NTB 25 um nuclear emulsions in the spectrometer focal plane. A thin, stainless steel absorber immediately before the emulsion stopped all particles other than protons. The 10 to 15 mil absorber did not significantly broaden the line-width. However, tracks in the emulsions did show slight departures from parallel trajectories. The absorber also ~ . r s Q r.- . . . . « . \A‘ .u. . v .. . . .. . . .l. .1 . ..... Z .. a C .. ... .w. . . ~ u . _ . a . . q. . .. . «H‘ . . V Q 1 ~ F4 o I C C :m i a. H. I C. E. a. C :.. ”a.“ C 9.. ... .a. v. A. 2. L. 7!. .u. . . . ... 3. c. .5 a. .. . :u .. 3 .. 7: ”a v. a v. .... . a. O m... m .. . H .... . n .4. ..¢ u . an. . . § . . a . r4 .... .3 .a. L“ .. .... . s a . .. A.” r . ... ... . . y. . M . 3. o. .. . nu .- 2. %. ... a. . I . . p.. 7:. a .. .. .A. .u ... ”a r. v . 2‘ A4 a. v. o .. . .g. H T. s a Q. ‘- § . . .4. a... um \ s I. § \~< 2. a, . A v a: A. . 99“ Q. .5 \\~ A4. A.. a . s |\ -\‘ decreased the particle energy thus enhancing track brightness. On-line determination of the focal plane line-width using the "speculator" technique of Blosser et_§l,lg was used to optimize the resolution initially and to monitor it during data collection. Targets of about 100 ug/cm2 thick- ness were used throughout the high resolution study and were prepared by vacuum evaporation on a 15-20 ug/cm2 carbon foil with a substrate of l or 2 layers of formvar. The effects of target thickness on resolution are discussed in Appendix I. The plate data resolution ranged from 5 to 8 keV (FWHM) and a typical spectrum is displayed in Figure l. Exposures on the plates were scanned in steps of u mils. To complement the high resolution data, states strongly excited in inelastic scattering were first studied using 20 a single-wire proportional counter in the spectrometer focal plane. A 6.0 mg/cm2 self-supporting foil, made by rolling, served as the target. The lead used in all target fabrication was isotopically enriched to 99.1u% 208 Pb and was obtained from the Oak Ridge National Laboratory. Resolu- tion of about #5 keV allowed cross sections for the first _ + + + + _. 3 , 2 , u , 6 , and 8 levels as well as the first two 5 states to be measured. Both plate and counter data were measured relative to elastic events monitored at a scattering angle of 90° with a NaI(Tl) detector. This angle was chosen since 90° lies near a relative maximum of the elastic cross 208 section for Pb and also gives good separation of protons 1». ’ D . . .33.: almom CM 393cm. cototoxm mm o t O m Km .0 Fe. 3 olmom {b 4.11: covaHOmmh mnH .Am .>o¥ m vsonm mfi mom ha omswppmom wcovoam mo Esmpommm HMUHQ>HII.H MMDme mwmzzz szzclu t 32: 20.8.... c. mmgocm cozozoxm m8 0km s 2.3 0&8 dIHlS WIN h 83d SINHOJ IO elastically scattered from lead and light mass contaminants in the target. The beam current was monitored with a Faraday cup and microampere current integrator. There was _generally good agreement between the two monitoring methods. Absolute normalization of the counter data was done by comparison of the optical model using Becchetti-Greenlees21 best-fit parameters with the measured elastic angular dis- tribution. Comparing the plate data with the counter results thus determined the normalization of the plate data. Absolute normalization of the counter and plate data is believed good to about 5 and 10 percent, respectively. Whenever possible, the more extensive counter results are displayed although both sets of data were measured in the range of 10 to 100 degrees. The counter data was taken with a 1.2 msteradian (20x20) solid angle while all plate data was collected with a 0.30 msteradian (l°xl°) defining aperture. Because nuclei in the lead region have large forward angle elastic cross sections, slit scattering from the entrance slit of the spectrometer can produce high particle backgrounds. For this reason, a narrow edge was machined around the opening of the defining aperture. This thinner portion sufficiently degraded 35 MeV protons to place them well out of the region of interest of the focal plane and also reduced slit scattering. . .. j o .. r. h... . ... I . . . . . ‘ _ ‘0. CE “5 A. has L4 _ . . v . :. A . ... ... ... ... .: .... c. .d ... ..r. ... C "I. ... ... .... ... .. r. ... c. ..... .. .... a. ‘. ... ... A. .1 .. .. .. C . . a. ... ... .. ... .... ... A. T. t .L v. i .... ... ... a. ... C . . . g . .. C S a .L. —. uh "HO ‘. A. C. .... a. S. - u Y. ... .: ..\ u .. s . Q. ... .u... .. .H .. .n .. .. r. a. C . r .. C ... ... ... .... r. ... ... ... ... .. ... ml 5. .1 o .3 .,L h . ... ... x u 2 .. ... ... .... . . ... v. .. ... ... I . . .. be r. .. ... r. 1. . . ... ... ... ... ... .. . a. . . ‘. .. .... ... u . ... . I . . ... ... . . ... ... .... .1. .3. . ... ...\.. ... . .. . .... ...... .. m. ... ...“ .... .. .... ...... z... .... ...z. ...... .. . .... . r. . Z 11 III. DATA A. Excitation Energies Average excitation energies were extracted for the approximately 150 resolved states. For each exposure the Spectrometer focal plane momentum dispersion was determined22 by using the positions, as determined from the plate scan, of reaction products. Clearly resolved states of 208Pb, 16O, and 12C with well-known excitation energies were used in the energy calibration. A few iterations were performed until the input calibration energies agreed with the average predicted energies. The methods used in analyzing the data are sketched in Appendix II. The results for all observed states are tabulated in Table I and the energies used for the calibration are indicated. For comparison the excitation energies determined by previous work are also given. The energies listed are from the results of a Nuclear Data compilation,23 the recent 5H MeV (p,p') experi- ment,2 and an intensive study by Heusler et al.2u of states below about H.5 MeV. As may be seen the final values for the calibration reference levels are in excellent agreement with prior measurements involving (d,py) and (n,n'y) high resolution work. The general agreement with previous deter- minations is good and appears to extend up to about 7 MeV of excitation. Due to kinematic broadening and to the displacements of the focal planes of protons scattered from different mass . ._ C... J .x. x. . h. s . b. . t . Z» —. ._ :— u. .m .w ...~ ~ m. .N H,“ - w. pw<$ .\ o~.~ O “.v_.~ll>—.~— ..H ~ .d I “.....m AW I vav~ i.~a-v>a -$~Hflv..wof.v.~.* .....ZZ ...L...“ ....w.......:..... A.;an~v>..: 3.0. 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K < 0 t 4.0 . .3 u C .u 0... 5:0; .0..-..- s~..§.~llo~ .wa-~’\.\. 13 :m -.0.0. 0000.0 000.0 .0. 000.0 000.00000.0 +0 000.0 000.0 0 000.0 .000.0 0 000.0 000.00000.0 +.00-0. 00.0 0000.0 00 .00.00000.0 00.0 .00.00000.0 -.0.0. 000.0 000.0 000.00000.0 000.0 0 .00.00000.0 .00-0. 000.0 000.0 00 000.0 000.0 .0. 000.00000.0 -.0. 000.0 0-0000 000.00000.0 000.0 -.0 000.00000.0 000.0 .0. 000.. 00 .00.00000.. -.0. 000.0 000.0 0 000.00000.0 .0-0. 0000.. 000.0 0 000.00000.0 .+0. .00.. 000.0 .0. 000.0 000.0 :- 000.00000.0 0A 000.00000.. .00-0. 00.0 000.0 00 000.. 000.0 000 000.00000.0 +.0. 000.0 0000.00000.. 0 000.0 I .0. 000.0 000.0V .0. 000.0 -0000 000.00000.0 0.0.. 000.0 0 000.00000.0 000.. 000.00000.. -0 000.0 -.0. 0000.0 000.0 0 000.0 000.0 0 000.00000.. 000.0 .0. 000.00000.0 +.0. 000.0 000.0 .0. 000.0 000.0 0 000.00000.0 000.00000.. -0 000.0 -.0. .00... 00.0 0-0000 0000.00000.0 0000.0 .0. 000.0000... 0000.0 .0. 000.0000... .+0. 00... 000.0 0 000.0 000.0 0 0000... 00 000 00 000 000 0 000 00 0 0000000 .000-00000 00 .000 0 .000 0003 0000000 00002 00000 00000000000 ..0.0.>0z 00 .0000000oo-.0 00000 ... . . .‘M . .1 . . :0 _. . c. .. .. 0 0 0. 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A 10.1.0012 3.. .5102: .0. . ......QII - 0. .4303. <00. 1M :m 000.0 000.0 .0. 000.0 000.0 0 000.00000.0 . 0. 000.0 000.00000.0 00. 000.0 0000.00000.0 000.0 0 000.00000.0 000.0 0 .00.00000.0 000.0 000.0 0 0000.00000.0 000.0 000.0 0 000.0 000.0 0 000.00000.0 000.0 .0. 000.00000.0 000.0 000.0 0 000.00000.0 0.00.000.0.0 .+0. 000.0 .1 0A 000.00000.0 .-0. 000.0 000.00000.0 .0.0. 000.0 000.0 0 000.00.00.0 .+0. 000.0 000.0 000.0 0 000.00000.0 000.0 000.0 .0. 000.0 000 000 0000.00000.0 - 000.0 000.0 000.0 ml 000.00000.0 0A 000.00.00.0 000.0 .0. 00.0 000.0 .0. 0000.00000.0 000.0 000.00000.0 000.0 0 000.00000.0 000.0 000.0 0 000.0 000.0 0 000.000.0.0 000.0 0 000.00000.0 -0 000.0 0-00 000.00000.0 -0 000.0 000.0 0 000.00.00.0 x x ... x 1. x ..x 00 0 0 00 0 0 0 0 0 0 0 0 0 0 00+ 0 .000-00000 00 .000 0 .000 0003 0000000 00000 00000 00000000000 ..0.0.>00 .0 .UmSCflPGOUII.H mqmmz :m .U®SCHPGOUII.H Mdm“._..n.. ...—...: __..;.... 0 I'll. I’ll)! I'll. II, Illul'\’ m».. o m....~ Z...— ..._ —._:_.0.v I.r|.' .. '1‘"- ['0] III. .IIlIr 4 Aga~ Q In 4 . o 0.34 .«v >5£¢ I 4 3?: .03 u :2 .r... 2;; I~¢§i-~NN \~‘A1o,v'| N ..~.-\ <.\. 16 Hmo.o 0H0.0 0m0.0 Hm0.o H:0.0 mm0.0 0A m00.0 000.0 0H mmm.0 000.0 mm0.0 0m0.0 Amv moo.OHOmo.0 moo.OHHmo.0 000.000:o.0 000.00000.0 moo.OHNmm.0 moo.OHmmm.0 000.000:m.0 0000.00000.0 0000.0000m.m 000.00000.0 000.00m:0.0 0OO.OHme.0 moo.OHHom.0 000.00000.0 0000.000m0.m 0000.00000.0 000.00000.0 000.00000.0 moo.OHHmm.0 m00.oumam.0 m00.0000m.0 m00.owm0m.m moo.00::m.0 0000.000mm.0 :m X .000I00zpm 0000: 00000 :0 mm COflpmaflaEOU x x 0 0 0mm 4 0”0 00 .000 N .000 A.Qnmv>mz :m A X IX 0 0<+ 0 0903 #000090 .00500PCOUII.H mqm:hg 3U. 1"" .ii ‘III'II’III'I”- Ill IVE- Pl‘il" '2. 'i' 4“ In :h'lul'llla I 4 0.0.033 .L 2.03 CL; cus.....fik~ h nN-i 9 VIII I 17 .000000 00000000 0000000000 000 00>0m a 000 00 "0000000szm mfiq+mvmm 0 u 00 m0000 000 .00000 0000000000 000 8000 000000000 000+0000: .000000000 000000000 00000000 0003 H0>000 .m00>00 I0 00 00000 0>0m 000 0:0 000 .0000 0003 0000>000 .0000000000000 0000m00 00 0000000000 00 0000000000 .00 .000 00 mm .000 00 0003 0300>000 5000 0000000 000000 000 000m .00000000000 >m0000 00 0000 00>00 fUQO'U .>02 00 000w0000 00< 000.00000.w 000.00000.0 000.00:mm.0 000.00:mm.0 000.0000m.0 moo.000:m.0 0000.00:o:.0 000.0 030 000.00000.0 000.000:m.0 0000.0000m.0 mu 000.0 m 0000.0000m.0 000.00000.0 0-0000 000.000mm.0 moo.0000~.0 000.0 000 000.00000.0 0000.00300.0 000.0 Amy 000.00300.0 x x A x 0 x Ix 00 0 m 00 0 0 0 m 0 0 0 m 0 0 04+ 0 :m .00010000m mm .000 N .000 0003 0000000 0000: 000nm 00000000500 0.0.0v>0z :0 .005000000II.H m0m-.> ' 1‘ 0 «1V 6 E:»»FL~, EItL h Fir» s 93L “A a n.‘ . O c . 1v Riv fly. I ‘ ' ‘ 9-1411 L ... 1 7‘ F»..tt. 1EEEFEEQ§IEEH LILFELLKL L '1 - u ...l. . u 2 ... 2 .1 2 5V1 PU Ad C ”U C .0 0 .fiU nU. 1 1 011‘ 23 5.383 5.815 5.777 5.317 ‘ 5.632 5.736 '50 1.20 5.888 5.720 5.733 = 5.323 22.0 5' - 5.163 5.370 ' 5.536 ..: 5.763 5.338 '- 111,111111111111 03080800308080030808003080800308080 FIGURE 3.--Same as Figure 2. ‘r- H. 2” 5.366 6.131 " 6.353 ‘ . .. L20 XZ.0 _ 10-2 MAI” , 5.883 8.21H 8.381 8.831 8.8H3 R 11.507 . 2.0 6.082 6.276 6.358 6.658 6.862 0. . _ _ x.50 x.50 _ > x.20 - x.50 -2 ‘ ‘ I 10 6.033 ' 8 888 — 6.313 6.383 ' . 6.876 , 0. . x3. 1‘“ _ I... x.50 10‘2 " ~ _ . .170 6.332 6.523 " 6.720 6.325 111,111 111 111-111, 0 30 60 80 0 30 80 80 0 30 80 80 0 30 80 80 0 30 80 80 FIGURE ”.--Same as Figure 2. 25 01 ' 'II 1x210 I I ' T I I 10-2 1 ‘f!’ 8.8H0 7.17H 7.382 0.1 A .I X.50 11.50 " 10‘2 _ 6.365 " 7.132 7.303 0. _ x.50 x2.0 10‘2 I A _ 8.882 7.218 7.5H8 0.1 .. r .. 1 1‘50 ~ ".50 10‘2I 0.1 10'2 0.1 x.30 3' 1072 , 7.080 10'2 7.11H 7.3H l l L l L _11 " , 1 030808003080800308080 8.188 FIGURE 5.—-Same as Figure 2. C 7n 'f‘I‘ TI ‘4 uJ- o —- 1 oh» ‘7'“ 1— A ,1 utcv 41-» A .4 ,1"--- .‘ {dung-Av- . . ’rrn ‘7'- -.J-4 ..Av ‘ I I nu“--. I ‘ v.4.r., ‘ ‘ Au-‘ .... '0 I, 3 3.: 3r, '3"..1 C . h '0 ‘:v\ d_:' F ‘ ‘ c. nYI "brh‘ x, "‘4 4 "s ‘ h- v 1 b ! ".3-1g‘7". . ‘0‘ 5 ‘ $ ‘ . “ .I‘rr?‘ . 26 do QQEIrepresent theoretical fits to the curves. Gaps in the angular distributions at certain angles are due to obstruction of the peaks of interest by reaction products from the various contaminants in the target. Since the plate results were normalized by comparison to the counter data, normalization errors due to the poorer quality counter resolution should be considered. The first 3- and first and second 5- levels, that is the levels emphasized in the normalization, were completely resolved in both sets of data. In the counter data, however, the 2+, ”+, 6+, and 8+ states were not completely separated from nearby levels. In the counter data, some neighboring states either were partially resolved from the stronger states, as in the case of the 7‘ level being almost completely resolved from the 2+ level, or had cross sections which were negligible compared to the more populated levels. In the latter case, the weaker peaks contributed no more than 5 per cent error to the counter data cross sections for the higher excitation energy levels. C. Discussion of the Collective Model A Distorted Wave Born Approximation (DWBA) angular distribution has a characteristic shape determined by the strengths of each 2-transfer involved in the transition. In turn, the strength of each l-transfer is determined by the strengths of the nonspin-flip and spin-flip modes of ."_- - vnvo -- -.‘pn- v.0--. .-.-v ---..- . _ .- CD-"' - . ...... ., — \ u-v -. a .... .. ..- - ...... _- ‘U 0‘ ‘ A! n — ‘ ...- \— ' Q .. VI .1 .. A‘ _ = " 5. ‘ - ll) .1 \ ~ I n. — 27 excitation. Since 208 Pb has a 0+ ground state, all natural parity transitions can involve only one R-transfer in the direct DWBA theory. For transitions to a natural parity state, knock-on exchange effects at 35 MeV usually preserve the shape of the direct cross section and merely increase the total cross section. For a spherical nucleus such as 208Pb, the collective vibrational model can be used to obtain the characteristic fi-transfer shape and also to give the deformation parameter, BL, which can be related to the rate of electromagnetic decay from the excited state to the ground state. The DWBA collective model uses a deformed optical potential as the form factor for inelastic scattering. The optical potentials are usually obtained from fits to elastic scattering data and a number of sets of parameters for 208Pb in this energy region has been determinedfi’s’g’25 Figure 6 displays the 35 MeV proton elastic scattering angular distribution measured with the wire counter. Also shown are the results of calculations for elastic scattering 208 from Pb using the Becchetti-Greenlees (BG) best—fit optical model parameters21 and also parameters resulting from a search on the data with the code GIBELUMP.26 The search was initialized with the BG values but there was no variation of the BG spin-orbit potential since 35 MeV polarization data was not available. Both the original and fitted sets yield predictions in good agreement with the F(C\ ICCs O.t\tt .11.”... ..H 333.3. 4'13. 28 103: I ' I I F . C I 10", 1 E. ZOBPB ELASTIC DATA 3 .—. L E =35 MeV . c. L p 3 ‘9 03 -—BECCHETTI-GREENLEES é ‘ ----FITTED OPTICAL MODEL 3 g : a . < 100_ 1 b E 1 ‘o _ 3 10_. - E E C I b "\ 4 1 1 1 1 1 0 H0 80 120 9mm. [degrees] FIGURE 6.--Comparison of the measured elastic angular distribution with calculations described in the text. ---. a- . a .n;- a. i \ “DI ~- - . ' a 01-- _ I on». .. - .'--~ . -\' _ A " .- "-‘.1., v \- .P‘Iu... " . ~ ‘n~v (11 (I! 29 data and differing only slightly from one another. Similar results were obtained in searches using real and imaginary geometries of other 208 Pb optical models as initial values and simply adopting their spin—orbit geometries. Two sets of CM DWBA calculations were performed for Q-transfers of 2, ”, and 6 to determine the sensitivity of the BL's to the optical potentials. In one set of calcula- tions, the BG optical model was used for the entrance channel and form factor while the other set used the fitted optical model values. Both sets had identical exit channel parameters. Due to the much deeper surface imaginary well there was a 30 per cent larger total cross section predicted with the fitted parameters than with BG. However, the ratio of cross sections for L=2,”,6 was the same for each set. This corresponds to an overall normalization of the DWBA and has been noted before.2 Because the BG parameters are functions of the particle energy, the energy dependence of the incoming and outgoing distorted waves may be accounted for. Since the asymmetric optical potentials may be used, because the elastic cross section was not measured at larger angles, and because the spin—orbit geometry could not consistently be determined in the search it was decided to use the BG model in all subsequent DWBA calculations. This also made renormaliza- tion of the CM unnecessary. ... ‘,., P.- -v.. 111 ‘73“ v 30 D. £-transfers and Deformation Parameters CM calculations were performed with the code DWUCK27 using the BG optical parameters. Tests involving Q-value dependence of the cross sections indicated little sensi- tivity and a Q=-5 MeV was assumed for each Q-transfer for each calculation. Coulomb excitation was included in the L=2 and 3 cases although only the smaller E—transfer receives notable contribution from this mode of excitation. Integra- tion was carried out to 20 fm and ”0 partial waves were used. The fits to the states are displayed in Figure 7 and 8 and are commented on below. The R-assignments were made by comparing the data with both the theoretical angular distributions and, where possible, the experimental cross sections for states with unambiguous fi-assignments. The BL's, the deformation parameters, were obtained from / Bizoexp oth' Both the BL and Z—transfer assignments are given in Table I for comparison with the measurements of Reference 2. Where possible those states with angular distributions of unidentifiable shape have J1T adopted from the work of Reference 23 or Reference 2”. Table II compares measured deformation parameters of states in 208 Pb that have been studied in (p,p') at many different energies. The deformation parameters appear to be energy dependent. Knock—on exchange does have similar energy dependence. However, as commented above, the optical model used in the CM can also lead to marked differences. 31 FIGURE 7.--Collective model fits for all identified states. Displayed with the fit is the excitation energy of the state and the deformation parameter, BL’ corresponding to orbital angular momentum transfer L. ['7' 32 K. “$5th 83%.. .....knxw .moduma mSKHJ 23.1mm Nmmdnxm wmosué mmoauma madnxm omosumm .... .HSE.‘ 33 .5 mpsmwm mm mamm11.m mmame omfioNHOm ow cm a om_om_om ow om o om~owu q C q _ - om ow om c omuowaom am cm 0 q q u d *4 wWOAuWWm okmdux ) .3 . o. kmoauka . N- ammmuxm . x a Nmk ..u m omfiowfiom ow om o d d - .23.an P r - «- A . u‘ . . s .11 . 0. nQU l A " «v 1 I-I. ,1 3~ A. u a-.. ‘3 .. "’ ‘v "0\ s \ § 8 I. a. . 3 u 1 A . .- h 4 1 . ..- 1 -. 3” TABLE II.-—(p,p') collective model results. EX(¥eV) 2.615 3.138 3.703 3.085 3.323 3.323 ”.610 J 3 5 5 2 3 6 8 E p 23.5a 0.12 0.072 0.033 0.058 0.066 0.057 0.035 30b 0.13 30.3C 0.11 31.0d 0.13 35.0e 0.126 0.058 0.033 0.058 0.067 0.062 0.030 30.f 0.11 30g 0.11 0.053 0.053 53? 0.11 0.055 0.035 0.058 0.063 0.06” 0.033 611 0.038 0.033 0.027 0.053 0.062 0.055 0.033 aRef. 1 bRef. 7 CRef. 9 dRef. 3 ePresent work fRef. 5 gRef. 6 §Ref. 2 1Ref. 8 u .-..a. v ..--.. . an... .11- a :3 o u . u -3... .. -.“ ‘s 41 v 5 in 35 D-l. The 1- states The levels at 3.831, 5.231, 6.261, 6.965, and 7.233 MeV have fairly similar angular distributions, as seen in Figure 9. All are fairly strongly forward peaked and have angular distributions that oscillate together in phase. These levels have been identifiedla’23 as electric dipole levels and the data appears consistent with these assign- ments. 13,15 and non- At energies below 35 MeV both resonant resonantl (p,p') experiments reported states at about 5.505 MeV. A 5.505 MeV state seen in a resonant (p,p'Y) study16 was assigned a spin of l- on the basis of its ground 207 13 indicated state gamma decay strength. Pb(d,py) results a 1- level at 5.506 MeV as did the two neutron transfer study of Reference 12. However, the 5” MeV inelastic proton study2 found an unresolved doublet at 5.515 MeV and assigned a tentative 3- spin. We observe an apparent multiplet at 5.51” MeV which has a large forward angle cross section, like the ”.8”1 and 6.261 MeV states, but is fit well at larger angles by an L=3 characteristic shape. These facts suggest that this excitation is a doublet with dipole and octupole members. States near 5.9” and 6.31 MeV have been seen in (d,pY) measurements13 as dipole levels. A two neutron transfer experimentl2 also tentatively reported 1- levels at 7.176, 7.319, 7.387, 7.”80, and 7.523 MeV of excitation energy. 36 T I T I l ' Eszi.8L+ V 01 «1. V 1"; 1 V 0.1 " EX=S.29 0 ¢ 10_2 “in Q 1 :' Ex=8.281 OJ v 1" V 10'2 ' 'vv 1 Ex=6.965 0.1 5<§$%,Q - an 10 2 9 0., 9 1 ' 15,57,239 0.1 V 'v V i.“ 10‘2 I ' 1 1 1 w 0 30 60 80120150 FIGURE 9.--Data for those states which have been previously identified as 1‘ levels. . .. ,. A Or , ‘- nro, " u I A 1 \ n u 4 8| . ,. Vv. - ..Y “f." 0v. ¢~:. v :0v~.4.. ,, .u“. f‘ ‘- ’a "u ‘- -ll\ ‘A ... f‘ l s V I up ‘9' (1’ (I) l (D 37 Here, there is no marked similarity in angular distributions of levels near these excitations with those of the levels identified above as 1‘. D-2. Search for 1+ states Considerable attention has been given to the search28’29 for magnetic dipole states in heavy mass nuclei. A recent study with 1800 electron scattering29 identified probable M1 transitions to levels at 6.2 and 7.9 MeV. Our data reveals two states which may correspond to the magnetic dipole levels identified in (e,e'). The strength of the state found at 6.233 MeV is given fairly well by a microscopic calculation using the 1+ wave functions of Broglia e£_al.30 (This calculation used the methods described in Section IV-B, below, and included central and non-central forces and exchange effects.) Not only is the magnitude well estimated but the shape is reasonably reproduced, as shown in Figure 10. A level at about 8.01 MeV has a cross section which peaks at forward angles as does the 6.233 MeV state but is unfortunately obscured by contaminants or adjacent 208Pb levels at most angles. This state may correspond to the 7.9 MeV level observed in the electron scattering study and is presumably the AT:1 excitation, the lower excitation 30,31,53 + being ATZO. Theoretical wave functions for l 208 levels in Pb all give ground state transition widths . + of about 2 eV and 80 eV for the first and second 1 levels, 38 I rllnnl l I Illllll 1—9—4 11L LI [1 11 L o 30 so 90 9mm [degrees] FIGURE 10.--Angular distribution for the 6.233 MeV level. The solid lines correspond to calculations done with both central and non-central forces; the dashed curves show results with only a central force. The asterisks indicate calculations including exchange effects. The curves without the asterisks show the direct contri— bution to the cross section only. u *4 1:! h I 7 - vaO-II ...-u .-x Okra ... .... '1‘... v cm... .- o * a Y'- ~u.». _, .. tln A. -‘; A e». ~ ‘1‘“ - . g. a ‘0 e 'I ‘~ “.- v; . - H' ”I’- - I“ . _ .‘I- u..‘ a .s ‘ ~ 0“ s e ,A ..‘2 :‘ "’1 \ _s ‘h N .h AL ~§ 'v‘dV- “ c. D: A I § . ‘1 ‘U a} ’,:.r‘ - u .‘ h .1 39 respectively. The (e,e') experiment reported transition widths of 11 and ”” eV for the 6.2 and 7.9 MeV transitions. The proton data is quite insensitive to mixing of the wave functions whereas the (e,e') excitation proceeds mainly through AT=1 transitions. Calculations with the wave functions of Reference 31 suggests that a 10 per cent admix- ture of the ATZl state into the ATZO state will produce agree- ment of theory with the experimental (e,e') results. This admixture does not affect the calculated (p,p') cross sections if the nucleon—nucleon interaction has a Serber exchange mixture. Thus, the present data supports identifi— cation of the 6.23 and 8.01 MeV levels as magnetic dipole levels. D-3. The 2+ states We have identified six probable quadrupole levels. The well-known 2+ state at ”.085 MeV is a dominant feature of any inelastic proton spectrum. Two nearby states at ”.1”l and ”.159 MeV are also tentatively identified as L=2 states and it seems fairly certain that the excitations at ”.”63, 5.56”, and 6.170 MeV are also 2+ states. The observed 2+ states have about 20 per cent of the total expected strength given by an energy-weighted sum rule (ESR).32 As mentioned previously, states excited in (p,t) and (t,p) studies12 and identified as 2p-2h quadrupole levels were not seen here. r (I) ' I .. 1 v. . .Ar 0 --. . AA A! . “ .. .. -§-- .. v-.‘. n A.- - .._‘- . . .A’ I. ... e . q. ~ 5 u “ (I! ‘u ”0 D-”. The 3- levels Many transitions involving angular momentum transfers of 3 were observed and transition strengths were extracted for them. The first excited state, with transition strength of 39.6 single particle units (SPU), exhausts about 20 per cent of an ESR,32 revealing it as a truly collective state. Totally, the observed 3- excitations contribute about 50 per cent to the isoscalar octupole ESR strength predicted for 208Pb. Further, the observed 3- strength is quite fractionated and many of the levels identified were pre- viously unreported. + D-5. The ” levels A number of ”+ states have been determined. The collective model fits to the well known ”.”23 MeV level and other L=” levels are shown in Figure 7. The angular distributions of the ”.”03 and 6.615 MeV states are fit equally well by L=3 and L=” characteristic shapes so that the R-transfer is not uniquely determined for these levels. The level at 5.689 MeV is quite collective with a transition strength of about 6 SPU. D-6. The 5- states Numerous states were found whose measured cross sections were similar to L=5 collective model calculations. The first two 5- levels at 3.198 and 3.709 MeV are very collec- tive with deformation parameters of 10.5 and 3.6 SPU, yawn. .v'v I ...a- 'I vlhv- 9,. ~ v-' u .. . c‘ ‘. -... ‘ n o ' I . ...A ~.. . ._ - \ Q' ‘ ‘ In; , L11 respectively. The states at 5.”83 and 6.688 MeV have inelastic transition rates of 6.3 and 5.2 SPU, respectively, revealing a rather large concentration of strength at high excitation. The 3.961 MeV level was previously suggested to be a ”- unnatural parity excitation with possible 23 doublet properties. Our assignment of 5- is in agreement with the conclusions of Reference 12 and 2”. + D-7. 6 states Besides the well-known 6+, ”.”2” MeV level other levels with shapes corresponding to L=6 were found. There is some ambiguity in assigning a spin of 6 to the 5.”l7 MeV level as it is probably equally well described by an L=7 shape. The ”.917, 5.”””, and 5.615 MeV levels apparently involve R-transfers of 6 but an exact assignment cannot be made. D-8. States with hi7 Transitions with large R-transfer have angular distri- butions which fall off less rapidly and whose maxima occur at larger angles than those involving small fl-transfer. For bi6 these two features generally make an assignment fairly unambiguous but for 1:7 the distinction is not so clear. The data for the ”.037 MeV level, for example, has a maximum near 60° fit by L=7 or L=8 curves but has a very rapid fall-off so that a JTr of 7— is concluded for this level. Reference 1” has suggested a (7-,6-) doublet at this ‘I‘ <7“ .1. - he ‘~ ‘1 u ... ”2 energy while Reference 12 identified a 7- both supporting our identification. As exemplified by this state and as noted by Lewis e£_al.2 the predicted collective model cross section for large momentum transfer usually under- estimates the forward angle data, the difference between the data and the theory apparently being greater for the high spin cases. This fact and the lack of distinct shapes for states with spins larger than 6 makes z-transfer identification tentative. IV. APPLICATIONS OF THE MICROSCOPIC MODEL A. Comparison with (e,e') for the Strongly Excited States Inelastic electron scattering allows the portion of the proton transition density, important to low momentum transfer (p,p'), to be determined fairly unambiguously. Unfortunately (e,e') gives little information about the neutron motion in nuclear excitations. However, it appears that for collective states the ratio of the neutron to the proton transition density is the same as the ratio of the neutron number to the atomic number of the nucleus.33-35 Bernstein33 has shown this prescription to work well for inelastic alpha scattering. In applying this prescription to (p,p'), we have assumed that the spin-flip and non-central forces contribute negligibly in transitions to the normal parity states. The rtl D -,... . 1~—' 1h .5 cl: II) (I, . l" ... ‘ . ‘-.. .‘_ fi~r A . ”3 JOJ DWBA form factor, F , for a transition to a state of spin J was obtained following Reference 36. Basically, JOJ JOJ N JOJ 3 F = (V + — V ) r dr I pp Z pp where pp is the proton transition density obtained from (e,e'). VJOJ and vggJ are the strengths of the Jth PP of the proton—proton and proton-neutron interactions, multipole respectively. Here, the interactions were effective bound state potentials (G-matrix) obtained from the separated Hamada-Johnston potential. To account for knock—on exchange the zero-range approximation of Petrovich37 was adopted. In this approximation a zero—range pseudo potential is added to each interaction to account for the exchange 36’38’39 have been successful process. Similar calculations in other nuclei. The charge transition densities were obtained from the work of Nagao and Torizuka40 and of Heisenberg and Sick.ul Since the effect of the finite proton size is small in the lead region, this correction was neglected and for each transition the proton density was taken to be the experimental charge density. The only exception was the 6+ level. Since the experimental best fit parameters were not reported”0 the (e,e') data for this level was fit using a transferred-momentum-corrected Born approxima- tion. The density had the radial form .- ”a J-l d r-C 2 ‘1 9:0?) 3 Nr‘ '51-]; (l+exp(—A——) ) where N is related to the B(EJ) for the transition and C and A are the usual nuclear surface parameters. Also, for the 3- level there was some ambiguity in the transition rates. Nagao and Torizuka give a B(E3)=”3.5 SPU while Heisenberg and Sick have used 39.512.2 SPU which was adopted from work of Ziegler and Petersonl‘t2 involving low energy electron scattering data. A recent measurement of Friedrich”3 gives a value of 3”.2i2.2 SPU. (A difference of about 5 SPU leads to about a 30 per cent difference in the (p,p') cross sections for the 3- state.) Here, the transition density of Heisenberg and Sick was used in the calculations for the 3-. Their B(E3) is in good agreement with the 83:39.6 SPU extracted here using the CM (Section III-D-”). The parameters of the transition density for each state considered are given in Figure 11. The first 3-, 2+, ”+, 6+ as well as the first two 5- levels are examined. The results of these calculations are given in Figure 11. The dashed curves show results with (long dash) and without (short dash) the exchange approximation. The solid curve was calculated with a form factor which was the sum of the (real) approximate exchange (e,e') form factor and an imaginary CM form factor. Complex coupling ” The has given improved fits in other studies of (p,p').u strength of the imaginary form factor was obtained by comparing the cross section of a purely real CM calculation ”5 FIGURE ll.-—Results of calculations for the strongly excited states seen in both (p,p') and (e,e'). The lower and upper dashed curves correspond to calculations with and without the exchange approximation, respectively. The solid curve includes complex coupling effects as explained in the text. ”6 10 I I I I I I = 1 I I I I 2+ ° ~. 3" a“ 9.085 [’6‘ . ,9.» 2.815 1_- F ,, \ ° , :1\\:‘ 00cc / \"/\\‘% ' \ ° \\~.~ \fhb \ I \ ~‘. ‘ 01 ‘\ \\ o A=2.93 \\\”: ‘ ' A=2.19 ‘ - - :0 § " C=6.25 ' E C=8.87 \\ , .. B(E3]=39.5 6pu C B[E2)= 8.1 spu 1 A 1 l 1 l 1 _ I I I [ T I I A=2.79 ‘ " \ c=5.90 \ 10-2 B[E'+)=15.0 spu do/dSZ [mb/sr‘] 4 l l l T I T r I I o 5 3.709 01- / on I \ ’1 \o\’°"‘ \‘fQ ' ” \‘w \ \Ow gag A=2.70 \\ 10"2 A: 2 73 \\ - - - C=5.83 \\ C: 858 \ ‘ B[ES]=21.S SPU B[ES]= 7.7 spu 10-31111111111111 0 30 60 90 O 30 80 80 8, m{decrees I. FIGURE 11 ...vv vu‘ov ... .;. .- .F‘A ...-.. Il' (I! ‘\ ’3' ‘- .“_ ”7 with the approximate exchange (e,e') results to obtain an effective deformation parameter. Since the 2+ state is the only one of these states significantly excited by the Coulomb interaction, the solid curve for this state includes both complex coupling and Coulomb excitation. The first 5' state is the only level underestimated by these calculations. Using the data of Friedrich1+3 for this state, a slightly larger estimate can be made but the data is still underestimated. This indicates that the neutron and proton transition densities are not in the assumed ratio of N:Z. Indeed, the wave function used in calculations in Section IV-C has a neutron density larger than N/Z times the proton transition density and gives a better prediction of this state's inelastic strength. For the other levels the slight overestimation is consistent with the use of the zero-range exchange approxi- mation.37 Further, the prescription used for the complex coupling assumes that the processes giving rise to the imaginary portion of the inelastic form factor are as con- structively coherent as the processes leading to the imaginary part of the optical model potential. This need not be true so that the present prescription probably gives an upper limit for the imaginary portion of the inelastic form factor. In conclusion, these results generally support the assumption about the ratio of the neutron and proton motions I; L'S. ~r cod ”A- v” ”8 and the dominance of the central, non-spin-flip forces in collective excitations. The transition to the first 5- state suggests that these assumptions may not always be true. The results also support the validity of the micro- scopic prescriptions that were used. B. Phenomenological Wave Functions This section considers the results of calculations done with the phenomenological wave functions of Heusler and von Brentano.2u of 208Pb data involving particle transfer, gamma-ray, and These authors, using a global compilation (p,p') resonant data, have examined the excitation energy region in 208Pb below about ”.7 MeV. This work has resolved many problems and raised interesting new questions. From shell model arguments, possible coupling schemes, and orthogonality requirements, spin and multi-component wave functions have been determined. The orthogonality conditions permit proton configurations as well as the relative signs of the proton and neutron components to be extracted. How- ever, the orthogonality is only approximate, resulting in some ambiguity in the signs. Microscopic model calculations using these wave functions were performed. Since many of the states examined have unnatural parity, contributions from the non-central forces may be expected to be comparable to those of the central potential. To perform calculations with non-central forces o.“ ...v -vef .. v, .— ...-r .uv4 ..d A\.~ -‘ A u \- H A ”9 the code DWBA70”5 was used. The numerical form of the program prevented use of externally calculated transition densities or the realistic effective interaction used in the (e,e') calculations. The Serber exchange mixture was used for the effective interaction. This effective force ”6,”7 to be a good representation of the has been found phenomenological force determined by fitting definitive reaction data and of the low momentum components of the separated Hamada-Johnston potential. The Serber mixture had strengths of -30:10:10:10(MeV) and the radial form was taken to be a 1 fermi range Yukawa. The tensor force was taken from the works by Crawley e£_gl.u8 and by Fox and Austin“9 and resulted from fitting the crucial (1+,T=0) to (0+,T=l) transition in 11+N(p,p')1”N(2.31 MeV) with a tensor force of OPEP form and with a r2-Yukawa shape. The range was obtained by matching the OPEP potential and the strength adjusted to fit the nitrogen data. This study assumed that the tensor isoscalar portion was zero. The Ef§ force was taken from studies by Fox and Austin}9 in which the spin-orbit potential was obtained by matching the cut-off Hamada-Johnston potential. The radial shape was given by two Yukawas with respective proton and neutron strengths (ranges) of 29.1 and 20.1 MeV (0.577 fm) and -l”96 and —752 MeV (0.301 fm). In all cases considered, the spin orbit force was always dominated by the tensor force and contributed negligibly to the cross sections. ..." “ 50 The harmonic oscillator wave functions used had an oscillator parameter, b, set to 2.”7 fm, a value consistent with 208 Pb(e,e0) results. Exchange is treated exactly in DWBA70. The BG model was used for the distorted waves, the outgoing parameters being adjusted to the proper exit channel energy. The calculations used a 0.15 fm step size and 15 fm integration limit. The results of both direct and direct-plus-exchange calculations are shown in Figure 12 through 1”. An asterisk indicates the direct-plus-exchange cross section. For these microscopic calculations, the results with only central forces are given by the dashed curves while the solid curves indicate results using the complete central+tensor+spin- orbit interaction. The 2- level at ”.230 MeV has both magnitude and shape very well reproduced by the calculations. The central force contribution to the cross section is very weak for this 2- state. The second and fourth 3- states are also shown. The first octupole level at 2.615 MeV has too complex a p-h character to be established phenomenolo- gically. The third 3- is a member of the experimentally unresolved triplet at ”.260 MeV. The theory for the dis- played 3— levels reproduces the shape fairly well but under- estimates the forward angle cross section for the ”.05” MeV state and is consistently low by a factor of 5 for the ”.698 MeV level. 51 0 30 so so 3130 90 6mm [d egr‘Bees FIGURE 12.--The calculations using phenomenological wave functions for the states shown. The meaning of the asterisks is the same as in Figure 10. 52 0.1 “’0 90mm [degrees] FIGURE 13.-—Same as Figure 12. 53 ' 30-0 90 Gem, [degrees] FIGURE l”.--Same as Figure 12. .qn“ 'vUU- ... n a~ .- ....- n .n-n —— - Q nan- .....-- . ‘h- — u... ‘A. ~- A‘ 'vu“ . I ‘AO'. "v .1. cl! ‘1 ( l) ' v N 1 ‘.\ I «I ,;— ."‘- .. . a‘ I H A §“h- . I.“ .‘v;.:‘ 5” The first three unnatural parity ”- states' cross sections are also shown in Figure 12. The first ”- level has a dominant (2g9/2-3pi}2) neutron configuration and has 1”,15,50 been observed in analog experiments and in (d,p) 11’13’17 It corresponds to the first shell experiments. model state arising from breaking the 3pl/2 neutron pair. For this state, the phenomenological wave functions allow a fair reproduction of the data. The experimental angular distribution falls off less rapidly than the theory but the phase is well predicted. The predictions for the second and third levels are both smaller than the data. Both the theoretical distributions for the first two ”- levels are characteristic of an l-transfer of 5 due to the large contribution of the tensor force which favors the higher of the allowed l-transfers. The third ”- level has a cross section underestimated by about an order of magnitude and has a shape quite different from the theoretical pre- diction. The angular distributions for four 5- levels are com- Pared with the theory in Figure 13. The fifth 5- state at ”.260 MeV, an unresolved component of the 3--”--5- triplet, is not shown. (Calculations using the wave func- tions for these three states suggest that the combined Strength can account for about 50 per cent of the observed transition rate.) The data for the collective 3.198 and 3.709 MeV states are stronger than predicted. The third . - 55 5- is also underpredicted while the ”.181 MeV level is well estimated. Predictions for the first three 6- states and the 7- level at ”.037 MeV all underestimate the experimental cross sections while the shapes are reproduced fairly well. This may be seen in Figure l”. The forward angle enhancement of the 7' level can not be reproduced by the theory. In summary, there appears to be a systematic under- estimation of the cross sections using these wave functions. As might be expected, the more collective states cannot be adequately described in a few p-h basis space. Also, the non-central forces apparently enhance the non-normal parity cross section most but in general provide little enhancement for the normal parity states. C. Theoretical Wave Functions In the lead region many shell model calculationsSl-53 have been done with both the Tamm—Dancoff and the Random Phase Approximations (RPA). The success of these calcula- tions is based on the purity55 of the double shell closure in 208Pb. Highly collective odd parity states which have many ph components are generally better described by the RPA. For example, the electromagnetic transition rates are often given accurately with little or no need of effec- tive charges. When comparison is possible, transition densities similar to those measured with (e,e') are often 56 obtained. In this section RPA wave functions for a number of states are used to describe inelastic scattering. Excitations of normal parity were considered first. The wave functions of Gillet gt_al.52 and of Kuo53 were used to predict cross sections for the first two 1-, 2+, 3-, and 7- states, the first four 5— levels, as well as the first ”+ and 6+ excitations. The Gillet vectors were used for the 2+ and ”+ calculations. As an estimate of the single particle strength, the neutron configuration (gg/z-iié/2)--which is prominent in the 2+ and completely dominant in the ”+ first excited states wave functions-- was taken to be the single configuration of the 6+ level. Scattering to the negative parity states was calculated with the vectors of Kuo. In the calculations the same central and non-central forces were used as in the phenom— enological wave function study. DWBA70 was also used and the RPA wave functions were converted to G-vectors (X'=X+Y, Y'=0) for all these calculations. The RPA model space involves only l'fiw ph excitations. This should allow a reasonable estimate for the lower-lying, negative parity states. However, the number of possible configurations leading to even parity states is quite restricted and thus the strong even parity states are not expected to be given well in this basis. Figure 15 shows calculations with the Gillet G-vectors for the lowest lying 2+ states, lying at ”.085 and ”.l”l + . MeV, and for the ” state at ”.323 MeV. The calculations ~CG\IE\ 57 \ :90 J, 1 l 1 J o 30 so so 9cm. [degrees \ I I I l 1 ‘9f‘\. 1 FIGURE 15.-~Calculations for the indicated states using theoretical wave functions as cited in the text. The curves are labeled with asterisks as described in Figure 10. 7v... ...” ‘v ’1‘. 1,— '\- II! (I) ~ .~ ‘3 a n J 58 for the 6+ state at ”.”23 MeV were done with the single configuration mentioned above. The second 2... state cross section is under-estimated by about a factor of two but does have its shape well reproduced. The non-central forces contribute substantially to this cross section even though the excitation is one of natural parity. This is due to the large spin-flip amplitude of the proton (h9/2-hII/2) configuration which is the largest component (0.88) of the wave function. The first ”+ and 2+ levels are underestimated by almost an order of magnitude. Correspondingly, the calculated B(EJ)'s for those states are much weaker than the observed transition rates, as noted previously.52 However, comparison ”0 indicate that for the lower with recent (e,e') results 2+ state an effective charge less than 1 is necessary to produce agreement with the magnitude of the electron form factor. For the ”+ level an effective charge of about 1.8 is required. These results suggest that for the 2+ and probably the ”+ states, inclusion of core polarization effects could bring the theoretical estimate into reasonable agreement with the experimental (p,p') cross sections with- out introducing deformed components into the wave functions. The 6+ level is badly described, the data being about thirty times larger than the prediction. This state is apparently seen in both the (p,t) and the (t,p) reactions 12 at 20 MeV and also in studies of the g9/2 analog 1u,15 resonance. No definite knowledge of its exact structure Z. a . .\~ 59 seems available but it appears complex. These results thus seem consistent. The cross section does display the forward angle enhancement which can be given by the non- central forces, especially in the exchange calculation. Figure 16 displays the results of calculations using the Kuo wave vectors. Both of the l- angular distributions have well estimated strengths but badly reproduced phases. The unusual shape of the calculations for the first 1' is due to the radial extension of the neutron spin-flip trans- ition density beyond the non-spin-flip density. At forward angles, the cross section is then dominated by the spin flip amplitude. Excitation via the Coulomb interaction is not included but should result in approximately a 10 per cent increase in the total cross section for the first state and about a 5 per cent decrease for the second. For the 3' levels, the fits to the angular distributions for both states appear satisfactory. The wave function for the second 3_ is dominated by just a few components but seems to give proper estimation of the inelastic transition strength. As shown in Figure 17, the results for the first two 5- levels are quite dissimilar. The wave function calculated for the 3.198 MeV level gives good predictions for both (PsP') and gamma decay transition rates. On the other hand, the second 5' has a B(E5) roughly one-half the measured Value whereas the (p,p') prediction is 10 times weaker than 60 9cm. [degrees] FIGURE 16.--Same as Figure 15. 61 90mm [degrees] FIGURE l7.--Same as Figure 15. 62 Hm scattering data. The third 5- at 3.961 MeV has a gmor estimate of the shape but the strength of the angular (fistribution is well given. The fourth 5- is underpredicted 1w a factor of 5 and has a somewhat poor agreement in shape. The Gillet wave functions for the first 3- and 5- states gave results smaller than the Kuo calculations and are not shown here. The first and second 7- excitations are also shown. The first of these very high spin states is underestimated by the calculation, especially at the larger angles. The forward angle plateau of the data is lacking in the predicted cross section for the first 7'. The second 7- is given well at forward angles but overestimated at back angles. Transitions to the unnatural parity states were studied using the vectors of Kuo and Figure 18 displays these results for the first three 2- and 6- states and the first, second, and fourth ”_ levels. As in the case of the phenom- enological wave functions, it is most interesting that the transitions to these states proceed only weakly through the spin-flip portion of the central effective interaction. It appears that almost the entire transition to these states ‘comes about through the tensor portion of the non-central forces, the spin-orbit force being negligible for the con- figuraticmm.considered here. There is very good agreement in time cases of the first ”' and the third 6' states. The 63 0 30 80 90 2 30 80 90 30 80 90 90_m_[degrees] FIGURE l8.--Same as Figure 15. .11 ~. ~\ ,,' 6” ”- at 3.919 MeV excitation appears very difficult to describe with either the phenomenological or theoretical wave functions. Comparison of the results of the theoretical with the phenomenological wave functions indicate that the theo- retical vectors give better predictions of the (p,p') transi- tions to the natural parity states, especially in the cases of collective motion. For the unnatural parity states, the phenomenological vectors give perhaps a slightly better prediction of strengths as compared to the theoretical estimates. In summary, the calculations with the phenomenological and RPA state vectors give results that are consistent with the adopted models. Due to the small ph basis, the former set of wave functions can not describe the highly collective states. On the average, however, both sets do well in esti- mating the cross sections for those states with little collectivity and with only a few dominant ph components. For the RPA results, the good agreement between the average of the experimental and the theoretical transition strengths :fixr the weakly excited states is to be expected. The large difference between the predicted and measured cross sections for the.positive parity states is a consequence of the l'fiw space and the one particle-one hole basis used in the RPA 52 structure calculations. The requirement for large effec- tive charges to reproduce the measured B(EJ)'s for these .v' rm” sh um] -,, ... ~u. v... .-., nu a.‘ ‘A 'v (D 65 positive parity states is consistent with the lack of calcu- lated (p,p') strength. As expected, the RPA vectors53 for the lowest-lying, negative parity collective levels give a good estimate of the (p,p') strength and require little or no effective charge. V. CONCLUSION 208Pb has been investigated using high I‘eSOlUtiOn proton inelastic scattering. Angular distributions for all resolved states have been presented and excitation energies have been extracted. Spins, parities, and deforma- tion parameters have been obtained using a collective model fit to the data. These results were generally found to be in good agreement with previous measurements. Microscopic model calculations using theoretical wave functions and phenomenological transition densities and wave functions were compared with the data. The highly collective states were studied with form factors based on (e,e') measurements and a simple model for neutron motion in these collective excitations. With a G-matrix inter- action for the nucleon-nucleon potential, the results were fairly consistent with the data but required complex-coupling “to match the observed strengths. Non-central forces were not used for these calculations and are not expected to contribute significantly to the cross sections. .- ...v ‘7‘ .-.. --.. t ...‘ §_‘ c... 66 The phenomenological wave functions of Heusler and von BrentanoZu were used with an effective interaction including both central and non-central parts to give reasonable descrip- tions for many of the states observed. Although, in general, the calculations underestimate the data slightly the results are encouraging. Angular distributions were also predicted for inelastic scattering using RPA wave functions. The strongly populated odd, normal parity states had cross sections comparable to the theoretical estimates. The cross sections of the unnatural parity states were also described fairly well using these wave functions but were typically underestimated by the calculations. The use of an effective tensor interaction based on the OPEP form, which saw reasonable success in describing transitions in the case of 1”N, appears to work well in the lead region. Continued study of the unnatural parity states promises that more knowledge of the tensor portion of the effective interaction can be obtained. PART B 207Pb and 20981 67 ..1 v. a... 'A. ‘4. ,5 a I. INTRODUCTION Nuclei that are only one or two particles away from a shell closure permit the valence nucleon-core interaction to be investigated. The lead mass region is well suited for such investigation due to the purity of the double 208P shell closure and the knowledge of many states in b. 207 209 This paper reports the (p,p') study of Pb and Bi 208 each of which can be considered as a Pb core with a valence neutron hole or proton particle. Inelastic proton scattering was used to excite a variety of states in these nuclei. Collective, single particle, and apparently complex excitations have all been observed and angular distributions recorded. Experimentally, 207Pb and 209Bi are difficult to study because of the high level density and fractionation of inelastic transition strength. In 208Pb many levels are well separated. In 207Pb or 209Bi, however, weak coupling to core excitations produces a spread of inelastic transi- tion strength among many levels. Often, members of the multiplet are separated from one another or other states by only a few keV of excitation energy. For example, the 3.1 09 MeV multiplet in 2 Bi, apparently arising from the h9/2 57 valence proton weak coupled to the 3.2 MeV 5- vibration in 208Pb, has doublet members separated by less than 5 keV, spans an excitation energy region of only 225 keV, and lies within 15 keV of other states. Such problems necessitate 68 69 the use of ultra-high resolution techniques for separation and identification of multiplet members from other levels. With data of high quality, spin-parity assignments for multiplet constituents and searches for weak coupled states built on high excitation energy collective core states are possible. Aside from the weak coupling excitations, inelastic proton scattering from these nuclei allows study of the single particle and single hole states and of the extent of core polarization in their excitation. Core polarization effects in transitions to the most well known single hole states in 207Pb58”59 209Bi60 and to the 113/2 proton state in have been examined. Here it was hoped to determine 208Pb core and the non-central the importance of both the forces in the excitation of some of these states. Section II discusses the experimental set-up and procedure. The reduction of the data, angular momentum transfer identification, and comparison with previous work are discussed in Section III. Calculations involving the weak coupling theory and the microscopic Distorted Wave Born Approximation (DWBA) are shown in Sections IV and V. II. EXPERIMENTAL PROCEDURE The experiment used 35 MeV protons extracted from the Michigan State University cyclotron with beams on target ranging between l/2 and l microampere, the smaller current being used on the lower melting point bismuth. Protons 209 207 scattered from targets of Bi and Pb were observed using ." Y"“" A- -', .~_-».A .. .. " An.»-,_.. — . nuv va¢-- . “‘ ex» ,- .. "' ‘Hvuv ' O "-'\-~q-. p. “"“‘-—v‘ c a P“ -. n_ . fi‘ "'-v.-. -v‘ I O .h -R- ‘ ‘ F,‘ : ~--..---_~A .. 0““: "w« V'_' .__ '7' Ovtev - A 3" P‘ .. -7'lh‘ V§ . . «‘_ , 'v ~V‘v-p. s4 “ ‘..:— e . A. ‘ . v. ‘ s‘ “ V ‘~1._ " 3Yh.hn "‘¢¢.‘..|— M. "“1— DWI.“ “VL. ~v ‘ - x .,‘._A "I. .. , ‘5‘ l\ . :‘a I ‘ ~ ‘ “~4 kO - .. an \" ‘. Q 11 » s V‘ 1“ d u N "1. I: 'w"- “V\ :K (I) 70 both a wire proportional counter and photographic emulsions in the focal plane of the Enge split—pole spectrometer. The high resolution cyclotron-spectrograph system was used to obtain typical plate data resolution of 5-10 keV full- width-at-half-maximum (FWHM). The plate data spanned the region of excitation energy between about 0.5 and 8.0 MeV. The counter data had a resolution which was detector limited to about 50 keV FWHM and examined the lowest 5 MeV of excitation. Initially, angular distributions were measured using thick lead and bismuth targets and the wire counter- scintillator set-up.20 Protons exciting the low-lying states were generally well resolved with good statistics. Measure- ment of the elastic angular distribution was also made. Comparing the elastic cross sections with the optical model calculations using Becchetti-Greenlees best-fit parameters21 determined the absolute normalization to about 5%. Comparing the completely resolved inelastic states in both plate and counter data gave the absolute normalization of the plate data to about 10%. Whenever possible the better statistics counter data is displayed. The high resolution data was recorded on Kodak 25 Um NTB emulsion with a piece of 0.015" stainless steel shim stock before the plate to enhance track brightness and to absorb heavier mass particles. Spectra were recorded from 10° to 100°. Fifteen angles were recorded for the plate data. Most plate data was taken with a 1° x l° spectrometer entrance slit but some 209Bi spectra were taken with a 2° x 2° 71 slit as a reasonable compromise of resolution and count rate. Before beginning a run, the resolution was optimized using the on-line focal plane line width determination system and dispersion matching.lg Typical spectra of 207Pb and 209Bi are shown in Figure 208 19. Also shown is a spectrum of Pb to allow comparison. 208 The fragmentation of Pb collective states into multiplets is apparent. Many single particle states were resolved and are also indicated. The increase in level density from 208 207Pb to 209Bi is striking. Discrete structure can Pb to be seen up to 6 MeV in the two lead spectra but the bismuth spectrum is essentially a continuum above 5.5 MeV of excitation. Since Bi is monoisotopic, few contaminants were found in the bismuth data, the major ones being oxygen and carbon from the thin carbon foil-formvar backing. The 207Pb targets were made from an isotopically enriched lead sample obtained from the Oak Ridge National Laboratory and was 99.81% 207 208 Pb, 0.13% Pb, and had small amounts of other lead isotopes. The lead targets also had backings. Target thickness was about 100 pg/cm2 and 3 mg/cm2 for the plate and counter studies, respectively. The effects of target thickness on resolution are discussed in Appendix I. III. DATA A. Excitation Energies The excitation energies of the 170 levels observed 207 209 in Pb and the 80 levels seen in Bi are listed in 72 FIGURE l9.--Typical spectrum of 207Pb, 208Pb, Multiplets built on strong levels in are apparent in the other spectra. and 209 Bi. 08Ph 73 1I1]III f'fl\ 1: -\ +/ "\ ~/ / I- (0 1b" 'fi/ .1/ III ma ”$5me >mz ZH >ommzm ZOHH62 mm" m H H >6: mm” m H (:5 oCmfim Hmoam (:5 353m mesa .I 1....2 .... hrs n — h b n P I u 10°” - p p b — n no“ 9” a set is identical. This ambiguity in normalization of the DWBA cross section has been noticed previously. For this reason and because of the lack of polarization and large angle data the BG optical model parameters have been used in all macroscopic and microscopic model calculations in this study. Use of these parameters gives excellent agreement with previous CM analysis of these .nuclei using the (p,p') reaction. In the collective model calculations, the code DWUCK27 was used with ”0 partial waves, integration limit of 20 fm, and integration step of 0.1 fm. Both the real and imaginary parts of the optical model were deformed and, since there is little sensitivity to the reaction Q-value, all calculations were for transitions to states lying at 5 MeV of excitation energy. Coulomb excitation was included in the L=2 and 3 cases but only in the former excitation is the contribution significant. The deformation parameter, BL, was calculated as the square root of the ratio of the experimental and predicted CM cross sections. There was 22 accounting for the initial and final state spins involved. For L greater than about 5 the forward angle CM fits to the data are not good. The data consistently shows forward angle strength not predicted by the CM. This fact and the rather similar angular distributions for L36 makes large L assignments quite tentative. The results for the CM fits are discussed below. The actual fits are shown in Figures 25 through 27 and the 95 FIGURE 25. --Collective 2model fits for all identified states in Displayed with the fit is the excitation energy of Bthe state and the deformation parameter, correspond- ing to orbital angular momenfum transfer L. 96 8828 8 am o o .w -2 mmssuma .o ” mmtmux m u .w -2 W .o w 3 n has": m rmmdnxm w ..w -2 w .e m . . 3 .N sweonma m mwkduxw W M 8m. w N-2 m been; ”- .0 .w s m m .. . -2 u ocean’s “N Fulllv "lull! FIIIIIV Pllllll PHI!!! 'lllllVV rmylvv PHI!" FIIIIVI Fulllv FIIIIII 'fllllll FlllllII F'"" 1 [HI Bow” om ow om o fiesta 8:813" Ne .... 3 so wwosura ormNnxm _ 8316 Ne mssnma K .3 mkmruxm o N10 . 1m ms 0. a em; 9983 meemuxm D NIOA m 03 we assume zmfiuxu omodumu H www.mux . Ne m 3 I . m 3 NNosuNa ortmuxm omSNH om om om o oWSN. om ow om o 1 m N 55me mmtmuxw b -o on N 8983 was" 0 o to n.9, Q 0. . wmodumm E o mmodumm Nmmnuxm kmmrnxm mmosnmm mmmonx 0 -2 N No meosnoa N n Nymruxm . to amoux . -2, m . N-o keosuMa a N 8983 - . :mo .1" m I. o assume a www.muxm armmsnxm . N-o N-o assume n .. .e e 3 Earth”. a, . . O O 00." . . . Ne ameoumu kssuom n 800$ . S . . . . I @8603 E o wmodumm ktmuxm 80an m u .H v s m NIOH assume .02 ossuNa ..S mnemuxu wmmsuxw _ _ h —C 1 Ex=3.510 85:0.025 . 0.1 1: . E E Ex=3.583 E 0.1... 85:0.023 ' , 1 .1 v! 1- Ex=3.820 g 01 a. 85:0.028 ; O 0.1 85:01.10 -2 10 3 . ’1 0. Ex=3.829 1 1 111ml 1 Mind; 111l111l 1 “Ind t =0.018 23‘s 35 10' s! E Ex=3.888 3 1 Ex=0.213 = 8 =0.022 ; 0.1g: 5 1: . E 0. E \“k E 10’2 .- A a x=1.633 ‘ E 0. "L=7 ! Ex=0.270 g 104., 85:0.010 i 97 1 l I l 0'1 I I I 86:0'01'1‘24 is. 87:0.017 0A 310'2 I 3 E =0.360' 3 E =6.170 3 1 x 1 X 31 . 86:0.007 . - V. a r 00 . j, 'v : 0.1 130-2 «i' . E X=6.188 : EX=LU+0LI - 01 37:032.; - ' 1. ' 1. Ex=5.389 g Ex=0.090 3i . Bs=0-027 ;, _ Be=0-009 ; 'v 1' E - | _ ' -I q 0. 1 ”—157 13 E -0 630 3 "33":8 3 tax—0028 3 ' '2 ’ j' 8: ' :7 10 . _____ \_ I E 04 ‘5, E EX-3.857 \ 3 1 0.1 1 0. 3 - L=7: ' V : L , L=8: 9' I -2 ‘ \, 2' -2 2' x=3.901 ‘ E Ex=q.671 E 7 0 89:0.025 ‘ _ 1 - a E -0190 = : ——L=7 3 it. 38:0'018 : ' v "'L=8 7 '2 2' 0.1 \ EEO E I 3 Ex=0.705 3 0.1 \ _ a a E i" 87=0-019 3 89:0.020 g ’ _. ‘7 _ ' -L 10 2 .510 2 1: Ex=0.785 ; £5,633,501 ; 0. - v' E . fl . .5 [ ° 5 - E 10'? " 4’10-2 , 4' x=5_523 1; EX=S.018 3% p7=o_027 I 89:0.021 _ o 0 30 60 90120150 0 30 60 90120150 0 30 80 8012015 FIGURE 26.--Same as Figure 25. Ex=5.039 ., 89:0.021 V 98 omSNH om ow om o .Hmmom 90% pan mm whsmwm mm mEMm11.nm MMDme ems.” om ow om o 0902 cm ow om o NNO.OHNQ me.Mwa .mwmux . N.2 mae.ouna m a. . :~.muxu o wmoauoa _ .-x N Nol . QEEIN mmesuka oNosuoa Nwesuma o mzru was wmo.onna so . x mwtmuxu kmaru u a pk 1.“. . NMO.ONW& O NW010HMQ 81.an . . oKNuJ mok.muxw rmtmux .15 wmosumu 1 ame.mux : N.e_ Tao.ouma rleoumu mmm.~uxm N . 1x .o Ero.ou a Resume ammo m- m . Smduxm Nmn mao.ouna _ , N-o~ as w so _~osuna kreeuns WWW-NHXU TwmnNflXU L h . p _ . 99 deformation parameters and L assignments are listed in Tables III and IV. D. i-transfers and Deformation Parameters for 207Pb 207 The results of CM fits to the Pb data are displayed in Figures 25 and 26. Whenever possible, comparison of the data with angular distributions for levels of known fl-transfer 207Pb, considerable fractionation of the 208 was made. In strength seen in Pb generally occurs. States are dis- cussed in the following sections according to L. D-l. Quadrupole excitations. The states at 0.571 and 0.899 MeV of excitation, ll,63-65,68 previously identified as single particle states, are excited predominantly with L=2. The rate of fall of the angular distributions are well reproduced and the phase of the data is also reasonably well given. These f5/2 and p3/2 neutron hole states have been shown58"59 to have significant contributions from quadrupole core polarization excitations. + . . The 208Pb 2 state at ”.086 MeV 18 apparently spl1t into a doublet with members at ”.103 and ”.l”0 MeV. 1’70 have identified strong quadrupole excita- Vallois et al. tions at ”.090 and ”.125 MeV. Within experimental error, the excitation energies and deformation parameters from that study agree with our values. However, a ”.115 MeV 100 3’61 in (d,p) suggests that a doublet may lie state seen near this excitation energy. Our data does reveal a weakly excited state at about ”.112 MeV which is unfor- tunately seen at only a few angles. When resolved its cross section is less than 5 per cent of that of the ”.103 MeV state. Tentative identifications of states involving L=2 transitions have been made for the states at ”.”22 and ”.527 MeV. Identification of the ”.656 MeV level as L=2 is fairly certain. D-2. Octupole excitations There were many transitions involving L=3 angular momentum transfer. This is to be expected since there are many lp-2h configurations that can arise from the large 208 number of lp-lh octupole configurations in the Pb core. The well known doublet with members at 2.623 and 2.663 MeV dominates any inelastic spectrum and was so intense at some angles as to be unscannable. Both members of the doublet have characteristic L=3 shapes. The ”.3”2 MeV level is believed to be an octupole 1’70 identified a state at excitation. Vallois et al. ”.3”Oi0.015 MeV as being an L=6 level. As there is no state observed in our data within 15 keV of the ”.302 MeV state we conclude that either a doublet is present at that energy or the initial L assignment is incorrect. 101 The level at 5.177 MeV appears to be a multiplet. An L=3 assignment has been made for the strongest member. D-3. States involving L=”. Collective model calculations for states involving L=” transitions were similar to only a few experimental angular distributions. The L=” strength appears concen- trated in only a few levels. The 2.3”0 MeV state, which has been identified as the f7/2 neutron hole state, has an angular distribution with characteristic L=” shape. According to direct DWBA theory this state can be reached only by L=2 or ”. The state at ”.313 MeV has been assumed to be the unresolved weak coupling doublet built on the ”.323 MeV 0+ 208 . 207 vibration in Pb. This Pb state has a small satellite at ”.287 MeV which is weakly excited but has an identifiable L=” shape. D-”. States with L=5. 208 As in Pb there are many states that involve L=5 transitions. In particular, the region from 3.20 to 3.62 MeV of excitation has many weakly excited levels that have Retransfers of 5. The states at 3.583 and 3.620 MeV both have L=5 shapes. The 2.728 and 3.”29 MeV levels were previously assigned70 L=6. We have assigned L=5 for both 61 states. The 2.728 MeV level is seen3’ in (d,p) with 2n=0. 102 20 The neutron configuration of gg/2 coupled to 6Pb(0.00 MeV) 3,11,65,68 which has been suggested for this state is con- sistent with both identifications. A significant fraction of the L=5 strength seen in Pb is not seen in 207Pb. Probably most interesting is 207 208 the lack of L=5 strength in the excitation region of Pb corresponding to the first excited 5- state in 208Pb. This missing strength is discussed in section IV-B, below. Higher excitation L=5 strength seen in 208Pb has not been observed in 207Pb. This may be due to configuration 207 mixing or masking of the strength by other Pb levels. We also noted a similar lack of octupole strength corres- 208 ponding to that seen in high-lying levels in Pb. This probably has the same explanation. D-5. States with L16. A few states apparently involve L=6 transfers. The weak coupling doublet with parentage in the6+ state in 208Pb apparently lies at ”.36” and ”.00” MeV. The 1.63” MeV state which is highly excited in single particle transfersll’63-65’68 is excited in (p,p') by L=6 or 7. Direct DWBA theory allows the transition to proceed through only L=5 or 7. All angular momentum transfer assignments for L=7 or larger are quite tentative. As noted above, this is due to the generally similar shapes of these high 2-transfers. States which possibly involve high spin transfer are found 103 at 3.650, 3.857, 3.901, ”.09”, 0.630, ”.671, 0.705, 0.785, 5.018, 5.039, 5.526, 6.170, and 6.188 MeV. Most of these levels have tentative assignments and many appear to have multiplet structure. E. fl-transfers and Deformation Parameters for 209Bi. The 209Bi(p,p') data displayed in Figure 27 has been compared with CM characteristic shapes. The large level density and the apparent extreme splitting of the strength of 208Pb core excitations made L assignment difficult. In general, the bismuth angular distributions were similar 207 to those of Pb. E-l. Quadrupole excitations. The single particle state at 0.896 MeV (J"=7/2-) seen in the (3He,d)66 and (01,t)67 reactions is populated primar- ily by an L=2 transition although L=0,2,0,6,8 are allowed for transitions to this state. Three distinct quadrupole excitations at 3.981, ”.092, and ”.157 MeV have been resolved. The total deformation parameter for this triplet is about 0.050. Bertrand and 209Bi, reported Lewis,71 in an inelastic proton study of an L=2 group centered at about 3.96 MeV of excitation and With a 82:0.009. These two measurements are in good agree- ment, The 3.981 MeV level has been suggested62 to be an unreSolved doublet. 10” E-2. Octupole excitations. There were a number of states seen with characteristic L=3 angular distributions. Most interesting is the dominant six-member group centered at about 2.6 MeV. This is the well-known multiplet resulting from the h9/2 proton coupling to the octupole vibration at 2.615 MeV in 208Pb. The i single particle level at 1.608 MeV also has 13/2 an angular distribution well fit by an L=3 CM calculation. This state has been shown60 to have a large admixture of the 13/2+ member of the 2.6 MeV multiplet. Other states with L=3 were found at 3.309, 3.803, 3.92”, 3.950, ”.177, and ”.210 MeV. The last two levels show a fairly large concentration of octupole strength in an excitation region where no comparable strength is found in 208Pb. E-3. Levels with L=0. Two low-lying states at 2.766 and 2.956 MeV were observed that previously were seen72 in (p,p') work near 15 MeV bombarding energy. There, the lower state was concluded to be a member of the multiplet built on the 208Pb. The upper state was assigned lowest 5- level in . + . . . a spin of 3/2 . Our data indicates that the cross sections for these states are fit only by the L=0 shape. This is in disagreement with the previous conclusions. 105 A strongly populated group near ”.3 MeV was also observed to have two members with L=0 shapes. The members lie at ”.286 and 0.362 MeV. The ”.001 MeV excitation, which is probably a multiplet, has been assigned L=0. The level at 5.509 MeV may correspond to the L=0 level at 5.20:0.5 MeV observed71 at 62 MeV, but we could not make an assignment of L. E-”. Transitions with L=5. The bismuth spectra have two dominant groups at about 3.13 and 3.56 MeV and with characteristic L=5 shapes. These groups have been identified in other (p,p') studies as L=5 excitations. The 62 MeV work71 extracted deformation parameters of 0.050 and 0.029 for the lower and higher states, respectively. We have obtained total deformations of 0.065 and 0.037 for these transitions. The disagree- ment may arise from problems in background subtraction in the higher energy data. We are in good agreement with the results given in Reference 72. No other L=5 identifications could be made. E—S. States with L36. A few states were identified as having angular momentum 207Pb data, transfer greater than 5. As in the case of the the experimental angular distributions for high i-transfers are difficult to distinguish because of the similar shapes. States at ”.116, 0.301, and 5.131 MeV showed possible L=7 strength. States at ”.011 and ”.532 MeV revealed possible 106 L=8 strength. No L=6, 9, or 10 transitions were found in the data. This might result from the fractionation of core strength by weak coupling. F. Summary of the Collective Model Results. The results of the CM fits are presented in Figure 28. There, the strength for each Q-transfer ranging from 2 to 9 has been displayed according to excitation energy for each of the three nuclei, 207Pb, 208Pb, and 209Bi. It is clear that the distribution of inelastic strength is quite similar in each nucleus. This similarity will be discussed in the next section. IV. THE WEAK COUPLING MODEL A. Discussion It is evident from the spectral plots of Figure 19 and from the deformation parameter verses excitation energy 208 display of Figure 28 that the strong excitations in Pb split into multiplets in 207Pb and 209Bi. The character- istics of these multiplets are that they are centered about the energy of the core excitation, their total strength is about equal to that of the core level, and the ratio of members' cross sections is roughly constant. The cross sections for 208 Pb states, which apparently are the bases on which these multiplets are built, are compared with the angular distributions for corresponding multiplet members in Figures 29 and 30. The similarity between angular distributions of the core state and states in the odd A nuclei is quite striking. 107 one 0 k w m r m m E o b p b P p b b I 165 mom T __ _ T I 1:00 wow I — — .4 I 1+.o.o new mum m k m m r m N 1 o L b pL: » _ 1 Irod . mom 1 , 85 T _ j g. :5 . 1 -rod 7 I. _ mom mod , ;T_ T 1 Irod . new 1 mod m m m m r m N d 0 p p h‘p— » p b I 1:0.0 mow T _ _ __ T I 110.0 T T moN I 1:00 Row mu m m m m r m N d 0 p L L 1— p F _ T _ __ 0. 170.0 1. 1 mom . fi- 1 m. 10.0 _ mom 00.0 r 1 I 1+.0.0 moN 00.0 Vb .chfluHmCMQPIQ mo hmnEs: 0 90m mwpoco COMpMpHoxo pmcflwwm poppoam ma aAm «900080900 soamehommp .Hoaosc @0930 one now myazmma H0005 m>flpooaaoo one mo hemessmll.mm mmstm 32>: >Ommzm ZO_._.<._._oxw w k w m r m N d 0 0 E _ E e _ _ T _ E T I 170.0 mom __ __ _ _ . 1 I 1:00 T T 1 wow. T _ _ 1: _ 1 I 1+.0.0 mom Nu m N m m r m N 0 0 P P — h P b 1 —= q — 1 I ”+0.0 I 100.0 W m0N “mad I ”+0.0 I 100.0 . wow u . 1 5i 1— INa 0 I 1+.0.0 w 1 I 100.0 H moN hNfio Mu m k w m r m N a 0 _ _ _ _ _ _ _ I 1:0.0 . mom 1 . T J I 1.70.0 m0N w0.0 1 — 1 I 110.0 new 1 00.0 mum m m w m r m N H 0 b p b P _ ~— t 5 .1 I 1:0.0 _ fl . mom m0.0 I 1:0.0 T mom 1 0 _ :, I 170.0 mom 00.0 .0 0 93130117808 NOIlVWHOdZ—IO 108 FIGURE 29.--Comparison of 208Pb angular distributions wifli gross sections for weak coupling multipletsin Pb built on the indicated 208Pb excitatimm The curves resglt from smooth interpolation through the 20 Pb data for the indicated.leveL dU/dQ (mb/er] 109 10 r . '._ , . [5 8’ 35.615] 1 2.663 MeV ' 0.1 ' ° 0 1 ‘ § : : 1 ' l' + [2 ‘8 44.323] 0.1 _ "' .2 v 1° - ° - 4.313 MeV 5.321 MeV x0.1 xO.2 10:::::‘: 1:1‘ I" - v , [‘2' ‘8 53.706] , [i ‘86 64.424] V 1 g 3.620 MeV ' 4 404 MeV xlO x5 0.1 ' ' ' 4.364 MeV . 1 % I I I [41: ‘8 7111720] 0.1 I ' m-z 5.526 MeV [§ ‘8’ 741037] 1 1 1 1 1 1 1 1 1, 1 1 1 I 1 I ' [2 (87 76.443] {‘8’ 83:60] 'v'v 0'1 , ' ‘ 4.630 MeV f V' ' 10‘2 ' ' ' ' 6.l88 MeV .0 o 4.671 MeV x 0.2 I I 1 I I fl; 1 I J I I I o l1o 80 120 * 1.0 so 120 ' 0mm [degrees] db FIGURE 29 .... ‘ JIWL.’ I' 1w i dcr/dQ [mb/er] 10 i 4.441 MeV x 9.02 0 ‘10 3.98I MeV xIOO 4.092 MeV XSO 4J5? MeV 1 llllllll 1 IAquI 4 11111111 A 11 I Alllull 0““. [degrees] ‘I' T I [3’69 32...] dU/dQ [mb/er] 2.492 MeV 1 X 0.1 «‘11 0cm. [degrees] FIGURE 30.-—Same as Figure 29 but for multiplets in 2.740 MeV xIO 2.564 MeV x 3 25mme 2.6I7 MeV x 0.3 L 120 .1 gr 1 111L111 11L 1 I lllllll da/dQ [mb/erl n llllull da/dQ [mb/sr) on O I 100. 110 IO u 8 10' IO i 3.I34 MeV e X I00 1 1 3.153 MeV x 30 3.168 MeV x l0 2.986 MeV I x 3 / 1- ' 3.2” MeV I ! i 3.09I MeV x 0.3 H 8 ..- O I 3.038 W L I 1 X o" '10 1 0mm (degrees) I l I I v I Q [3 ® 53.708] 3 1; I e I 3‘ 3.597 MeV 3 x d f i i 3 466 MeV} ! x l0 9 2 - I 3.703 MeV 1° 1 f x 3 1 I r .685 MeV : f . 3 579 MeV‘i x 0.3 E 1 l 1 l 1 ~10 so 120 0mm. (degrees) 2 0 9 Bi. 111 These properties are given by the weak coupling model74 which assumes that a valence particle or hole nucleon interacts only weakly with a collective core excitation. This assumption leads to a number of predic- tions which have been applied to the data assuming a 208Pb core and which are summarized in Tables V and VI. These predictions are also discussed below. It should be noted that Cleary et al.75 have found that weak coupling to excitations in a 210Bi core can equally well describe levels in 209Bi in the excitation energy region between 2.98 and 3.65 MeV. There is, however, no evidence to decide the more proper alternative. According to the weak coupling model, members of a multiplet have cross sections, cm, which are related to the core cross section, 00, by a simple spin-statistics factor. If Jc’ Jw’ and jm are the spins of the core excitation, the weak coupled particle, and a particular multiplet member, respectively, then (2jm+l) 0' = C. m (2Jc+l)(23w+l) Summing this expression over possible multiplet spins predicts that the total multiplet strength should equal that of the core. Due to experimental difficulties, the data for these nuclei were taken at slightly different scattering angles. Since the cross sections vary fairly rapidly with angle, a direct comparison of the total strength 112 .oco ow H0500 >HHMOflvcmpfi .0 AH+.0mvw m0 oapmp 0:9 memHQSOU Um>a0mmscs pom Aa+fibmvflmN "Sam mmpmcm pmvnmwmz cwmmm 00.0 00.0 +N\0H.+0\0H 00H.0 000.0 000.0 000.0 000.0 0 00.0 00.0 +N\ma.+m\ma 000.0 000.0 000.0 000.0 000.0 0 00.0 00.0 +0\0 000.0 00.0 m0.H +N\0 H00.0 000.0 000.0 000.0 000.0 m 00.0 00.0 IN\0H, 000.: 00.0 00.0 IN\0H 000.0 000.0 000.0 000.: 000.: 0 00.0 H0.H IN\mH 000.: 00.0 00.0 IN\H 000.0 000.0 000.0 000.0 000.: 0 00.0 00.H IN\0.IN\0 000.: 000.0 000.0 0H0.0 000.0 0 00.0 00.0 IN\0 000.: 00.0 00.0 IN\0 00H.: 000.0 000.0 000.: 000.: N 00.0 00.0 +N\0H 000.: 00.0 00.0 +N\mH 000.0 000.0 000.0 000.: 000.: 0 00.0 NH.H +N\HH 000.0 00.0 00.0 +0\0 000.0 000.0 000.0 000.0 000.0 0 00.0 00.0 +m\0 000.0 00.0 00.0 +N\0 000.0 00.0 NH.0 000.0 000.0 0 A>mzv A>mzv “>020 .n .n H $900 000000 0.0 .m A.m00400%. Ampoovqa emmzm m g .nm pom pom m#H:mm& mafiamdoo xm0311.> mqmmzv A0020 A>mzv oapmm :00 0m Aflmvmqmwfi Amsoovqm Mmmzm whoom ed .0000 90m meadmms mafiaasoo M00311.H> mqm0pmvcmp £0 apmcmhpm HMpOp >s0> mam mpcwacwflmmm cfiam may msmmmcmswla 0m0£# 90m A H AH+.0000 a a "65m >msmcw w mam: can “0+.000.mN e p: . . mm 00.0000.0 10\0 000.: 10\0H.10\HH :0.0000.0 .10\0.10\H 000.: IN\0H 00.0400.H 10\0H.10\0 000.: 000.0 000.0 000.: 000.: a: 00.0000.0 10\0.10\0 000.: :0.0Hm0.0 10\0H 000.: 00.0HHH.H 10\HH.10\0 000.0 000.0 000.0 000.: 000.: 00 A0020 A>mzv A0020 1n 1n 900 00000 0.0 .m “.mvmqmwfi Ameoovqm mmmzm m m 4 .Umdcflvaooll.H> mqm0.6) amplitude neutron (g9/2- pi}2) component. Thus, the inelastic strength for excita- tion of the core 5' level is severely hindered by the missing pl/2 strength. 208 B-3. Coupling to the Pb second_5- state We observe states at 3.583 and 3.620 MeV which are definitely L=5 excitations and whose summed strength agrees fairly well with the core-particle model. However, the relative intensities are not in good agreement with the predictions. Since a number of other L=5 states lie nearby, this disagreement may have a possible explanation in the configuration mixing of these levels. 119 Reference 70 reported states at 3.575 and 3.615 MeV excitation for which R-transfer assignments could not be made. Alster79 reported L=5 excitations in 207Pb near 3.u and 3.7 MeV that have combined strength equal to that 208 - Pb 52. to support a weak coupling configuration for these two of the Thus, inelastic scattering results tend levels. 208 B-u. Coupling to the Pb quadrupole excitation. The levels at H.103 and H.1H0 MeV are excellent candidates for weak coupling members of a multiplet with 208Pb. The parentage in the 4.085 MeV 2+ excitation in inelastic transition rates are in good agreement and the intensities agree fairly well with the weak coupling model prescription. Alster79 detected 100 per cent of the core cross section in his (d,d') study and Vallois 70 reported an intensity identical to that of the et al. core but observed relative population of the levels not in agreement with the theory. 120 B-5. The unresolved multiplet at H.313 MeV Although there were no experimental indications of multiplet structure for this level we conclude that the H.313 MeV state corresponds to a weak coupling doublet 208Pb. Other studiesl’70’79 . + . built on the H level in reported a single level at this energy and observed a cross section equal to that of the core state. We also observe the same strength as that of the core vibration so that a doublet assignment for this level seems fairly certain. B-6. Other possible weak coupling levels 208 + . The 6 (H.H2H MeV) and the 8+(H.610 MeV) in Pb are both fairly strongly excited in (p,p') and could be 207 207 expected to lead to multiplets in Pb. The Pb levels at H.36H and H.HOH MeV, with L=6, and the levels at H.630 and H.671 MeV, with L=8, have relative intensities and summed cross sections in agreement with the weak coupling model predictions. 207 208 Although L=7 levels observed in Pb and Pb have tentative spin identification it seems that multiplets with parent 7' core states have been found. The total strength and location near the core excitation energies suggests identification of these levels as weak coupling 208 states. The lowest 7- state in Pb, at H.037 MeV, leads to two levels at 3.901 and H.190 MeV in 2mph. The summed strength is slightly less than that observed in 121 the core and the relative intensities are in fair agree- ment with the model. The 7‘ levels in 208Ph at 5.720 and 6.HH3 MeV may correspond to degenerate doublets in 207Pb at 5.526 and 6.188 MeV. However, the 207Pb states are separated from the excitation energies of the corresponding core states by a much larger energy gap than the other levels dis- cussed above. The strength of these levels is essentially equal to that of the core states. The large energy separation and the uncertain L assignments, however, makes identification of these levels as weak coupling multiplets quite tentative. Lastly, the doublet with constituents at 5.321 and 5.336 MeV, apparently 5/2+ and 7/2+ states, respectively, may have parentage in the 5.3H5 MeV octupole excitation in 208Pb. The total core strength is nearly reproduced and the relative intensities are about in the ratio given by the model. Again, a possible explanation of the missing strength lies in mixing with nearby octupole levels. C. 209Bi Results‘ C-l. Coupling to the 3- core state In the particle-core coupling model, coupling of the hg/2 proton to the 208Pb octupole vibration can lead to a septuplet of states. Our study and a number of other charged 72,73,78 particle studies of this multiplet have only resolved six members. However, assuming a (2J+l) cross 122 section dependence, the strength of the 2.599 MeV state suggests that this level is a degenerate ll/2+, 13/2+ doublet. Coulomb excitation81 has shown that his level is a doublet with members separated by only about 2 keV, the larger spin state lying higher. We have found the total strength of this multiplet nearly equal to that of the core excitation. The assigned spins are in agreement with those given in References 72,73,78, and 81 and the relative intensities agree quite well with the weak coupling model predictions. 208 C-2. Coupling to the Pb first 5- state Spin assignments for this multiplet have been made and compared with the weak coupling theory in Table VI. A total strength greater than that of the core excitation was observed. The intensities follow a (2J+l) rule quite well and, as shown in Table VII, the agreement with previous spin assignments is good. In all assignments but that of 57 the l/2+ level of the multiplet has not Francillon et al. been located. Since this 1/2+ state is expected to have a very small cross section, identification of this level is expected to be difficult. The 3.309 MeV level, identified by Prancillon g£_al. as the 1/2+ state, has a distinct L=3 shape in our data. Unless a doublet lies at this energy it appears that the 3.309 MeV state can not be a member of the multiplet. Cleary72 suggested that a very weak state seen + . at 2.8H7 MeV may be the 1/2 level but the cross section was 123 TABLE VII.--Spin and parity assignments for the 9/2- x 51 multiplet in 2098i. EX(MeV) Present Work Ref. 57 Ref. 72 Ref. 73 2.766 - - 3/2+ _ 2.986 ll/2+ 13/2+ l9/2+ 13/2+ 3.038 3/2+ 3/2+ 5/2+ 3/2+ 3.091 5/2+ 7/2+ 7/2+ 5/2+ 3.139 13/2+,19/2+ 11/2+,19/2+ 11/2+,15/2+ ll/2+,19/2+ 3.153 7/2+,15/2+ 5/2+,17/2+ 9/2+,17/2+ 7/2+,17/2+ 3.169 17/2+ 15/2+ 13/2+ 15/2+ 3.211 9/2+ 9/2+ - 9/2+ 3.315 - 1/2+ — - 12H so small that an angular distribution could not be measured. Our spectra show no states near 2.8H7 MeV. Using techniques independent of any weak coupling assumptions, Cleary also identified the 2.986 MeV level as having spin 19/2+. However, the strength he measured for this level was much less than that predicted by the weak coupling model assuming Jn=l9/2+. The strength that was measured is consistent with our spin assignment and the weak coupling picture. Being very sure of the spin assign- ment, however, Cleary attributed the difference between the weak coupling model and experiment to mixing of this level with the higher lying 19/2+ state associated with the decuplet built on the 208 Pb second excited 5-. Our analysis of the two L=5 multiplets, however, indicates that mixing of these two states is not required if one assumes that the 2.986 MeV level has spin 11/2. It should also be noted that Cleary concluded that the 3.211 MeV level had a microscopic configuration based on coupling of the h9/2 particle to the unnatural parity H- level in 208Pb. Our bismuth data indicates that the 3.211 MeV level is the 9/2+ weak coupling member of the 5; multiplet. Our assignment of doublet spins to the 3.153 MeV level is consistent with the results of Reference 73 which found two members at about this energy and with separation of about H keV. That work also suggested possible doublet structure and spin assignment for the 3.13H MeV level and concluded that its members are separated by at most 3 keV. 125 208 C-3. Coupling to the Pb second 5- state Five members of a multiplet near 3.6 MeV have angular distributions similar to those of the second 5- level in 208Pb. The total cross section is slightly greater than that seen in the core. It also seems that many of the levels are degenerate since coupling of the valence proton to the core excitation is expected to result in 10 states. This apparent degeneracy makes the spin assignments quite uncertain. C-H. Other possible weak coupling levels Excitations involving angular momentum transfers of 209Bi that lie near the excitation 208 2 and H were identified in energies of the first 2+ and H+ levels in Pb. In both cases the total strength of the core was not observed and it seems that some fragmented strength has not been resolved. However, spins have been assigned assuming that all possible strength was observed and that the relative intensities are given by the (2J+l) rule. Therefore, the spins given in Table VI for the L=2 and L=H multiplets are quite tentative. About 75 per cent of the core quadrupole strength was found. Cleary72 reported an additional L=2 excitation at H.213 MeV and observed about 72 per cent of the expected strength. Reference 62 has suggested that the 3.981 MeV level is really a doublet. A gamma-ray resonance 126 experiment82 on 209Bi identified L=2 transitions to levels at 3.977, H.083, H.156, H.176, and H.206 MeV, the lower three levels corresponding to our identified L=2 states. The levels seen here at H.177 and H.210 MeV have definite assign— ments of L=3, although doublet structure is possible. It seems that complete identification of the 2+ and H+ weak coupling 209 multiplets in Bi requires higher resolution than currently possible. V. THE SINGLE PARTICLE STATES AND A MICROSCOPIC MODEL 207 209 Both Pb and Bi have states strongly populated in single particle transfer reactions and thus identified as single particle levels. Most of these states have been observed in the present (p,p') study. It is expected from . 83 electromagnetic measurements 58,60 and other inelastic scattering experiments that the inelastic transitions to these states involve strength greater than that given by a model involving a single valence nucleon. A. The States in 207Pb To explain the measured angular distributions for o . . . — _ + the 1nelast1c scattering from the first 5/2 , 3/2 , 13/2 , and 7/2_ excited states in 207 Pb, DWBA calculations were made which included only the valence orbits. Figure 31 compares these theoretical results with the data. The curves give both direct and direct-plus-exchange predic- tions. 127 The valence calculations shown in Figure 31a used a central nucleon—nucleon force and an approximate treat- 37 This exchange approximation ment of knock-on exchange. has been shown to predict cross sections slightly larger than those for exact calculations, the overestimation being larger for small 2-transfers. For the direct amplitude, the projectile-target interaction was taken to be the two-body effective bound state interaction (G-matrix) derived from the Hamada-Johnston (HJ) potential. In these calculations, harmonic oscillator wave functions were used with the size parameter set to 0.H05 fm-l which reproduces the results of elastic electron scattering on 208Pb. The optical model parameters for the results shown in Figure 31 were those of Becchetti and Greenlees,21 although use of other sets gave similar results. In Figure 31a, only the dominant, non-spin-flip (S=0) transi- tions are displayed. The calculations underestimate the data, the data being 3 to 10 times stronger. The shapes of the angular distributions predicted by the theory are generally not in good agreement with the data. A previous study,87 using central and tensor forces for the 20 MeV data58 for these states, suggested important tensor contributions in the transition to the 3/2- state. It is interesting to determine if non-central forces could significantly improve the fits to the data. Calculations were therefore carried out still assuming 207 a simple valence description of Pb and using the code H5 DWBA70 which allows the use of spin—orbit and tensor 128 FIGURE 31.-—Measured differential cross sections and valence orbital model predictions for single particle states in 207Pb. (a) Predictions using a purely central force. The broken and solid curves give the direct (D) and direct—plus—exchange (DE) results, respectively. (b) DE results using the code DWBA70. The broken curve gives the predictions using a central force only. The solid line displays calculations including non-central interactions. 102 dU/dEZ [lib/SP] 101 10° 129 VALENCE CALCULATIONS r l I r l r F I I r I I , [o] . [b] A “... /\ M“. /\ A. 3' , A. 3' \ \ “ 2 / \ “ 2 \ " A \ A J \ A“ \ A \ ‘ \ ,\ \ \\/ \ O \/-\ O \ N \ - a \ ,\\ N \\' ’ M \\ \ c. 00 \ .~ 5' d\ 0“. S- \/\ O... \ .— V \ 2 \d/ 2 \ a \’ \ \ ®%¢ \/\ \ 6° a) \- G one I.\ 0 - 1 , \ “9. z \ I‘ o J \ \ \... x \ \’ g V V V " w 13+ v V ‘— V /\ '2 l \ ’ \ 0 90 80120 0 Ho 80 120 90m. [degrees] FIGURE 31 130 two-body forces and treats exchange exactly. The central portion of the nucleon-nucleon effective force was taken to be a Serber exchange mixture; the Yukawa radial shape had a l fermi range and strength of -30 MeV for V0. (With this even-state, central interaction, results compare well with the HJ and the approximate exchange calculations as can be seen in Figure 31b.) For the non—central analysis the tensor and L-S potentials were identical to those used 208Pb microscopic calculations, above. in the Figure 31b displays the results using the central- plus-non-central forces. In the DWBA70 calculations, contributions from both 8:0 and 8:1 transitions were included. For each state, the tensor dominates the spin- orbit contribution, even in the case of the 13/2+ state where the allowed orbital angular momentum transfers are 5 and 7. The angular distributions are somewhat improved in shape but are still lower than the data by factors of 3 to 6. The predictions for the 13/2+ state show the most dramatic increase. Calculations with DWBA70 using Woods-Saxon wave functions give enhanced forward angle cross sections but renormalization by factors of 2 to 6 is still needed. The renormalization of the two-body force needed to match the data is related to the effective charge in electromagnetic transitions, both being corrections for 33 35 core polarization effects. Bernstein and Astner et al. have given a semi-quantitative relation between these two parameters. Using the results of the calculations with 131 harmonic oscillator wave functions and assuming the proton- proton force is half as strong as the proton-neutron force, effective charges of 0.75, 1.1, 0.62, and 0.H2 were re complicated excitations of the core particles are éilpparently significant. Such core polarization effects haeare calculated using two different models. First, the EDIuenomenological model of Love and Satchler85 was used. 3?}1e core polarization (CP) form factor (FF) was summed CZO‘herently with the direct—plus-exchange valence FF for 1:}1e S=0, L=J transition of each state. The strength of 1:}me CP was chosen to give the fits shown in Figure 32a; ”Elle.CP contribution was always larger than the valence 'tfiaxmu Becchetti and Greenlees optical model parameters VVEEre used in the collective model for the core. In this Inacroscopic model,85 a radial matrix element of rL r‘elates the CP strength to the effective charge; these mai‘trix elements were calculated using Woods-Saxon wave 1/3 functions in a well of radius 1.2 A F, diffuseness (3-7CJ F, spin-orbit strength of 25 MeV, and depth adjusted 132 FIGURE 32.--Measured differential cross sections and core polarization model pregictions for single particle states in Pb. (a) The macroscopic core polarization prediction is given by the solid line; for comparison, the broken curve shows the DE valence model. (b) the DE microscopic core polarization results are given by the broken curve. The solid curve shows results using complex coupling. 102 101 O—b O N 0—0 O H dU/dQ [uh/SP] 102 101 133 CORE POLARIZATION CALCULATIONS l 1 I [ r 1’ l 1 T '1, T [0] 4 [b] .\ " ‘ . ,x 3‘ \ 3' \ \ -A \ ‘ 2 ‘91:, 2 ‘ M \\ ,t‘ \ ‘\ O V \ ‘ o , \ \ \ O \f\ . ~ 5" \ ,. §' \\ 2 a. 2 f\\/-‘\ \ '\_ \"\ - . " I \ '” o 7- .. 0 - \ ~ .. / \ 0. Z \-’\ 2 ~ ’ \ ‘ 2 \ —\ % %\ T \ .‘0 O~\ \.’ \ \ \ \ \ 1.3+ V £L§+ ___’/"\ V’ 2? ____/’-\ ' 2 \flw" \ ,'\ ‘ ' v, \ \\,-\ 1 l 1 l \1 ,.l l I 1 ll 1 l 7 0 “TO 80 120 0 “*0 80 120 9mm. [degrees] FIGURE 32 13H to give the correct binding energy. Expressed as l/3)L, these matrix elements have values of /(l.2 A 0.625, 0.722, 0.778, and 0.716, in order of excitation energy. Effective charges of 0.7H, 0.95, 0.61, and 0.H3 - - - + there extracted for the 3/2 , 5/2 , 7/2 and 13/2 levels, Inespectively. These values are consistently smaller than tlle effective charges obtained at 20 MeV using the same HKDdel. This apparent discrepancy is probably due to ccontributions to the cross section from exchange effects vvluich are more important at 20 MeV and which were not lilicluded in the lower energy calculations. However, the eatffective charges extracted here compare very well with 1:110se extracted from the renormalization of the valence . . + . (zealculations given above. For the 13/2 level, this CP ITuodel cannot give the forward angle enhancement shown in IDCJth the data and exchange calculations. Second, CP effects were calculated with a completely lTuicroscopic model. Admixtures of l particle-2 hole core €3)acitations in each state were determined using first CP, ifKDr a state of spin j was given by lj>CP = |j> +2 A(j'Jj)|(j'J)j>, 'tTME sum running over j' and J. The ket |j> denotes a VEfiLence state of spin j corresponding to the appropriate thetrtron hole. [(j'J)j> refers to a component of total 135 Spin j resulting from the coupling of a neutron hole of spin j' to a particle-hole state of the core with angular Inomentum J. The amplitude of a particular component is given by A(j'Jj) = -<(j'J)j|V|j>/AE wllere the energy denominator E=Ej-Ej,-EJ. The energies fcor the orbitals were taken either from the zero deforma- ‘tzion Nilsson scheme or from experiment. The orbitals zixlcluded are listed in Table VIII. Harmonic oscillator cvwave functions with length parameter a=0.H05 fmml were ‘Llsed. The coupling potential, V, was the Kallio-Kolltveit 59’60 in this mass region ifcmte.86 Similar treatments ‘Iiave given encouraging results. For the transitions from 1Ihe ground state to the 3/2- and 5/2- levels, respective B(E2) values of 189 and 231 e2me were calculated using Tihese wave functions and using no effective charge; these Vfialues are in fairly good agreement with experimental Imeasurements.83 Distorted wave calculations using these CP wave fhanctions are displayed in Figure 32b. The broken curve Egives the results for the direct-plus-approximate exchange Chalculations. Only central forces were used. In each Guise the experimental strength is underestimated. UIIfortunately, numerical limitations prevented calcula- 'tiCHls using DWBA70 and including non-central forces. 136 Table VIII. Proton and neutron orbits used in the core polarization calculations. Lack of J subscript indicates both j=£:1/2 were used. PROTONS NEUTRONS Particles Holes Particles Holes Oh9/2 0hll/2 Oi11/2 281/2 1f 281/2 . 1g 0g 0i ld Oj 1d 2p 08 2d 0h 1g 1p 1h 1f 0j 0f 381/2 2p 2d 0k17/2 Oi13/2 1h 2f7/2 38l/2 0119/2 0k17/2 2f7/2 0 119/2 137 The solid curve in the figure shows results using a complex FF. The imaginary portion of the collective vibrational model FF was added to the approximate exchange microscopic CPFF. The strength of the complex FF was obtained from a CM fit to the data. As seen in other instances,uu’59 introduction of complex coupling improves the agreement; the strength seems well estimated although the large angle data is still overestimated. To summarize, the strengths of the inelastic transi- tions to the first four excited states in 207 Pb are fairly well predicted by a microscopic model. However, using realistic interactions with non—central components and accounting for exchange effects, calculations reproduce only 20%-50% of the observed cross sections when simple neutron hole wave functions are used. A macroscopic core polarization description of these states is consistent with lower energy results. Microscopic core polarization wave functions give reasonable estimates of electro- magnetic strengths using no effective charge but, with central forces, predict inelastic cross sections slightly lower than those observed. Addition of an imaginary portion to the real, microscopic CPFF gives the best fits. The importance of the tensor and spin-orbit forces in this CP description remains to be investigated. B. The States in 209Bi 209 The single particle orbits seen in Bi lie at 0.896, 1.608, 2.825, 3.118, and 3.633 MeV of excitation energy 138 and have spins and parities of 7/2-, 13/2+, 5/2-, 3/2-, and 1/2-, respectively. Following the above procedure, inelastic scattering to these states was first calculated using a simple valence proton model. The calculations used an effective bound state interaction, used the BG optical model for the distorted waves, included the results of knock-on exchange using the approximation of Petrovich37, and were done with the code DWUCK.27 All possible LSJ triads were included. For the 13/2+ level twenty such triads are possible. For each state, the cross sections for each LSJ transition were summed to give the total cross section. For the 13/2+ level, the LlJ transitions were comparable in strength to the usually dominant LOL transitions. The results of these central force and valence particle calculations are given in Figure 33 by the short dashed curves. In all instances the calculations fall at least a factor of 10 below the data. The effects of the non-central nucleon—nucleon forces ”5 Because of were investigated using the code DWBA70. numerical limitations only the cross sections for the l/2- and 3/2- states could be calculated. The Serber exchange mixture was used for the central interaction and the spin-orbit and tensor forces were identical to those used above. The long dashed curves for these two states shown in Figure 33 show the results of these non-central and central forces with valence particle calculations. Apparently, '--v 139 FIGURE 33.--Calculations for the single particle states in 209Bi. The meaning of the curves is given in the text. 1H0 2.x} 96s 120 80 H0 9mm [degrees] FIGURE 33 1H1 non-central forces cannot sufficiently enhance the theoretical cross sections to match the strength of the data. Finally, microscopic core polarization calculations were done. The 2p-1h admixtures in the wave functions for these levels were calculated using first order perturbation theory as above. For those states whose quadrupole trans- 83 the core polarization ition rates have been measured, wave functions give B(E2) values in fair agreement with experiment. Values of 22 and 572 e2fmu were calculated without effective charge for the 7/2- and 5/2_ transitions, 83 are 2H and 288 e2fm”. respectively. The measured values Transition densities obtained with the resulting wave functions were folded with the effective bound state inter- action used above. The zero range approximation was again used to account for knock—on exchange and the code DWUCK27 was again utilized. The results of these calculations are given by the solid lines in Figure 33. In all cases but the 13/2+ transition the agreement with the data has greatly improved. In the case of the 3/2- level the calculated strength falls only about a factor of two below the data. For the 5/2_ cross section the calculation gives a good fit to the data. The worst case is the 13/2+ calculation where the core polarization results essentially reproduce the valence cal- culations. In the core polarization results the LOL transi- tions have become more dominent while the LlJ transitions 1H2 have lost much of the strength possessed in the valence model. The net result is that the cross section remains about the same as it was in the valence calculation. This state has been showneo’66 to have a large admixture of the weak coupled l3/2+ state. The effect of this admixture has been studied60 in a (p,p') experiment at 39.5 MeV where good agreement with the experimental cross section was obtained only when the weak coupled admixture was included. Since the perturbation prescription used here cannot produce the coherent 2p-lh components found in the admixture, the present results for the i single particle state are to be expected. 13/2 To summarize, it seems that the single particle states can only be explained when core polarization effects are treated. The microscopic calculation involving simple 2p-lh and 2h—lp models for these single particle states in 209Bi and 207 Pb apparently can account for much of the observed core polarization strength in transitions not involving contributions from coherent excitations of the core. VI. CONCLUSION The (p,p') reaction has allowed an intensive study of the macroscopic behavior to be made. In both 207Pb and 209Bi collective model fits to states enabled the transfered angular momentum to be identified. A large number of states 1H3 in both nuclei had features corresponding to the weak coupling of the valence hole or particle to core excitations. In 209Bi the extremely high level density and fractionation of strength permitted only a few multiplets to be studied. Of these, the weak coupling groups corresponding to the first 208Pb had most of 3- and the first and second 5- levels in their strength identified and were found to conform to a weak coupling prescription. Spins and parities were assigned using this fact and were found in good agreement with previous 207 studies. The less dense level structure in Pb apparently permitted more weak coupled states to be identified. Most 208 of the states expected to be built on the very strong Pb core excitations were observed and a few high-lying 207Pb states were found corresponding to high lying core states. Most interesting was the absence of a weak coupling multiplet 208Pb. This missing with parentage in the lowest 5- level in strength may possibly be explained by examining the ph structure of the core state. The single particle states in 207Pb and 209Bi were excited in this (p,p') study and examined using microscopic models. As expected from electromagnetic measurements, transitions to these states were found to be greatly enhanced by the core polarization effects. Calculations with the single valence nucleon, exchange effects, and non-central forces apparently cannot reproduce the observed cross sections. A first order perturbation theory calculation using a large number of neutron and proton shell model orbitals 1HH gave a core transition density comparable to that of the valence particle. The DWBA calculations with the core polarization density and purely central forces gave reasonable 209Bi reproductions of the data in all cases but that of the 13/2+ state which has been shown to have significant mixing with the weak coupling 13/2+ lying at higher excitation. It is concluded that these single particle states are properly described only in models which properly account for core polarization. APPENDICES APPENDIX I Optimum Target Thickness In most nuclear experiments the best resolution consistent with the highest count rate is desired. The target thickness, 06x, can affect both the resolution and the count rate in particle experiments. With other factors fixed, target thickness is related linearly to the count rate but there is no clear relation of thick— ness to resolution. For this reason the Optimum target thickness for high resolution (p,p') was determined experimentally. A number of bismuth targets were made with similar backings but of varying thicknesses. Care was taken to insure thickness uniformity and the foils ranged from about 50 to 1300 ug/cm2. The relative target thickness was measured using a 900 monitor and the Elcor charge integrator. The thickest target was measured with the alpha guage, and all other thicknesses were calculated relative to it using the monitor-charge results. It was assumed that the target effect was a function of the density of electrons in the target material and not of the atomic electron structure. Of course, with this 209Bi would hold for the assumption, the results found for entire lead mass region. Using H0 MeV protons, the cyclotron—transport-spectro- gragflq system was tuned for best resolution using a thin 1H5 1H6 target and the "speculator" technique of Blosser et al.19 The 10 x 2° solid angle aperture was used. All parameters were held fixed except the spectrograph magnetic field and the target thickness. The data obtained is displayed in Figure I-l. There the resolution of the elastic peak in keV is plotted against the target thickness. It has been assumed that the focal plane line shape is Gaussian. The errors in the resolution correspond to the statistical uncertainties in the speculator measurements. The target thicknesses are probably accurate to about 10%. For sufficiently thick targets the straggling contri— bution to the line width is expected to dominate the intrinsic thin target line width. The dashed curve in the figure gives the results of adding an assumed intrinsic line width of 6.5 keV in quadrature to the straggling effect which was calculated assuming a Vavilov distribution. The solid curve displays the results from linearly combining the assumed width and the straggling contributions. It appears that the linear folding of the effects compares best with the data. Since the actual energy distributions determine the proper method for combination, the proper combinatorial technique is not clear. Also, target non-uniformities could possibly contribute anomalously to the measured resolution. From this data it appears that targets of 100 to about 250 ug/cm2 areal density affect the resolution very little. The targets finally used in the high resolution runs were 1H7 .COHHSHomms co mmmcxoflflv remedy mo mvomwmm m£HII.HIH mmeHm @5683 mmmzonE Emmi 8+; . oo_NH . omoH owm . 0mm . om... . owN . o I I mmwzonIh - _ p p b >02 of "mm enaearmmoN ...mom<._. .m> ZOHHDJomwm . — . p p _ - l m (D (I) l\ [AW] HIOIM BNI‘I C) H H H NH 1H8 made about 100 ug/cm2 to allow for the uncertainties in these measurements and for the bombarding energy being 35 rather than H0 MeV. 1H9 APPENDIX II Analysis of the Data The plate data was scanned in vertical strips whose height was dictated by the optical systems of the scanning micrOSCOpes. Each band was scanned so that extraneous background was excluded. For each exposure, the separate 87 passes were combined using the program JABBERWOCKY written by S. Ewald. This program allowed combination of the separate vertical passes in two ways: straight addition or addition after shifting of the passes so that the centroids of specified peaks were alligned as closely as possible. The latter option permits compensation for skewness in the focal plane images or zeroing errors in scanning. The program used a least-squares, Gaussian fitting routine to indicate which of the two methods yielded the tallest, thinnest peaks. In almost all cases, the straight addition mode gave the better line width. The counter data was taken using the data acquisition program TOOTSIE.88 With the data in counts-verses-channel number form, the 89 was used for the data reduction. This program program MOD7 permits background approximation with polynomials and allows peak areas and centroids to be extracted. Although a number of numerical peak-fitting routines were available for reduction of the data, they were tested and found less desirable to use than MOD7. The very narrow line shape 150 (the peaks were only two to four channels wide at half maximum) and the small number of counts in most peaks prevented these routines from giving results that were believed to be more consistent or more reliable than those given by MOD7. For a few cases, comparison indicated that equivalent peak areas and centroids were obtained using either method of analysis. Further, Use of MOD7 is probably faster than use of the numerical codes. With the reduced data, the programs22 CALIB and MONSTER were used for further analysis. The correspondence between excitation energy and focal plane position was found with the code CALIB which can perform a search on beam energy, scattering angle and focal plane parameters to determine the best fit to the positions of peaks of known energy. For our data, the searches were limited to the angle and to the focal plane variables because, since particles other than protons were excluded from the emulsions, the beam energy could not be uniquely determined. Instead, the bombarding energy was determined using the bending magnets' N.M.R. readings and a correction empirically established using the momentum cross-over technique. Beam energies can be calculated better than 1 part in 1000 with the correction. Much of the data was taken at a single bombarding energy and, since the spectrometer is run in the energy loss mode, there is little sensitivity to the actual beam energy. The focal plane parameters from CALIB were entered into 151 the program MONSTER which was used to calculate the excitation energies of peaks and the laboratory to center- of-momentum conversion. Output from that program was used 91 which was used to catalogue and in the program DMBEX normalize the data. With the large volume of data collected use of such a program was indispensable. DMBEX served to identify all peaks whose corresponding excitation energies were within a given energy interval of a specified energy. With this criteria, the program referenced cross sections for plotting, statistical analysis and other usage. APPENDIX III 208Pb Angular Distributions 1552 >Jm>~wuwnmwu .7my monk . o. o 43"” m.~na m.mm a.da« ~.cs n.m :.mm« m.:: 3.: o.mad m.o: o.n m.mmfi m.om H.m “.mm" ~.~m .m" .ms“ n.0m .0” .Ho« «.mm .m» .mn «.am .om .onm H.3m .m: .nma d.om .nn .cnm H.0m «menu «rnum «Fur». «menu «rmsm «rut» Henam «yusm «Cote. ann.>u r can. : ax. "ana>my sm:.a .xu m.n.:m: enm.a .xm mun. om¢.n N.wt who. smc.: m.za «.u m.msm «.mm m.m m.wse m.m n.m n.m:m «.3: 6.5 c.0am «.0: .ma .amm ~.om .mu .«m: m.mm .am .mmm ”.cm .3“ .sem «.wm . e.“ m.mm m.oofi omo. mmo. m.oc«_ . m." 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Mom wotm Moom . Nah momo moNM _ com 0.": mohm . o.mna m.mm _ m.m n.m~ m.nn _ n.m m.«m m.mm _ n.m m.m¢ m.nm _ .mfl .mmd n.mx ~ $.n m.mm «.mm . “.mm “.mm . M.” ”.0. n.mm _ ~.m ".m. ..mm . M.“ 0.0m “.mm . ..fl .0. ..n _ .mH . h o.~“ _ o.m~ o.“« _ n.m m.m«m o.n“ _ .fld .nn n c.5fi . k.“ m.Hm 0.5“ _ .om .m. u.a _ .mm .mm« ~.m . m ya a » m an - m m 4 n.: .mw». m. < m .m. n m a. . : _ m . :1.m m1 _ m>mu mmm.m»umw_ mnm«>mn mum.m»wmw_ m.mm>myr.o..m..xm m.mwwmsrmw .M..xm. m.wm>mu;mvm.M»unm. m.mmmam mmm.M».xw. APPENDIX IV 207Pb Angular Distributions utions strib C q .1. lar D 7Pb Angu 20 ,APPBNDIX IV v-(r O 0 (IN “"9““:me t')v‘l‘~O\N'\ (:flngoooocoo...ootn.n:kn :wcnmammcmmmwmuwo - 00 ~\Y >td I.) )‘(ooumanenmuu‘omn )‘finloooooonooo. mnmmnmnmmmmmmrxu. 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N“ _ .flm .nm m.n« .0" .m «.md _ .md .mm m.ofl .om .an m.ud «now <7m~m <»mr»_ macaw «rmnm mr mmn.m .xm «-D~>m .r m :m. cum a.fi~>mr mmm.s ox a.1~>m: m:m.: uxm fl-w.>mr mom.a ax. flnfi‘> 3 tum.s .xu _ mca Mom mono“. . _ _ . no“ «on mono“. m.m moha «.nm _ w... mono _ . _ . m.m m.nm m.nm _ o.m m.nm m.nm _ “.0 H.nm _ m.” w.¢ “.0m _ _ m.flm H.nm * m.n m.um o.mn _ 0.. «.0: «.mn . m.nm m.om _ a.“ m.m m.om _ a.“ m.» ".om . :.m« «.mn . m.n m.nm n.mo _ ..m n.mm n.no . a “.mm o.mn _ m.m m.mH «.ms . 4.~ o.mfl o.mn . m.«m fi.no _ m.o m.mo ¢.nm _ n.: «.mo o.mo _ m m n.mH u.~o . o.m m.n« 5.50 _ m.m o.n~ “.50 . o.mm o.mo . 0.0 m.nn 4.na _ m.¢ o.mn :.om . a m h.m a.nm _ m.m m.c n.mo _ m.m ¢.nm o.mo _ m m.:; :.nm _ m.m “.mn «.mm _ m.m 0.3m o.mm _ m m n.m« :.n: _ m.m :.n :.om _ m.m 0.54 4.0m . : o.m: 3.0: . ."a .«m m.mm _ .0” .mm m.mm _ m m n.mm «.mm _ m.: «.ma :.n: _ m.m «.mm :.ns _ .n H.mm o.mm . .m” .Nmfl k.~m . .Nfi .mofl n.nm . m.m “.5: m.mm _ 0.0 n.ad o.mm _ H.“ +.hm c.1m . ”a .yn m.mm . .mfl .«ofi «.mm _ .mn .flma o.mm . .nfi .5m 5.5m _ m.o m.mm m.mm _ 4.» n.0m m.«m . .wd .sm n.5m J .m" .mnm m.\« _ .nm .mmm m.u« . m.m :.mm «.mm _ m.m m.na n.nm _ .ma .n: n.nm * m.m n.on o.mm _ .mm .oma o.mfl . .3m .nmm o.m" _ .mm .m. m.ua _ o.w m.mm o.~m . m.s m.m: «.mm _ .nm .ma” n.." _ ..m u .qmm m. .n« _ .mm .nm. m.m« _ .om u .mo H.nm _ .m m.nm m.n« _ w.m w m.\o m..fl . .om .no o.~" . n rm <»mr»_ : mam wn mmm.a .xu mmmm>unrm¢n.a .xm m.m.>mrrm«e.a oxu mmmw>wy’mmm.:».nw_ mmmw>mwr~mm. 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