.151 STEIN 0F SEVERAL @fififlm} sud SHEER. NUCLEE; “A THE (p,d2 ifiéfi'flfii‘é A? 35 fiée‘? latest: £69 i'iza fiaqveo 42% 535‘ D. firgl‘filfilfi SMTE 33538233? James Aiien Rice ‘373 This is to certify that the thesis entitled A Study of Several Odd-Odd s-d Shell Nuclei via the (p,d) Reaction at 35 MeV presented by James Allen Rice has been accepted towards fulfillment of the requirements for Ph.D. Physics degree in A A University Major professor Date June 10, 1973 0-7639 LIBRA R Y Michigan State “7"‘7W‘ - L- {3 -' i E E .‘k ‘u‘d ABSTRACT A STUDY OF SEVERAL ODD-ODD s-d SHELL NUCLEI VIA THE (p,d) REACTION AT 35 MeV BY James Allen Rice 36 38 22 34 C1, and K have been studied States in Na, Cl, via the (p,d) reaction at an incident proton energy of 35 MeV. Reaction products were analyzed with the Michigan State University split-pole magnetic spectrograph. The deuteron spectra were recorded both with a single-wire, position- sensitive proportional counter, at a total resolution of ~50 keV, FWHM, and on nuclear emulsion plates, with re- solutions of 8-18 keV, FWHM. Levels to 6 MeV of excitation in 22Na, 34C1, and 38 36 K, and to 8 MeV in C1 have been ob- served and excitation energies assigned to an accuracy of :3 keV per.MeV. Angular distributions were measured from 30 to 60°, with special emphasis on the region from 3° to 35°. This has allowed a precise definition of the forward angle shapes for 1-0 and i=2 single neutron pickvup angular distributions in the s-d shell. A careful screening of deuteron optical- model parameters available from the literature was con- ducted in an effort to reproduce the experimentally observed James Allen Rice shapes via distorted wave Born approximation calculations. The best overall fits to pure R-transfer distributions for the A>30 nuclei were obtained with standard finite-range, non-locality corrected calculations which include a density- dependent damping of the Vpn interaction. A good 2:0 fit to the 23Na(p,d)22Na data could not be obtained for cal- culations which also yielded good fits for the.A>30 nuclei. Spectroscopic factors, z-values and parity assignments, and excitation energies from the present work are compared with previous experimental studies and recent shell model calculations. The agreement between the present experimental results and theoretical predictions is good for low-lying levels in the residual nuclei, but observed i=3 angular dis- tributions and spectroscopic factors for higher excited states indicate a need for consideration 0f 2 (or 4 or 6) particle excitations to the f-p shell in the ground state configurations of the A>30 target nuclei. A STUDY OF SEVERAL ODD-ODD s-d SHELL NUCLEI VIA THE (p,d) REACTION AT 35 MeV BY James Allen Rice A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1973 For Linda, with whom all things are possible. ii ACKNOWLEDGEMENTS I wish to express my appreciation to the entire cyclotron staff for their generous assistance in making these experi- ments possible. Specifically, I would like to thank: My Thesis AdVisor, Professor Hobson Wildenthal, for his aid and counSel in all aspects of this work-—conception of the experiments, data taking and analysis, and the writing of this manuscript; Dr. Barry Freedom for many useful discussions concerning the DWBA and for suggesting the approach used in the analysis of this data; Professor Jerry Nolen for his aid in the excitation energy analysis of the data and many discussions of nuclear physics in general; Richard Au, Larry Learn, and John Collins for their invaluable computer assistance; David Show for his assistance during many long nights of data taking; The many plate scanners who extracted accurate data from the nuclear emulsions; Andy Kaye for his good-will and most efficient efforts in obtaining photographs; Sandi Bauer for typing this thesis; and the National Science Foundation for its financial support throughout my graduate career at MSU. Finally, this thesis most certainly could not have been realized without the continuous encouragement of my parents, and the patience, hard-work, and self-sacrifice of my wife, Linda. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS. . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . LIST OF FIGURES O O O O O O O O O O C O I. II. III. IV. INTRODUCTION . . . . . . . . . . . THE 23Na(p,d)22Na AND 35C1(p,d)3'+C1 REACTIONS 11.1. Introductory Remarks . . . . . . 11.2. Experimental Procedures and Results . II.3. Analysis of the Angular Distributions. 11.4. Discussion of Results . . . . . . 11.4.A. Levels of 22Na . . . . . 11.4.3. Results for 3“C1. . . . . 11.5. Conclusions . . . . . . . . . THE 37C1(p,d)36C1 REACTION. . . . . . . 111.1. Introductory Remarks . . 111.2. Experimental Procedure. . 111.3. Excitation Energies. . . . . . . 111.4. Angular Distributions . . 111.4.A. General Discussion . . . . 111.4.B. Analysis of Experimental Angular Distributions . . . 111.5. Discussion. . . . . . . . . . III.5.A. Energy Levels. . . . . . 111.5.B. 2 and n Assignments. . . . 111.5.C. Experimental CZS Values . 111.5.D. Comparison with Shell-Model Cal culations . . . . . . . 111.6. Summary. . . . . . . . . . . THE 39K(p,d)38K REACTION . . . . . . . 1V.l. Introductory Remarks . . . . . . 1V.2. Experimental Procedure. . . . . . 1V.3. Excitation Energies. . . . . . . iv Page iii vi viii 10 4O 40 42 48 50 50 52 57 60 60- 65 85 85 86 88 91 95 97 97 98 100 Page IV.4. Angular Distributions. . . . . . . 108 IV.4.A. Discussion of DWBA Calculations 108 IV.4.B. Analysis of Experimental An- gular Distributions . . . . 118 IV.4.C. Assignment of z-values . . . 129 1V.4.D. Discussion of Values Extracted for C28 0 O O O O O O O 130 1V.5. Discussion of Results. . . . . . .g 134 IV.5.A. Comparison with Previous Experimental Results . . . . 134 1V.S.B. Comparison of Results with Struc- ture Theory . . . . . . . 137 1V.6. Conclusions . . . . . . . . . . 140 LIST OF REFERENCES 0 O O O O O O O O O O O 142 APPENDIX A o o o o o o o o o o o o o o A-l MONSTERZ O O O O O O O O O O O O O O I A-l l. Cross-Section Transformation . . . . A-l 2. Excitation Energies . . . . . A. . A-2 3. Particle Group Positions. . . . . . A-7 4. Contaminant Identification . . . . . A-7 5 o MUlti-angle Averaging o o o o o o O A-a APPENDIX B O O O O O O O O O O I O O 0 3-1 ELASTIC SCATTERING DATA . . . . . . . . . . B-l Table LIST OF TABLES Page Excitation energies, z-values, JH and T values and pick-up spectroscopic factors for states of 22Na. All C28 values extracted from the pre- sent data have been normalized to yield 0.59 for the ground state. . . . . . . . . . ’19 Excitation eneriges, z-values, JTr and T values, and pick-up spectroscopic factors for states of 3t*Cl. All CZS values extracted from the pre- i sent data are normalized such that CZS=O.35 for the ground state. . . . . . . . . . . 20 Optical-model parameters used in the analysis of the 23Na(p,d)22Na and 35Cl(p,d)3‘*Cl data. . 36 States used for the energy calibration of the 37Cl(p,d)35Cl reaction data. Some energies in 22Na extracted in the present work and in a pre- vious (p,d) study are shown to illustrate cali- bration consistency. . . . . . . . . . 53 Energy levels in 36C1 observed in the present study and in other works. . . . . . . . 61-62 Optical-model parameters used in the analysis of the 37Cl(p,d)36Cl data. . ‘. . . . . . 66 Experimental values of 2 and C282 for the 3'7C1(p,d)35Cl reaction as observed in the pre- sent investigation. All assignments are based on the DFRNL analysis, with the spectroscopic factors normalized to yield CZS£=1.10 for the transition to the 36C1 ground state. . . . . 34 Experimental values of C28 for transitions from.37C1 to 36Cl. Absolute values for the ground state are presented in parentheses. All other values are normalized such that CZS£=l.lO for the ground state. . . . . . 39 A comparison of CZS(£) values obtained in the present study with those from various shell model calculations. . . . . . . . . . 92 vi Table 10. 11. 12. 13. 14. 15. A1. Page States used in the energy calibration for the 39K(p,d)38K reaction data. . . . . . . . 104 Energy levels of 38! excited in the present investigation of the (p,d) reaction and in previous studies of other reactions. . . . . 106 Optical-model parameters used in the analysis of the 39K(p,d)38K data. . . . . . . . . 111 Experimental values of 2 and C281, Obtained from the DFRNL analysis for transitions from 39K to 38K as observed in the present in- vestigation. All values are normalized so that Czsz for the ground state is 1.75. The assumed j-values are 3/2 for £=2, 3/2 (n=2) for 2:1, and 7/2 for i=3. . . . . . . . . 123 Experimental values of C282 for the transitions from 39K to 38K. The absolute values for the ground state are presented in parentheses. All other values are normalized such that CZS=1.75 for the ground state. . . . . . . 132 Experimental and theoretical values Of C28 for single neutron pick-up from 39K. . . . . 138 Extrapolations from the MONSTER2 momentum matching fits to known energy levels. Nominal energies and calibration parameters were ob- tained from a complete calibration run on the test spectrum. All other energies (MeV) are obtained from a fit to the first three (0.000, 0.130, 0.459 MeV) levels after the indicated shift the given parameter had been assumed. . . A—6 vii Figure LIST OF FIGURES Page Complementary spectra from the (p,d) reaction on the 23Na, 23Na-35Cl and Li-35Cl targets, measured at 35 MeV and 14°, as recorded on nuclear emulsion plates. The resolution of the deuteron groups is 15-20 keV, FWHM. Selected peaks are labeled with excitation energy assignments from the present work, the "boxed" values indicating levels in 3”C1. . . . .. . . . . . . . . . . 14 A spectrum from the (p,d) reaction on the 23Na-35Cl target, measured at 35 MeV and 8°, as recorded on nuclear emulsion plates. The resolution of the deuteron groups is 8 keV, FWHM. All excitation energy values are from the present work, with those "boxed" indicating levels in 3"C1. . . . . . . . 16 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)22Na re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated l-value for mixed-l distributions. . 24 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)22Na re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution Of the first in- dicated z-value for mixed-2 distributions. . . 26 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)22Na re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated s-value for mixed-t distributions. . 28 viii Figure Page 12. Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)36Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated n-value for mixed-2 distributions. . 72 13. Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)36Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first in- dicated z-value for mixed-z distributions. . 74 14. Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)35Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated s-value for mixed-t distributions. . 76 15. Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)36Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first . indicated i-value for mixed-2 distributions. . 78 16. Experimental angular distributions for states in 36C1 as observed in the 37C1(p,d)35Cl re- action at 35 MeV. The solid curves are fits Of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated R-value for mixed-2 distributions. . 80 17. Experimental angular distributions for states in 36C1 as observed in the 3"Cl(p,d)35Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated 2-value for mixed-2 distributions. . 82 Figure l8. 19. 20. 21. 22. 23. Page A spectrum from the 39K(p,d)33K reaction, measured at 35 MeV and 30°, as recorded on nuclear emulsion plates. The re- solution of the deuteron groups is 10 keV, FWHM. All 38K excitation energy values are from the present work. . . . . . . . . 102 A comparison of fits to representative an- gular distributions from the 39K(p,d)33K reaction at 35 MeV with the three chosen types of DWBA calculations. All fits were performed over the 3° to 35° angular region. The curves are identified as follows: DFRNL, ----FRNL, and —— ——ADIABATIC. . . 115 A comparison of ADIABATIC, FRNL, and DFRNL calculations (see text and Table 12) with =0 transitions in the 3‘*S(p,d)33S reaction at 35 MeV. . . . . . . . . . . . . 117 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the amount of the i=0 component in mixed 2=0-£=2 distributions. . . . . . 121 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the amount of the i=0 component in mixed 2=0-£=2 distributions. . . . . . 123 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the amount of the i=0 Component in mixed £=0-£=2 distributions. . . . . . 125 xi Figure 24. B1. B2. B3. B4. Page Experimental angular distributions for states in K, as observed in the 39K(p, d)3 8K re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the amount of the i=0 component in mixed £=0-£=2 distributions. . . . . . 127 Proton elastic scattering spectra recorded at 40° with a single—wire proportional counter o o o o o o o o o o O o o B-3 Measured proton elastic scattering dif- ferential cross-sections for the 3Na-35Cl target 0 o O o o o o O o o o o o B-S Observed proton elastic scattering cross- sections for the 23Na—37Cl target. . . . . B-7 Measured proton elastic scattering cross- sections for the 39K target. . . . . . . B-9 xii I. INTRODUCTION The nuclear shell-model assumes that a given number of nucleons occupy specified orbitals about an inert ”core" much the same as atomic electrons move in orbitals in the electro-magnetic field of the nucleus. These "active" par- ticles are assumed to be responsible for most observable properties of the nucleus. Indeed, spins, parities, and magnetic moments of many nuclei may be predicted solely on the basis of the number and kind of nucleons which occupy the last, or highest energy, subshell consistent with a systematic stacking of nucleons in the lowest unfilled or- bitals. A detailed theoretical description of the nucleus is assumed to be obtainable in terms of a Hamiltonian characterizeélby a sum of one and two-body matrix elements, which result from interactions of individual nucleons with the core and a two-body interaction between pairs of active nucleons, respectively. Nuclei with mass numbers between 17 and 40 are members of the s-d shell, i.e., the last nucleons occupy the ldS/Z' 251/2, or 1d3/2 orbitals in the simplest picture. Shell- model calculations for these nuclei have shown considerable advancement in the last decade. Early works considered couplings only in the highest occupied orbit, with all other subshells comprising the core. Considerations of this sort led to predictions for only a small number of low-lying ex- cited states. Calculations allowing two-orbital excitations l showed better agreement with available experimental data on ' spin, parity, and energy assignments for low-lying levels. Sophisticated computer codes and calculational techniques have allowed recent theoretical studies in which the basis states have been expanded to include the entire s-d shell. Both empirical and least-squares adjusted single particle energy parameterizations have been used for the one-body matrix elements, while theoretical and empirical two-body interactions have been studied. In general, the recent results show good correspondence with the data, particularly for those nuclei with either odd-even or even-even combinations of protons and neutrons. Calculated spectra for the odd- odd nuclei, however, are often in even qualitative dis- agreement with experimental results. The structure of these nuclei appears to be most sensitive to the details of the nuclear Hamiltonian and, therefore, any descriptive theory for the s—d shell would be severely tested in its attempt to reproduce sound experimental data for the Odd-odd systems. A critical comparison of recent Hamiltonians most cer- tainly relies on accurately observed properties of the odd- odd s-d shell nuclei. Excitation energies, spins and parities of nuclear energy levels and spectroscopic factors for single-nucleon transfer may be observed via direct re- action nuclear spectroscopy. Direct reactions take place in a time interval comparable to the time necessary for the 23 projectile to traverse the target nucleus (~10' seconds) and therefore, do not "see" collective effects in the target nucleus and are assumed to involve only one-step processes, i.e., the target nucleus is not excited above a ground state configuration before any particle transfer occurs. Those in which the incident projectile absorbs a nucleon from the tar- »get nucleus (pick-up) or deposits a nucleon in the target nucleus (stripping) are called single nucleon transfer re- actions. The target nucleus, therefore, undergoes a change in mass number (A) of i1 and the resulting residual nucleus may be left in any of its energetically and quantum mechani- cally allowed energy levels. In reality, any nuclear state may be described as a sum of weighted components, each corresponding to the probability that given shell model or- bitals are populated by specified numbers of nucleons in particular angular momentum couplings. The spectrosc0pic factors observed in transfer reaction experiments are a measure of the overlap, a quantum mechanical correspondence, of initial and final state configurations. When only one nucleon is transferred, therefore, one expects to probe specific shell-model wave function components for the initial and final nuclear states. The choice of an appropriate reaction for nuclear spectroscopy studies depends on the available projectiles, targets, and detection and analysis apparatus. The Michigan State University cyclotron provides high resolution proton beams with currents sufficient to allow experimental runs of reasonable brevity. Several of the odd-odd s-d shell nuclei which can be reached through single-neutron pick-up from stable targets are 22Na, 34C1, 36C1, and 38K. Natural 23Na 39 23N 35 7 35 K metals and isotopically enriched a— C1, Li- C1, and 23Na-37Cl compounds are commerically available. All are and easily evaporated at moderate temperatures and thin targets may be routinely produced. The preperties of the MSU cyclotron and split-pole magnetic spectrograph allow charged reaction product groups of closely similar energy to be clearly separated, detected and analyzed. The structures of 22Na, 34c1, 36c1, and 38 K are, therefore, subject to study via the (p,d) reaction. Precise excitation energies for these four nuclei have previously been assigned only to those states below the 3-4 MeV region. Any extension of the experimental under- standing of these nuclei naturally includes a precise de- termination of higher lying energies. Accurate extraction peak centroids is allowed by the high particle group re- solution (8-10 keV, FWHM) obtained on nuclear emulsion plates in the present work. A comprehensive spectrograph cali- bration scheme and least-squares fitting procedures have made possible the assignment of excitation energies in the residual nuclei to accuracies of :1 keV/Mev of excitation. This represents a significant improvement over previous charged particle studies, allowing a more critical comparison with calculated spectra and the rationalization of the results of different kinds of experiments. The spectrum analysis for these studies was performed with the computer code MONSTERZ (see APPENDIX A) on the MSU Sigma-7 computer. In the direct reaction process, one may attempt to picture the nucleus as a sum of several spherically- symmetric potentials. This approximation is the basis of the Distorted Wave Born Approximation (DWBA) predictions with which the present data are compared. Parities of energy levels in the residual nuclei, orbital angular momenta of the neutrons transferred in (p,d) reactions and spectroscopic factors may be assigned on the basis of such comparisons of individual experimental angular distributions with DWBA predicted distributions calculated for given neu— tron quantum numbers and appropriate final-state excitation energies. Shape comparisons yield the transferred neutron orbital angular moemtnum quantum numbers (2) and, hence, the parities of the residual states (n residual=fltargetnneutron with n =(-1)£). Magnitude comparisons indicate re- neutrOn lative strengths for the i-values involved in a given transition; hence, a measure of wave-function component amplitudes. Previous single neutron pick-up experiments ((p,d), (d,t), (3He,a)) observed angular distributions which generally did not include angles smaller than 10°-15°. The present work measures distributions in t° 30: providing a critical test of the forward angle DWBA shapes. The use of different currently popular proton optical model parameters had little effect on the calculated (p,d) dis- tributions. However, the DWBA-predicted differential cross- section shapes were found to be noticeably dependent on the choice of deuteron parameters. The experimentally observed shapes for pure i=0 and i=2 transfers in the A>30 nuclei were best reproduced when the interaction responsible for the reaction, Vpn' was damped by a simulated nuclear matter density dependence, and a broadly based set of optical- model potentials was used to describe the outgoing deuteron. 23Na(p,d)22Na shapes has The empirical Q-dependence of the not been successfully reproduced, particularly those for 2=0 neutron transfers. All of the DWBA calculations were per- formed with the computer code DWUCK using standard Q-dependence techniques. The results of the present experiments are presented in three autonomous sections, one for the combined 23Na(p,d)22Na 3 37C1(p,d)36C1 and and 5Cl(p,d)34Cl works, and one each for 39K(p,d)38K. Each section includes a summary of pertinent previous experimental and theoretical studies, and the experi- mental and analytical techniques employed for the particular work under consideration. Theoretical implications of the present energy level, parity and single neutron pick-up spectroscopic factor assignments are discussed in conjunction with recently utilized shell-model Hamiltonians. 2 II. THE 3Na(p,d)22Na AND 3 5C1(p,d)34Cl REACTIONS 11.1. Introductory Remarks 1-4 of the nuclei in the Recent shell-model analyses regions A=18-24 and A=30—38 indicate that the nuclei whose structures depend most sensitively upon details of the model Hamiltonian are those which have odd numbers of both neutrons and protons. While the general features of the spectra of doubly-even and even—odd nuclei emerge more or less satis- factorily from such shell-model calculations, the calculated spectra of the doubly-odd nuclei are often even in qualitative disagreement with the observed level sequences. It thus appears that the definitive test of microscopic many-body theories of the Spectroscopy of light-medium nuclei will come in the attempt to explain the rich store of details observed in the experimental study of these particular nuclei. 22Na and 34C1 are pivotal to understanding the The nuclei structure of the s-d shell. In an s-d shell-model their wave functions are constructed of 6 particles and 6 holes, re- spectively. This number of active nucleons is large enough to allow the full consequences of the particularities of the two-particle component of the nuclear Hamiltonian to become manifest. At the same time, the dimensionalities of the model states are such that extensive theoretical work, in which the full s-dtshell-model space is employed to describe the wave functions of these nuclei, is available. This latter point is important because it allows the exclusion of the possibility that the theoretical results might be con- taminated by effects arising from intra-shell basis truncation. Shell-model calculations made with Hamiltonians of the Kuo-Brown5 type or with two-body matrix elements derived from simple central potentials fail to reproduce many simple as- pects of the 22Na and 34Cl energy level spectra, such as, 1,2 for example, the spins of the ground states. Hamiltonians derived in less straightforward fashion have been used to achieve some improvement in the agreement between theory and experiment, but it seems fair to say that a full understanding of these systems has not yet been achieved. The aim of the present experiment, part of a systematic study of doubly-odd 6'8 is to provide definitive experi- mental information on some aspects of 22Na and34 nuclei in the s-d shell, C1 so that a more rigorous critique of present and future structure cal- culations is possible. The hope is that a clarification of the structure of the As22 and A934 systems will facilitate progress in understanding the behavior of the nuclei in the middle of the s-d shell, Ae24-32, where the correct details of the effective two-body nuclear interaction are essential. we present in this report the results of a study of the 23 35 (p,d) reaction on Na and Cl at 35 MeV. The principle re- sults obtained relate to excitation energies and angular die- 22 34 tributions of states in Na and Cl, and the z-values and associated spectrOSCOpic factors of the neutrons picked up in the formation of these levels. There is considerable 9-14 22 of the levels of Na and a 15-23 on 34 experimental knowledge rapidly growing body of data Cl. WOrk relevant to the characteristics of the T=l states of these nuclei has 22Ne24’25 345 26,27 also been done with the nuclei and Since an extensive particle-transfer study with good energy resolution is available10 for 22Na, a large amount of funda- mentally new information was not expected to emerge from our 23Na(p,d)22Na data. Rather, we aimed to obtain more precise experimental excitation energies for higher lying states, an alternate set of spectroscopic factors to complement those from the (3He,4 He) reaction, and, with the aid of the higher energy resolution of the present work, a clarification of a few (but important) questions concerning the low-lying states. Our results for 34 Cl make a considerably more significant contribution to the state of knowledge about this nucleus. We are able to resolve many more states than has been possible 22 and, even for easily resolved states, in previous experiments our extensive angular distributions provide evidence for re- versing some previous z-value assignments. These z-values and their associated spectroscopic factors, and the precise ex- citation-energy assignment made in the 3—5 MeV region of ex- citation, serve to advance our experimental comprehension of the mass 34 system to a condition almost comparable with that of A922. 10 The present data are of interest from a reaction theory standpoint also, in that the angular range, energy resolution, statistical accuracy, and large number of transitions combine to provide stringent criteria for evaluating the usefulness of ordinary DWBA calculations for the (p,d) reaction at these energies for medium-light nuclei. The value of this aspect of the present study is enhanced by the concurrent analyses of (p,d) data6’8 on neighboring nuclei. 11.2. Experimental Procedures and Results The present experiments were performed with the MSU 28 Cyclotron and Enge-type29 split-pole magnetic spectrograph. The beam energies for the various experimental periods ranged from 34.9 to 35.0 MeV, and beam currents on target ranged between 300 and 800 nanoamps. The beam on target had a co- herent energy spread of about 20 keV, but by using dispersion 30 in the spectrograph in conjunction with the tech- niques discussed by Blosser, et al.,31 resolutions of better matching than 8 keV (FWHM) were obtained for 20—25 MeV deuterons at the focal plane under optimum conditions. Particle detection at the focal plane was accomplished either with nuclear emulsions or with a position-sensitive 32 wire proportional counter. The latter type of data, limited to a resolution of about 50 keV by the characteristics of 11 the counter, was used to supplement and confirm the results obtained by scanning the nuclear emulsions. Three different types of targets were used in the pre- sent experiment in order to circumvent the difficulty of ob- taining a Clean C1 target. Targets of LiCl (35Cl enrichment 299%) were used to obtain spectra free from sharp states which would arise from other chlorine compound contaminants. However, the continuous background resulting from the (p,d) reaction on the Li isotopes lowered the quality of these spectra and made it difficult to obtain accurate cross-sections for weak transitions. Sodium Chloride targets (35Cl enrich- ment 299%) provided data on C1 transitions which nicely come plement those from the LiCl targets. Finally, in order to remove ambiguities resulting from overlaps of peaks from Na and Cl levels, a target of Na metal was bombarded. All of these targets were fabricated by vacuum evaporation onto thin carbon foils. Figure 1 displays spectra, measured at 14° with nuclear emulsions, which result from bombardment of the three types of targets used. These targets were of moderate thickness and the combined spectrograph—cyclotron energy resolution was not fully Optimized, resulting in peak widths at half-maximum intensity of 15-20 keN. Representative particle groups in Fig. l are labeled as to energy of excitation. Figure 2 dis- plays a spectrum measured at 8°, with a NaCl target, for 12 which the energy resolution for deuterons at the focal plane was at the best level obtained in this set of experiments. The excitation energies measured for levels of 22Na and 34C1 in the present experiment are used to label the peaks in Fig. 2 and are presented in Tables 1 and 2. These en- ergies are obtained primarily from spectra measured at 8°, 11°, and 160 with a resolution of m8 keV, FWHM. In the case of many weakly excited levels, these data were supplemented by the data from the thicker targets of all three compositions. The energies were assigned as follows. The nuclear emulsion plates were scanned with a computer-linked microscope system33 in which a 25-cm-long precision screw served to position the plate under the microscope objective. A stepping motor on the screw served to increment both the plate position and a position signal which was read into the computer whenever a contact was activated to signal the observation of a track. In this way, the track-density spectra were generated with high accuracy and reliability as regards both peak positions and intensities. The dominant peaks in the Spectra were then tentatively assigned to known levels in 22Na, 34Cl, 150' 12C, 35Cl, and 23 11C, Na for which accurate (:1 keV uncertainty) excitation energies exist. All of these residual nuclei 35 23 were formed from the (p,d) and (p,p) reactions on C1, Na, 12 16 and on the C and O contaminants in the targets. The momenta of the deuteron and proton groups corresponding to Figure l. 13 Complementary spectra from the (p,d) reaction on the 23Na, 23Na- 5Cl and Li-35Cl targets, measured at 35 MeV and 14°, as recorded on nuclear emulsion plates. The resolution of the deuteron groups is 15-20 keV, FWHM. Selected peaks are labeled with excitation energy assignments from the present work, the "boxed" values indicating levels in 3“C1. 14 H gunman HACOHOUCO+mzu o+o_d Nm om ml ms TH ml . . . . . - e m m 4 I: l .N l o 2 NE W m m r m E m2 Srmsaimmed > r L . h S b > h p t 1[l[lril||rllhr v ‘AVIIL II?) OH 3 O n U a a . d a a l. o a .0 l 1 7a . . . CL 028% 30sz .55; 35mm .1 . . . , _ . . . . , . P , . . , . _ . ,2.“ I: Z l 2 : _ . u ‘M _ ,_ w r2 ,__ __ l I, we a s It. .. WM. mmnum oZNNE.&ozmm mil. r . > p b u... L! b . r p b S » t > p- Ll . . > . . .er 15 A spectrum from the (p,d) reaction on the 23Na-35Cl target, measured at 35 MeV and 8°, as recorded on nuclear emulsion plates. The re- solution of the deuteron groups is 8 keV, FWHM. All excitation energy values are from the present work, with those "boxed" indicating levels in 3"‘01. Figure 2. 16 Ill!!! [11111111 11111111 I' prmlT 1’1 1 '[TTTTTTI'I [1111111 1 ITHUIII ‘1“.— 6908 19 28 61149 12 ZOSS 26 “4843(9‘911592 ‘v’ ' gens 12'21 1289 10 p'dng] 2U: 23No[p,d]22NO 9L: 80 ...°i$‘z(p.d)!582 22 Plofe Distonce[cm.] 828+: 1:14-13 98 h h 889+: Ep= 35 MeV [215 198+» 262 h 20 18h 35C|[p,d]3L+C| 18 (\l ”2321(p'dl3u 16 "'°09,[p‘d O C) 3" m N O H C) O C) H 10‘+ 103 102 'LULlJ 9101-0 Jed s+unog Figure 2 17 population of these states were then calculated from the nominal settings and operating parameters of the cyclotron (beam energy) and spectrograph (scattering angle, magnetic field strength, position of emulsion plates, and non-linear corrections to the focal plane position vs. radius of our- vature line) and from the nominal Q-values for the reactions. When the total spectrum spanned two emulsion plates the gap between the plates was also specified. At this point all, or any desired subset, of the above parameters were adjusted so as to produce a least-squares fit between the set of precision energies used as input and the energies calculated to correSpond to the measured peak posi- tions. The changes in the nominal parameter values which oc- cur when an adequately large data set is used as input are well within the experimental uncertainties associated with the various parameters. For example, typical beam energy changes are 510 keV out of 35 MeV, angle changes are 10.10, and plate-gap changes are 0.0 to 0.1 mm. The appropriate final calculated excitation energies agree with the input values to :1 keV on the average. As input, we used essentially 34Cl below 3 MeV excitatione'ls'm'34 67,89 11 12C, all level energies in 22Na and 34 C and 34 and first excited states of the ground states34 of 15O and 16 68’97 of 23Na and the ground 0, and the ground and first 35 two excited states Cl. 18 We found that a statistically significant better fit to the input energies could be obtained if the 35Cl(p,d)34C1 Q-value was changed from its nominal value34 of -lO.422 MeV to -10.420 MeV and the 23Na(p,d)22Na Q-value was changed from -10.193 MeV to -10.l95 MeV. These changes are not in- consistent with the assigned uncertainties of the nominal Q-values,34 and at any rate, the excitation energy assign- ments depend only slightly upon whether the nominal or the adjusted Q-values are used. The levels whose excitation en- ergies are of primary interest fall in the middle 15 cm of the 50 cm (two adjacent 25 cm plates) of exposed emulsion. The 15 cm on either side of this region are thus simultaneously calibrated to many precisely known energies and this cali- bration is interpolated into the middle region, where it is confirmed by one or two additional known states. The uncertainties we assign to the excitation energies listed in Tables 1 and 2 are consistent with the scatter ob- tained both in analyzing the same data with different variants of the analysis procedure described above and in analyzing data taken at different angles with the same procedural de- tails. The uncertainties are compounded from jitter in the measured peak positions, irregularities in the detailed mag- netic field and focal plane structure, and inaccuracies and incompleteness in the set of input energies. The angular distributions we present for the 23Na(p,d)22Na 3 and 5Cl(p,d)34Cl reactions were compounded from all of the 1.9 T 1e 1, Excitation ener ies 3-2 values nd T values and k-u ectrosc ic ab factors for stages 8&2 2Na. All €35 values °x{r‘°t'i mptg ngp data have been norma ized to yield 0. 59 for the ground state. Ex (keV) J',T 2(238222282) 100 x 025(2),c’s<3+2)--(23N222288) 000‘ 000”"“‘1 3’,0""='f 2‘ 2c ,59‘ ,59‘ .59c 58321 583 . 1‘,0 0,2 2 2,19 1,22 ,28 85721 857 0*,1 2 2 ,2 , ,<7 89121 891 8*,0 2 2 .87 ,58 .57 152821 1528 5‘,o 193721 1937 1’,0 o 3, 3, 3) 7 195221 1952 2*,1 2 2 ,81 7,89 :5 198821 1983 3*,0 2 2 ,28 ,37 ,29 221121 2211 1',o 1 1 27. 27. 257121 2572 2;,0 1 1 20, 21, 298822 2989 3 ,0 (2) (2) , 1 ,13 ,<2 305921 3059 2’,0 2 2 , 3 0, 3 , 3 352021 3521 3-,0 (3) ,(2) 370722 3708 6’,0 398322 3988 1*,0 0,2 0 1, 3 2, 0 3, 807222 8089 8*,1 2 2 ,12 18,18 ,17 829223 8298 ,0 831923 8319 1‘,0 0,2 <1, 1 1, 0 838122 8380 2*,0 0,2 0,2 1, 5 8, 3 2, 2 886623 8888 (8-),0 852528 8522 (7’),0 858322 8583 2-,0 1 1 8o, 38, 882322 8822 ,0 8708 (5‘) 0 877022 8770 0-8‘ 0 (2) . 9 508128 5081 1.2., 0,2 1, 2 509828 5099 512323 5117 517223 5185 (2)‘,1 0,2 0,2 2.18 , 9 1 .15 532123 5317 583723 5880 - 1 1 11, 8, 580223 5805 2 0,2 1, 2 571928 578928 57“° 582828 5830 n.e. 588125 5858 0.2 <1. 2 5938 595828 5953 ,1 1 1 50. 5|. 599228 5995 2 2 .15 J3 608228 8088 aPresent work. b Reference 9. cReference 10. dReference 11. .Reference 13. {Reference 12. 8Reference 8. 2() Table 2. Excitation energies, L.values, JI and T values, and pick-up spectroscopic factors for states of 3“Cl. All C25 values extracted from the present data are normalized such that C2$=0.35 for the ground state. 8x (keV) 0",? 2 100 x 025(8).czs(8+2)--(350123“01) 000a 000””,d ° 0‘,1b’°'d 2‘ 2d , 35‘ ,83f , 313 , 85h 18721 188 3*,0 2 2 .105 .108 .120 85121 851 1:,0 0,2 0,(2) 11, 23 18. 15 0, 28 88821 888 1 ,0 0,2 2,(0) 8, 28 1. 32 18, 0 123021 1230 2*,0 0.2 0 23. 20 18. 9 50. 0 188721 1888 2*,0 0,2 (0) 5, 11 2. 18 18. 0 215821 2159 2127 2*,1 0,2 2 8, 11 12, 5, 11 32, 0 218121 2181 2,3‘,0 2 . 8 , o 2880-. J22 237723 2377 8*,0 (2) , 3 . 258021 2579 1*.0 0.2 (0) 5, s 0, 8 261121 2611 ,0 2 (2) , 25 0, 82 aesu-e J88 272122 2722 2-,0 3 3 , 3 312922 3128 1‘,o 0.2 2 1, 20 8, 8 333822 3332 ,0 2 (2) , 25 . 38 assu-e J53 338322 3381 3303 2‘,1 0,2 2 28, 2s 35, 25, 12 75, 0 358522 3585 3-,0 1 380223 3801 8<-),0 383823 3532 5',0 3 3771 1'.0 (1) 388525 398228 398(0) 3918 0‘,1 , 1 396828 398828 3982 3-,0 3 807828 8075 8~,0 3 818528 8180 2-,0 1,3 { 8072 1*.1 17, 8 821722 8115 2‘.1 0,2 18,20 30, { 0, 18 30.0 832828 8352 (1)-,0 1 8818 (1-3)-,o 1 888525 8880 (2.3)-.0 1 8518 (2)',0 1 881328 8805 (1-3)',0 1 868225 8636 8622(1-3)',l 1 872025 8720 8587 8‘,1 2 , 21 ,21 . 5 886026 (8875) (3*) 898225 (8891) (2*) 898025 . 897525 897(0) 5227 0 .1 .80 899823 0,170 500823 5318 555016 5380 aPresent Work. bReference 15. cReference 16. dReference l7. eEnergies for states in 3H 5; References 26,27. fSpectrosc0pic factors for 35Cl(d.3He)3“S; Reference 25. 8Reference 2. hReference 22. 21 data accumulated from the different targets and with the different detection mechanisms. Of course, when lack of re- solution prevented unambiguous values from being obtained in particular cases, such data were rejected. Also, in some cases the track density of strongly excited levels was too high to permit accurate counting by the scanners, so that counter data alone was relied upon. The angular distributions 22 for states in Na are shown in Figs. 3, 4, and 5 and those for levels in 34 C1 in Figs. 6 and 7. Not all states listed in Tables 1 and 2 could be observed at enough angles to per- mit measurement of meaningful angular distributions. These states were at best weakly populated and are not included in Figs. 3-7. The cross-section scales in Figs. 3-7 were assigned by comparing the (p,d) differential cross-sections as measured with the wire prOportional counter to the (p,p) elastic dif- ferential scattering cross-sections in the vincity of the maxi- mum in the 300-50o region. The counting rates for the elastic scattering were manageable for the counter in this region and the Na and Cl peaks could be resolved clearly. The elastic scattering distributions were normalized to the predictions obtained from the Becchetti-Greenlees optical model potential formula37 (see APPENDIX B). The experimental-angular distri- butions for 23Na and 35C1 in this region are rather dissimilar and both were simultaneously well fit with the Becchetti- Greenlees predictions. we estimate a 10% uncertainty for the 22 accuracy of the optical model cross-sections in this region, and estimate a 10% probable error for the mechanics of relat- ing the experimental (p,d) yields to the (p,p) yields. Thus, the combined total uncertainty in the overall cross—section normalization of our angular distributions is estimated to be in the range of 15%. The relative uncertainties from distribution to distri- bution should be less than 2%. The chemical stability of sodium chloride appears to be maintained under evaporation and bombardment, so the relative Na to Cl cross-sections should also be good to 2%. II.3. Analysis of the Angular Distributions The angular distributions displayed in Figs. 3—7 were analyzed with the distorted-wave Born approximation (DWBA)38 to obtain 2-values for the neutrons transferred in the (p,d) pick-up process and the associated strengths, or spectrdscopic factors. This analysis was carried out by least-squares fit- ting a combination of 2=0 and 2=2 (or 2:1 and 2=31 curves, predicted for a transition of given Q-value, to the 3°-3So experimental data for each state. The solid curves in Figs. 3-7 show the combined-2 theoretical distribution fits from which the spectroscopic factors were obtained. The dotted curves indicate the contribution of the smaller z-value pat- tern to the combined (solid line) distribution curves. Figure 3. 23 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)“Na reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contribution of the first indicated 2-value for mixed-2 distri- butions. 24 1022.2221022222210222-22 : Ex: 000 89V 1 : Ex: 583 80V ‘2 Ex= 857 keV ‘ : L: 1 I L:0+2 : : L:2 : 10 2 10 g 10 . 3 l . .‘ . 1: 80 ‘ 80 510222-,2.102,22.-1022,22- \ : Ex: 891m . Ex=1528 82v é . Ex=1937 80V 3 2 L=2 8 : 5+ 1 : L=0 8 E 2 D d p 1 f 1 > 1 b 4 1m; 1? 1 b b 1 : 4 ’ 1 r 1 F 3 p O} : 1 Q 10‘1 10"....q'0'l‘en. _2. . . ‘. 2 1 _2: ‘ . . ‘ #4 : _2}. f b 10 l 20 80 80 1° 0 20 80 60 1° (W0 '0 10222-21- 102,,222 102-.2.2 : Ex=1952 kOV : Ex=198H kOV : Ex=2211 IIOV 8 L32 4 ; = 1 = 10 10! L 2 1 10 L l 10'1 p v '7'“ v vvtwv‘ vvvvvw . . aauan‘ A AAA.“ ; aalaaa‘ H m ' . . LAM 10‘1: E , -2.: , 0 10 (We c.m. ongle[degrees] 10'?! Figure 3 [Figure 4. 25 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)22Na reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contri- bution of the first indicated l-value for mixed-2 distributions. p F 82242531 1.28 L=1 102 - 2 2 . 2 2 Ex=3520 keV r L=3 4 10E ( ) 1: 2 a 10'“ ‘ E. I 0.. I 10‘2 A J; 22‘ 0 20’ 90 102 2 v 2 22 Ex=9072 80V 1 i L=2 % 10E E i i 1 1 I ' e . . 1 -1‘ ‘ 10 E E -2: . 2 ‘f A 2 1° 0 20 80 c.m. ong|e[degr‘ees] Figure 4 26 102 . 2 - . 2 : Ex=2988 82v 10E 3 . 3 3 . 80 80 102 2 2 . 2 , 5 Ex=3707 22v 3 10’ ‘ E E 1; I E E 10'1E . i?8¢+’+++a 10: *2‘0 ‘8‘0 ‘80 102 2 2 2 2 2 : Ex=H319 kOV 3 10'; L=0+2 1‘ 1b 1 E 3 -1’ 1 10 e 1 10-2NKL ’L'L: 0 20 80 80 102 2 2 2 2 . : Ex=3059 89V 3 2 L32 4 E 1 1E 3 _.: : I ? _2r A A 1 1° l 20 80 102 - . 2 . 2 E Ex=3993 kOV : : L=0+2 3 10E 1 1, 10‘1 104'? 102 - 2 2 2 2 ’ Ex=‘+361 kOV 102 L=0+2 Figure 5. 27 Experimental angular distributions for states in 22Na as observed in the 23Na(p,d)“Na reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 350. The dotted curves show the contribution of the first indicated 2-value for mixed-2 distri- butions. 28 102 102 102 : 6232583198 a _ 624512215? 1 Ex=TSH§7 7.29 I = I I L=0+2 I L=l 1 10 L 1 10 1 10 L 3 <0 : \ 1 Q i tE; ‘ so 03 102222,,10222222 '13 Ex=5958 kOV g E Ex=5992 22v L=l « » L=2 \E; 10E . 1o, 1 ‘t3 . -2 2 2 - . . I -2: 1 2. A . . 1° :0 20 80 0 1° 0 20 *‘80 0 c.m. ongle[degrees] Figure 5 Figure 6. 29 Experimental angular distributions for states in 3“C1, as observed in the 35C1(p,d)3"Cl reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the contribution of the first indicated z-value for mixed—2 distri- butions. Ex; ObO Tkeg L=2 H O i y... H I? v 17" -2 . A . A 4 1° 20 H0 so 102 v r r , , Ex= 868 uev L=0+2 6:515:31“ ‘ L=0+2 1 10‘2{ 30 102 . , v v , E Ex: 1'1‘7 heV » L=2 < 1"! . 1. ‘ m‘ -1' 10 g -2 - A A A 10 o 20 40 102 - r ,r T - * Ex=1230 Rev 1 , L=0+2 102 is 1, , . r : Ex=2181 keV g 10% L=2 ; 1% 1 10'{ . 1 - i * 1° 20 ‘ 20 $0 ‘ BO Ex; Hél Tum/V L=0+2 éx='18é7 Lov' L=0+2 éx='23§’7 fuel! (L=2) c.m. ongle[degrees] Figure 6 Figure 7. 31 Experimental angular distributions for states in 3"C1, as observed in the 35C1(p,d)3"Cl reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contribution of the first indicated z—value for mixed-2 distri— butions. 32 1ozoooiv102,rir. 102.1frv Ex=2580 keV é : Ex=2811 uev : : Ex=2721 kev i L=0+2 < » L=2 ‘ ~ L=3 ’ 10F 3 ICE E 10f 3 1 : : 1 4 h J > 4 . 1E 1 m‘ lo-lr E 1 .II .'I 1 L4 PL L A 4 10-2» A A A 1 L 1 20 H0 80 0 #26 90 0 $102-r,rl 102-rov, \\\ : Ex=3128 keV . Ex=333q keV » L=0+2 L L=2 h—l L 102',r,v1021,r,o E Ex=L+217 keV 3 ’ Ex=L§720 keV : 10’ L=0+2 * 10> L=2 ; 3 E ‘ a 1! 3 i I I I -1 . 1° E ' : 10_2> A A L L A d -2} A L A A A 1 o 20 um so 10 n 20 L+o so c.m. ongle[degrees] Figure 7 33 Many previous studies of the (p,d) and (d,p) reactions in the 15-40 MeV range of particle energies have experienced serious difficulties in analyzing the experimental angular 39,40 208 distributions with the DWBA. Detailed studies on Pb 16O are particular examples. The difficulties involved and obtaining good fits to given i-value transitions at parti- cular energies and maintaining stable, good fits and con- sistent spectroscopic factors over a range of fiLvalues, beam energies, and Q-values. Problems specifically involving the relationship between DWBA predictions and experiment as a function of the Q-value of the reaction (corresponding to dif- ferent bindings of the transferred neutron to the core) have 41'42 in the f-p shell with the aid been studied extensively of sum-rule arguments. A general feature of past DWBA analyses of (p,d) angular distributions has been that the local, zero-range predictions were improved, vis a vis the experimental shapes, by intro- ducing a cut-off in the radial integration somewhere near the nuclear surface. It has been proposed43 and demonstratedlu"47 that an alternate prescription, the "adiabatic" deuteron, to the usual elastic-scattering-based deuteron optical model po- tential can, in a more physically motivated way, provide all of the benefits obtained by the use of cut-offs. A second alternative, also more plausible and successful than the sharp cut-off technique, involves making finite-range and 34 / non-locality approximation corrections and, in addition, introducing a density-dependent damping of the Vpn inter- action.48 The many angular distributions obtained in the present experiment, measured with good statistical accuracy and en- ergy resolution in the 4°-40° angular range, provide the basis for a very thorough critique of current DWBA procedures for (p,d) reactions on medium-light nuclei. We have carried out DWBA calculations using a variety of different prescriptions for the various input parameters and have compared the results with our data. The present DWBA calculations were all made with the 49 computer code DWUCK. The parameters of the optical model potential for 35 MeV protons were obtained from the formulae 37 50 of Becchetti and Greenlees. The formulae of Fricke, gt_gl., predict discernably different elastic scattering angular dis- tributions for s-d shell nuclei, but the DWBA predictions for (p,d) seem largely insensitive to changing from one proton potential to the other. 51'55'98 deuteron optical- When any of the conventional model potentials are used, the calculated shapes of the z-o and 2-2 distributions agree much better with our experimental test cases in the finite-range, non-local (FRNL) approximation than in the local, zero-range (LZR) approximation. (The non- locality parameters used were the standard values of 0.85 and 0.54 for the proton and deuteron, respectively.) The best 35 results obtained with any of these various potentials appear to be obtained with the "Set I" values of Hinterberger, gt_gl.51 (see Table 3), which is gratifying since this potential is probably the best grounded in terms of mass and energy de- pendence. The Hinterberger gt_3l. "Set II" and the Newman, 52 potentials yielded results very similar to each other stei- and not too different from those of "Set I". The critical success of Hinterberger "Set I", relative to potentials of different origins, lies in its correct re- production of the forward angle (ecm;200) i=0 and 2:2 shapes. Its principle failing, shared by all the others to a greater or lesser extent, is its overestimation of cross-sections at larger angles (ecml300),a failing which grows more pro- nounced as the Q-values become more negative (excitation en- ergies increase). Previous investigations led us to expect 43 46 al. that both the "adiabatic" and the "density-dependent" terations to the conventional DWBA procedure would improve the predictions at these larger angles. The "adiabatic" po- tential, designed to account for effects resulting from dis- association of the deuteron, is put together from proton and neutron optical model potentials (taken from Ref. 37 in the present instance) according to a particular prescription.43'44 The adiabatic-potential calculations were carried out in the LZR approximation, since the FRNL corrections did not yield significantly different results. 36 .nm mocohouom cw cw>ww mm ow oocopcoaoouo mxaco >o: 00.0" u now who ssozm mosam> . WCOMHUMU'H £POD .HOhO .sm oocosouom Beau msouofimpoa coapsoc vac cou0hm mm: oocohouomo .Hm oocoaouomn .um monogamous o mmaaca =~.H maul mm.o :~.H coapopuaom nouns mouupm o» pouwsmv< pcsom cosusoz Alo.o mm.H m mm.ou~m.mm can qzxuv econopsmo 5H.H mn.o Ho.a ~.m mm.o ~m.H mm.m mm.o ~m.H o.m ms.o 5H.H nm.m: occuosm " .Q Hosmav vaomm AoHe.o m~.H m mm.o|mm.:m paw qzxmv acopouaoa 5H.a mn.o Ho.H ~.m :m.o mm.H nm.m :m.o mm.a o.m ms.o 5H.H mm.m: weepopm no .a m ZNNAU V 2mN name AEuv “any A>ozv “Ewe “Ems A>ozv AEMV hams A>ozv “Ewe Afiuv A>ozv o.H 0mm om:H om> hmm mmp mm: >m >.H >3 mm as m> oaowwpom .muov Huzmnv.avaomm paw MZNNAo.aVo2m~ ecu Mo wwm>aocm one cfl pom: mnouofimpma Hoooeuaoowuao .m magma 37 The "density-dependent damping" of the Vfin interaction48 provides an alternate means to reduce cross-sections at larger 2/3 angles. We use here the damping factor F(r)=(l.0-l.8450(r) ). where p(r)=0.l7[l+exp(x)]-1, x=(r-roAl/3)/a and "re" and "a" are the radius and diffusivity of the neutron bound-state well. The density-dependent Vpn damping was studied in con- junction with FRNL calculations which used the Hinterberger, et al. ”Set I" deuteron potentials. We have analyzed our data in detail with the following DWBA calculations (see Table 3): (l) The Becchetti-Greenlees37 proton parameters and Hinterberger, et a1.51 "Set I? deuteron parameters, using the FRNL approximation. These calculations, henceforth referred to as FRNL, are thus completely orthodox and unadjusted. (2) This same combination of proton and deuteron parameters and computational approximations, but with the addition of the density-dependent damping of the Vbn in- teraction, henceforth referred to as DFRNL, and (3) The Becchetti-Greenlees proton parameters and the adiabatic deuteron parameters in the LZR approximation, henceforth re- ferred to as ADIABATIC. The results of these three types of DWBA calculations are compared with each other and with some of our experimental 3 data for the 5Cl(p,d)34Cl reaction in Fig. 8. The virtue of the DFRNL shapes is clearly evident over the range of ex- 34 citation energy in C1 shown therein. Figure 8. 38 A comparison of fits to representative angular distributions from the 35Cl(p,d)3“Cl reaction at 35 MeV with the three chosen types of DWBA calculations. All fits were performed over the angular range from 30 to 35°. The curves are identified as follows: —————DFRNL, —----FRNL, and ——-——ADIABATIC. 39 Ex=t12so Lev' L=0+2 .-- 0’ ~‘ 0 10'2 0 *‘2b ‘ so ‘ so 0 ‘=2b ‘ so c.m. ong|e[degr‘ees] Figure 8 ‘ so 40 11.4. Discussion of Results II.4.A. Levels of 22Na Experimental evidence on the energies, spins, parities, and other properties of levels in 22Na has been accumulated principally at Brookhaven (see the literature cited in Ref. 9) via studies of the gamma-ray decays of these levels, and at the University of Pennsylvania via charged particle trans- fer studies. These works have resulted in precise excitation energy assignments to all of these low—lying levels plus some higher excited states, and a rather complete catalog of what levels exist up through 6 MeV excitation. With the (p,d) re- action at 35 MeV, we observe evidence for the existence of all but 2'of the 38 previously identified levels below 6 MeV excitation in 22Na (see Table l). The two unobserved levels are very weakly excited in analogous reactions. We observe one new level, at 5.719 MeV, unresolved in previous work. Our assigned excitation energy values agree with previous assign- ments to within the l-2 keV combined uncertainties up through 4 MeV excitation. Between 4 and 5 MeV, agreement in excitation energies between the present and previous results is still good, although uncertainties and deviations are both in the 2—4 keV range for that region. From 5 to 6 MeV, there are some significant discrepancies between the present assignments and previous values, which, in this region, have all resulted from 41 magnetic analysis of charged particle reactions. These dis- crepancies seem to involve spacings between levels rather than more understandable systematic deviations of scale. The present assignments (Table 1) for the z-values of the various transitions are, in all cases, consistent with the consensus assignments of d" and with the results of the anal- 23 4 10 ysis of Na(3He, He)22Na data. The relative values for spectroscopic factors extracted from the present data agree 4He) qualitatively with the numbers obtained from the (3He, work. However, the failure to obtain a good i=0 fit to the data with the present DWBA calculations leaves a large un- 2S (i=0). There are some in- certainty in our values for C dividual deviations between present and previous spectroscopic factors, such as the different ratios of the strengths of the first 3+ state to the first 4+ state, which might indicate some differences either in the behavior of the DWBA for these two kinds of reactions or in which alternate reaction mechanism is the most significant contributor to the direct single-step process. The results of the analysis of (p,d) data taken at 17.5 MeV for the lowest few states35 are also consistent with the present analysis. The observed features of the positive-parity levels of 22Na, as regards electromagnetic decay and single-nucleon transfer population, have been extensively interpreted in the 10,36 framework of the Nilsson model. The most detailed 42 shell-model analysis of this system,4 carried out with com- plete consistency for the A=19, 20, 21, and 22 systems, treats all of the same observables with a uniformly higher degree of success. The spectroscopic factors predicted for 23Na-vzzNa transitions are listed in Table l. The shell-model predic- tions agree with the experimental results for spectroscopic factors within reasonable uncertainties for the first six states. The 2:0 spectroscopic factor for the first 2+, T=l state, predicted to be C28=0.07, is observed to be less than 0.01. Even though the magnitudes are rather small, this might be an important clue to a failing of the wave functions in- volved. Larger i=2 spectroscopic factors are predicted for the second and third 3+ states than are observed, in particular for the third, at 2.968 MeV excitation. 34 11.4.3. Results for C1 34C1 have been assigned by The energies of the levels in a combination of gamma-ray decay and single nucleon stripping experiments. The combined uncertainties of the two kinds of experiments are such that unique identification of states above 3.5 MeV excitation is not always possible. we present in Table 2 a composite of the results of these previous experi- ments, but do not attempt to quote errors. The uncertainties in the energies of levels below 3.5 MeV are all based on gamma ray measurements and should be good to the order of a kilovolt, or better. 43 The level energies extracted from the analysis of our data, and their assigned uncertainties, are in agreement with the existing values up through 3.5 MeV excitation. The largest deviation, 3 keV, occurs for the "3129" keV state. All levels previously well established to lie in the 0.0-3.5 MeV region are seen in the present data. The level located 17 by Erskine, et al. at 1924 keV, and not seen in any other work, is not observed here. Nonetheless, its existance is 34Cl, not implausible in the context of theoretical spectra for which predict a few low-lying levels with vanishing spectro- sc0pic factors. Above 3.5 MeV we fail to observe several states seen in previous work. All of these levels would be expected to be weakly populated via pick-up. This, together with the high density of peaks in this region, makes ob- servation of these levels at enough angles to insure unam- biguous identification difficult. At the same time, we excite several levels in the 3.5-5.0 MeV region which have not been previously reported. Most of these are also weakly excited, but a few have significant strengths and are hence of special interest in the present spectroscopic picture. The third 2+ and the first l+ levels are known 34S (see Table 2) and 34 to lie close to 4.1 MeV excitation in should occur at about the same energy in C1. All theoretical calculations predict a significant i=2 pick-up Spectroscopic factor for this 2+ and a strong 2=0 strength for the 1+. The 44 "level” we observe at 4217 keV has both of these properties. The 1+ and 2+ levels in 34S are separated by 43 keV, the l+ lying lower. The first two 2+, T=1 states in 34C1 are raised 34 in excitation energy relative to their positions in S by 32 and 78 keV, respectively. The second of these levels has three times the i=0 pick-up strength of the first, and we may . . -l 3 . conSider it, crudely, as a 81/263/2 state relative to the 2 3/2 shift is quite probably associated with this empirically es- d nature of the first 2+ level. The difference in energy tablished difference in the wave functions. The first 1+, T=1 state should be (31}2dg/2) in nature also. All structure calculations agree on this point, and the stripping data in consistent, though not confirmatory, with these predictions. The third 2+ level is empirically determined to be mainly d§/2 in character. Thus, if the energy shifts observed for the lowest two 2+ states were to be replicated by the third 2+ and the first 1+, the l+ level would move up by 46 keV more than the 2+. This difference would almost exactly cancel out the 43 keV gap between the corresponding states in 34S. Hence, the very close degeneracy 34Cl would not be a completely unreasonable of these levels in possibility. However, it must be noted that the total shift of these levels, which.must occur if they together form the 4.217 MeV peak, is greater than that observed for the lower two excited T=1 states. Nonetheless, if this peak is not a doublet we have a rather clear-cut discrepancy with theory on our hands as regards spectroscopic factors. 45 The excited 0+, T=1 states, populated strongly via the 36Ar(p,3He)34Cl reaction, should be very weakly populated in the present single nucleon pick-up experiment. We have tentatively assigned the 3942 keV state as 0*, T=1, but this is based solely on energy proximity. Likewise, we associate 34s with levels we some of the other T=1 states observed in observed in the 4-5 MeV region. We do not believe that either of the two strongly excited levels at 5 MeV excitation (4998 and 5008 keV is the third 0+, T=1 state, but suggest the 4975 keV level as a possibility. The i-values we assign are all consistent with the con- sensus Spin assignments and stripping 2-values. Our results are in repeated disagreement with the previous neutron pick- 22 as regards dominant i-value assignments and spectro- up study scopic factors for all but the most trivial cases in the low- lying spectrum. Results are compared in Table 2. At higher energies, the lack of adequate resolution in the previous work resulted in a failure to realize several doublets, such as those at 3334 and 3383 keV, and at 4998 and 5008 keV. It should also be noted, parenthetically, that the comparison between experiment and theory in Ref. 22 is further vitiated by an inconsistent treatment of the isospin coupling factor. There are striking similarities between the (sd)-6-con- figuration spectrum of 34Cl and the (sd)6-configuration Spectrum of 22Na. Despite the formal theoretical identity and the resemblance of the sequences of the first few levels, 46 it must be remembered that the single particle energies and the Pauli Principle limits on orbital occupation dictate that states in 22Na are dominantly formed out of dS/Z configurations while the features of the low-lying levels of 34Cl arise from some mixture of d3/2 and 31/2 couplings. The first step to understanding the structure of these latter levels is to de- termine the way in which 51/2 and <13/2 particles contribute to each of the individual wave functions. The two kinds of reactions which most directly relate to this issue are single-nucleon stripping from 338 and one nucleon pick-up from 35C1. The (3He,d) and (d,p) reactions on 33S have been studied with good energy resolution. 17,26 The results of the z-value assignments from these works are noted in Table 2. If a simple dg/z model is assumed for 33S, the measured stripping spectroscopic factors indicate + + that the "dg/z" states of J";r = 0 .1. 3 .0. and 1+,0 are the ground, first, and third excited states, with the l+ strength being slightly fragmented into neighboring l+ levels. The 2 3/2 and 3383 states in a ratio of about 2 to 1. Many of the levels (d ) 2+,l configuration seems to be spread over the 2158 show some 2:0 strength, indicating a significant lack of closure in the 81/2 orbit. A much more realistic shell-model treatment, allowing all three s-d shell orbitals to be active, accounts for a large portion of the details of the stripping results (see Ref. 3, FPSDI Hamiltonian results). 47 If we assume the simplest model, (dg/z), for the 35Cl ground state, then the present pick-up results express the following qualitative picture. Again, the 0+,l and 3+,0 states resemble (dg/Z) states. The (dg/z) configuration is spread almost equally over the first three 1+,0 states and is again split between the 2+,l states at 2.158 and 3.383 MeV. This time, however, the ratio is l to 2. The dominant impression yielded by the spectroscopic factor results is, however, one of complexity. Simple shell-model pictures are only faintly suggestive of the complex structure of the low-lying levels revealed in pick-up and stripping. This detailed structure‘ observed in pick-up is also, however, quite well reproduced by the same three-orbit shell-model calculation just mentioned. The predictions this calculation yields for pick-up spectroscopic factors for the levels of 3401 are presented in Table 2 for comparison with the experimental results. The correspondences between the lowest eight or so states, and for a few selected higher levels, are quite good. This, to- gether with the almost comparable success obtained for stripping, indicates that the complex shell-model wave func- tions for these levels have many of the properties required of a realistic and thorough description of the physical states. There are several discrepancies between theory and experiment for higher-lying states. The lack of spin assignments for some of these higher states prevents a more definitive critique of the model results. In Table 2 we have therefore entered 48 some theoretical states which have significant spectrosc0pic factors and appropriate energies in line with states of un- known spin. The spectroscopic factor predictions from this shell- model calculation are actually more successful than are the predictions for energies. There are some inversions in level orderings and a serious compression of the theoretical spec-4 trum. These features, as well as the Spectroscopic factor failings at higher excitations, clearly indicate the need for still better calculations. The present experimental results verify, however, that the present calculations form a secure foundation upon which more advanced theoretical work may be based. II.5. Conclusions The DWBA analysis of the 35Cl(p,d)34Cl transitions yields good fits to the angular distributions and stable Spectroscopic 23Na(p,d)22Na data is not fit so well. In factors. The particular, no formulation of parameters and adjustments we attempted yielded an acceptable i=0 shape for Na while pre- serving a reasonable i=2 prediction for Na and simultaneous good fits to the Cl data. The spectroscopic factors extracted from the data are well reproduced by recent shell model calculations in the domain of approximately the lowest 10 levels. The spectroscopic 49 factors also facilitate identification of T=1 levels by com- parison with 35Cl(d,3He)34S results. Several strongly populated states still remain without a unique spin assignment, and when these are fixed, the final combined experimental pic- ture of 34Cl will offer a challenging and hopefully rewarding problem to structure theorists. III. THE 37C1(p,d)36Cl REACTION III.l. Introductory Remarks The simplest shell-model description of 36Cl arises from the couplings of three d3/2 neutrons and one <33/2 proton. An obvious model extension is the inclusion of 51/2 excita- 56-58 tions. Recently, the set of configuration basis states has been further expanded to include the 1d5/2' as well as the 3,59 281/2, and ld3/2 orbits, and initial calculations in- volving excitations to the f-p shell have also been made for 60-61 Several residual interactions various s-d shell nuclei. and model Hamiltonians have been used in the recent studies, yielding different results for some predicted observables. There is an obvious need for accurately determined experi- mental quantities in any attempt to critically evaluate, and suggest improvements for, these various models. Since cal- culated spectra for the odd-even and doubly-even s-d shell nuclei Show good correspondence with available data while pre- dictions for the odd-odd nuclei are often in qualitative dis- agreement with experiment, sound experimental knowledge of the doubly-odd systems is essential to a useful critique of recent theoretical studies. Although many levels have been previously observed in 36C1, excitation energies have not been assigned to high ac- curacy and the spins of several low-lying levels are not as yet unambiguously determined. Only a few single-neutron 50 51 pick-up experiments leading to states in 36C1 have been per- 22'62“65 Spectroscopic information is consequently formed. sparse, with the bulk of the experimental spectroscopic fac- tors available for the strongly populated positive parity levels below 4 MeV excitation and only one negative parity state. The present work is a continuation of a comprehensive study of doubly-odd s-d shell systems via the (p,d) reaction at 35 MeV.6-8 We have attempted to observe and catalogue 36Cl as possible, assigning them precise as many levels in excitation energies and extracting Spectroscopic factors for the neutron transfers which populate them. Deuteron spectra recorded on nuclear emulsion plates with a total energy re- solution of 10—18 keV, FWHM, allowed the assignment of ex- 36C1 to ~8.2 MeV with an overall ac- citation energies in curacy of $1 keV/MeV. Angular distributions for states up to 8.2 MeV have been taken over a 30 to 55° range, with spectro- scopic factors extracted and 2-values assigned for transitions producing analyzable distribution patterns. The forward- angle data allowed essentially parameter-free i=0 spectroscopic factor extraction and a critical test of theoretical i=2 shapes. The present results will be compared with previous experimental works, and their implications for theoretical studies in the upper s-d shell will be discussed. 52 III.2. Experimental Procedure Targets for the present experiment were made by evaporating a sodiumrchloride compound (enriched to 96.5% 37C1 isotope) onto 30 ugm/cm2 carbon foil backings. in the The targets were kept under vacuum. Consequently, target thicknesses (20-120 ugm/cmz) were estimated from deuteron yields and assumed scattering chamber geometry. 35 MeV protons from the Michigan State University sector-focussed cyclotron were used to induce the (p,d) reaction leading to 36 22 states in C1 and Na. Reaction products were analyzed in the MSU split-pole magnetic spectrograph, deuteron spectra being recorded both with a single-wire proportional counter32 and on 25 micron thick nuclear emulsion plates. Spectra were recorded with the counter at closely spaced laboratory angles from 30 to 550 with a total resolution of 50 keV, FWHM. The spectrograph acceptance aperature was 0.6 msr for the angular region of greatest importance (30 to 30°) and 1.4 msr for angles greater than 30°. Data acquisition and particle identification is this portion of the experiment were accomplished in the MSU Sigma-7 computer. These data allowed extraction of complete angular distributions for the 36 37C1(p,d)36Cl levels in C1 below 2 MeV excitation. The 2 and 3Na(p,d)22Na Q-values34 dictate an overlap of their separate deuteron Spectra for excitations greater than ap- 36 proximately 2 MeV in C1. Consequently, for higher 53 ‘excitations the counter data generally provided useable cross- 3601 levels separated 22 section measurements only for those 36 from others in C1, and from any in Na, by more than the deuteron peak resolution. 23 37Cl and Na were Protons elastically scattered from observed in an experimental configuration identical to that used in the (p,d) measurements, except for an appropriate ad- justment of the Spectrograph magnetic field. The 3 )37 2 Cl and 3Na(p,po)23Na data were recorded at 7Cl(p,po laboratory angles from 250 to 50°, and assumed to have the values predicted by optical-model calculations using the Becchetti-Greenlees proton parameters37 (see Table 6 and Appendix B). Normalization for the (p,d) data was made re- lative to these elastic cross-sections. A total uncertainty of 15% is assumed to arise from uncorrelated 10% uncertainties in the optical-model predictions and the normalization pro- cedure itself. The 23Na(p,d)22Na angular distributions ob- served in this experiment show complete consistency in both shape and absolute magnitude with those obtained in another, independent study at this laboratory.7 When peaks from the 37 23Na reactions coincided, the cross—section as- 36 Cl and sociated with the transition to a Cl level was, therefore, deduced by subtraction of the independently measured 23Na(p,d)22Na cross-section for the appropriate energy level and angle. Similar corrections for those cases where levels 54 34 3 in C1, strongly populated via 36 5Cl(p,d)34Cl, coincided with those in C1 were made after an appropriate consideration of the enrichment factor. Deuteron Spectra were also recorded at angles from 40 to 45° on nuclear emulsion plates. Various runs yielded total particle group resolutions of 10 to 18 keV, FWHM. An example of the best resolution spectra is shown in Fig. 9. The spectrograph acceptance apertures were the same as those used in recording the counter data. The plates were shielded 3 from He and 4He particles by 10 mil Mylar strips and levels in 36C1 to approximately 8.2 MeV excitation were observed. At each angle, the deuteron Spectrum to roughly 4.8 MeV excitation in 36C1 was recorded on one 10 inch long emulsion plate, with the remainder of the deuteron groups and the pro- 12 16 23 37 ton groups from scattering on C, O, Na, and Cl falling on a second, abutting plate. Elastic proton spectra recorded with a NaI monitor detector at 90° to the beam, and a beams current integrator were used to achieve relative normalization of all proton and deuteron spectra. Normalization of the plate data to the counter data was accomplished by cross- 36 section comparisons for selected low-lying levels in C1 23 and Na at several forward angles. 55 A spectrum from the (p,d) reaction on the 23Na-37C1 target, measured at 35 MeV and 14°, as recorded on nuclear emulsion plates. The resolution of the deuteron groups is 10 keV, FWHM. All excitation energy values are from the present work, with those "boxed" indicating levels in 36C1. Figure 9. ZZIS mam ——- FY4111] A _ e 89 h —T-j mm “'1‘“ *7 $1114 —— * 'j - {SE-Eh , ——-—-— (1) [:43] N ' 6180a ”1113:? 23No[p,d]2‘2No Ep= 35 MeV: 9L: 14° =- _‘= : . ——:= ”3&1 i ““1 ease Lia-1:1 'IIIPII _-=='“——_' 7— 37C|[p.d]36Cl ‘0‘5 cd , - h Ogllp 1091 20 ___.— 1122 [334: null 1 l hull: 1 1 [Hull 1 I hulli ( ) uulll 1 [“1111 1 l O 18 m N m N O O O H C) O C) H r—Q F4 H 'Cuul 9101-0 Jed s+un63 Plo+e Distonce[cm.] Figure 9 57 III.3. Excitation Energies Excitation energy analysis and assignments were made on the basis of centroids extracted from the best resolution nuclear emulsion spectra recorded at 4°, 8°, and 14°. The 36C1 presented in Table 5 are a weighted energy levels in average of the results of two analyses involving these data. The first method involved much the same procedure used in the analysis of the 39K(p,d)38K reaction. 'The low~lying excitation energies in 36C1 have not been reported to 1 keV accuracy. Consequently, any energy calibration in the pre- sent work must rely heavily on the precisely determined energies in 22Na.66 The energy analysis involved a fit to these and other reference energies via a least-squares ad- justment of the beam energy, scattering angle, and the constant, linear and quadratic coefficients of a Bp vs. 67 for the 8° and 14° spectra focal-plane-position relationship (see APPENDIX A). At angles <8°, effective use of this fitting procedure is greatly hindered by the overlap of all elastic proton levels on the nuclear emulsions. The second plate was assumed to be directly adjacent to the first. Table 4 displays the reference peaks chosen. These levels were used only where accurate, unambiguous centroids could be extracted. Appropriate target loss corrections were made for all reference levels. The best overall results were obtained 58 Table 9. States used for the energy calibration of the 37Cl(p,d)36 reaction data. Some energies in Na extracted in the present work and in a previous (p,d) study are shown to illustrate calibration consistency. Reaction Excitation Energy Levels in 22Na(keV) Levels in 22Na(keV) (keV) in the from previous work from this work Residual Nucleusa 37 C1(p,d)36C1 ground stateC 23Na(p, d)22Na ground3state 0003 0003 583 0530.1d 58331 58331 657.0 $0.1“ 557:1 558:1 890.893o.2d 89131 89031 1951.8 3o.3d 195231 195232 1983.5 30.5d 198831 198832 2211.k 30.32d 221131 221132 2571.5 30.3d 257131 25713 2 2968.6 30.8d 296832 297138 3059.4 -o.8d 305931 30513u 398332 3988-8 807232 uo723u 858332 ”81 8 595838 595935. 15 5992- 8 5993- 5 120(p.d )110 ground state 7C(p,d)l 39C ground state 23Cl(p,p)23§: ground state Na(p, p) ground+state 160 uul. o -1. 0e 120(p, p)120 ground state C(p, p) ground state aUsed for present calibration. II.2. CAdjusted as described in text. See Sec. dReference 66. eReference 68. 59 when the mass table Q-values for the 23Na(de)22Na and 3 34 7Cl(p,d)36C1 reactions were manually adjusted by —2 and -1 keV, respectively. This is consistent with the adjust- ment of the 23Na(p,d)22Na Q-value required in the analysis 35Cl(p,d)34Cl data (see Sec. II.2.) and within the Q-value of errors quoted in the latest mass tables for both reactions. The corrections to the nominal beam energy required by the fit for both angles was +9 keV, with scattering angle cor- rections <0.3° in both cases. These changes are within the accuracy to which the experimental apparatus and analysis sys- tems yield precise experimental parameters for any given run. In an effort to obtain the best possible overall ex- citation energies from the present data, a second fitting pro- cedure was employed for the 4°, 8°, and 14° spectra. The beam energy and scattering angle corrections and the geo- metrical calibration parameters found in the above analysis were used for the 8° and 14° spectra. Close approximations to these parameters were used for the 4° spectrum since the experimental configuration was essentially the same. This time, a linear, least-squares fit to the deuteron momenta 36 22Na (see for appropriate reference levels in C1 and APPENDIX A and Table 4) was required. Again, the appropriate Q-value and target loss corrections were made. The ex- citation energies shown in Table 5 are an average of the results of these two calibration procedures. The errors quoted 60 include jitter arising from the two calibration methods employed and estimated systematic errors. Table 4 also indicates some excitation energies in 22Na returned in the present study, and a comparison with those found from a previous investigation via the (p,d) reaction (Sec. II.2.). The overall consistency in the energy cali- bration schemes is clearly evident and, consequently, there was little motivation to alter the previous 22Na excitation energy assignments based on the 23Na(p,d)22Na reaction. 22 Therefore, all Na energies shown in Fig. 9 are those assigned in Sec. II.2. III.4. Angular Distributions III.4.A. General Discussion All orbital angular momentum quantum numbers (2) for the transferred neutrons and corresponding Spectroscopic factors have been assigned to transitions observed in the present work on the basis of fits to distorted-wave Born approximation (DWBA) angular distributions calculated using the computer code DWUCK.49 The optical model potentials are of the standard form: . d U(r) = VRf(rR,aR)+1(W’Vf(rv,aV)-4W3FasF a; f(rSF,aSF)) h 2 1 d +,-» m c) vso 'E a? f("'so"“so) 2 ° Tl’ + ( 621 Table 5, Energy levels in 36C1 observed in the present study and in other works. Excitation Energy (kev) (p,d)“ (d,p)b (n.7)c (n,1)d (n,y)e (3He,a)f (38e,.)3 (p,d)h (p,d)i 000 000 000 000 000 000 000 000 000 78931 78918 790 79012 788 78(0) 793315 780315 787 115531 115338 1155 115732 1155 115(0) 1155315 1150315 1153 150031 159935 1508 150518 1599 150(0) 1508315 1500315 1599 1951 195831 195835 1952 195933 1959 195(0) 1970315 1950315 1955 2158 2315 285732 287235 2872 287233 2859 289132 289735 250(0) 2897315 2890 251732 252235 2517 257531 257935 2583 257535 258(0) 2582115 2573 279933 281535 285331 285815 2857 285533 287(0) 2905115 2858 289812 290015 299532 300035 2999 297915 3055 305115 310337 320838 321238 333132 333835 3335 387032 387837 350(0) 3892325 3877 355538 3558 359813 350517 3501 358035 3535 (3551) 3570ia 372233 372817 378(0) 3735125 (3831) 3822 3852 395233 397037 3970 399033 800037 3989 803038 808037 8010 8059 818837 8137 820533 (8253) 829932 (8300) 833(0) 8333325 8297 831533 832337 881338 8885 850837 8897 852833 8525 855133 855038 8550 852(0) 8550325 850738 8501 8590325 8518 8593 “720:3 873818 873838 8780125 875538 8750 883038 883838 8838 885218 885738 888833 888738 8879 890(0) 8980325 891938 895338 895518 8972 500818 5009 509038 51.815 515018 5150 521318 5198 5231 Tatle S. (Cont'd) €12 Excitation Energv (keV) (p,d)a (d,p)b (n.1,)C (n,y)d (n,y)e (38¢,a)’ (3m...)8 (p,d)h (p,d)i 528938 525918 5250 531818 0 5339-8 537538 585918 0 9 5517-8 5518-8 5510 555038 558818 550518 552218 570238 570138 0 0 9 5738-5 5731-8 5730-25 575538 575(0) 583518 587118 591338 590538 595738 595238 9 O 10 5985-8 5972-8 5000-25 503218 509538 509018 0 o 0 5185-5 5155-8 5150-25 518818 5190325 525(0) 535815 535538 537918 . O O 9 5823-8 5885-8 588(0) 5850-25 588035 587818 5890325 551038 + 4' § 5550-5 5585-8 553(0) 5580-25 559535 551835 558338 558038 5580325 575035 5750325 577835 582535 585(0) 5880325 589335 5890325 700738 708815 708(0) 7090125 715535 717(0) 7150125 751235 755715 755(0) 7580125 755535 775515 787035 818835 aPresent work. 8Ref. 63. bRef. 73. hRef. 22. cRef. 72. 1Ref. 65; (all evels 220 keV except .Refe 76. f 9 Ref. 5“; (-20 keV). 63 r.--r..A]'/3 a O where f(r.,a.) = -[l+exp( l l i VR is the real well depth, while WV and WSF are the volume and surface imaginary well depths, respectively. VSO is the strength of the spin-orbit potential. A standard, uniformly 1/3 charged sphere of radius Rc=rcA was used for the Coulomb potential. The proton Optical model parameters of Becchetti and Greenlees37 were chosen for use in all DWBA calculations pre- sented here. Use of the parameter set presented by Fricke, 50 et al. had little or no effect on the predicted (p,d) an- gular distribution shapes. A lack of extensive deuteron elastic scattering data for the appropriate mass region and energy led to a search of the available literature in an effort to find a suitable set of optical-model parameters. Deuteron potentials proposed by Perey and Perey,53 Newman, 52 51 Schwandt and Haeberli,54 98 et al., Hinterberger, et al., Mermaz, et al.,55 and Cowley, et al. were tested in an effort to reproduce pure i=0 and i=2 empirical angular dis- tributions recorded for the (p,d) reaction on several nuclei in the 3528239 region at Ep=35 11ev.6"8 This investigation indicated that calculations in the local, zero-range (LZR) approximation for all of the standard deuteron potentials were clearly inferior to the shapes pro- duced when finite-range and non-local corrections (FRNL) were 49 introduced. The standard non-locality parameters 0.85 and 64 and 0.54 were chosen for the proton and deuteron, respectively, while the finite-range parameter49 for the neutron bound-state was chosen to be 0.621 in all cases. FRNL calculations using the ”Set I" parameters of Hinterberger, gt_31.51 provided the best overall fits throughout the mass region, although the pure i=0 fits were found somewhat lacking in the observed Q-dependence and all calculations tended to predict cross- sections significantly greater than the data for 0>35°. In some cases, the superiority of this parameter set was not overwhelming although the usefulness of this potential was most gratifying since it is the most broadly-based deuteron elastic scattering parameter set currently available. The "adiabatic" deuteron model of Johnson and Soper,43 46,48 45 used in (p,d) analyses in the oxygen and lead regions, was also investigated and found to produce poor forward—angle i=2 shapes. The Shortcomings of the FRNL calculations were found to be at least partially alleviated with the introduction of a 46,69 density-dependent damping of the an interaction. The damping factor used here and in the other concurrent s-d shell 7,8 studies via the (p,d) reaction, is a general Fermi form F(r) = (1.0-1.845 p(r)2/3), where p(r)=0.l7[1+exp(x)]-1, x=(r-roAl/3)/a, and "r0" and “a" are the radius and diffusivity of the neutron bound-state well. 65 The normalization factor suggested by nuclear matter con- 69 siderations produces an overall renormalization of the calculated DWBA cross-sections, and has been omitted. A more thorough treatment of this deuteron parameter in- vestigative procedure may be found in Sec. IV. The present data has been analyzed in detail using: (1) the Hinterberger "Set I" deuteron parameters (FRNL), (2) the same parameter set and calculational approximations as (l) with the aforementioned damping correction to the an inter- action (DFRNL), and (3) the adiabatic deuteron prescription in the LZR approximation, henceforth referred to as ADIABATIC. These parameters are shown in Table 6. Angular distributions resulting from these three calculations are compared with each other and with the distributions observed in the present 36c1 in Fig. 10. experiment for transitions to four levels in. The virtue of the DFRNL calculations is clearly evident over a wide Q-value range for the present data. III.4.B. Analysis of Experimental Angular Distributions DFRNL fits to the angular distributions observed in this 36 study for the population of states in C1 via the 37Cl(p,d)36Cl reaction are shown in Figs. 11, 12, 13, 14, 15, 16, and 17. States observed at an insufficient number of angles to allow plausible 2-value assignments are not shown. 66 .am monogamom cw cu>wm no a“ cocoocunoolo “mace >0: ooo.ouxu now use cacao mooao>o .sm oocosomom £09m wnouososoa Sampson one covonn mm:.momo .Hm.mumn .sm.e8e8 hwsoco some (daemon nouns ovoum ocsom s~.s maua me.o s~.a on counsms< sonusoz AoHaoxe name name Asozv name name A>8ze name name A>aze on one own ems emu ems am: so. >8 >3 an en es escapees .opoo HmeAo.aVHobm one no mamaaoco can cw pom: msoumaonoa HooOEIHMOfludo .o manna Figure 10. 67 A comparison of fits to 3representative angular distributions from the 7C1(p, d)36 C1 reaction at 35 MeV with the three chosen types of DWBA calculations. All fits were performed over the angular range from 3° to 35°. The curves are identified as follows: ————DFRNL, ----FRNL, and — -— —-ADIABATIC. 68 1o2 b r éxer789'887 éx;26;51k89 L=2 L=0+2 6555711859 L=0+2 éxg92891888 L=2 ..... v‘ ‘e o ‘ 20 ‘ 8o ‘ so 0 ‘ 20 *‘80 ‘ so 4c.m. ong|e[degr‘ees] Figure 10 Figure 11. 69 Experimental angular distributions for states in 36C1 as observed in the 37C1(p,d)36Cl reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contribution of the first indicated z-value for mixed-2 distributions. 70 Ex; 000 Lev' L=2 Ex; 789 thel/ i L=2 1 10'1 10'2 ‘2‘0 ‘8‘0 ‘10 o éx=19§8 levfi'; L=0+2 102 6x=2991 Lev' L=0+2 51.42517 1.8 (L=3) éx=vllsv5 1:th A AAAAA L=0+2 102 - . . r - _ Ex=2‘+67 kOV : r L=l 5 10E, 1 ‘1 1 g : "Q 1 -z’ - . . . 1° 0 20 80 0 102 - . - . . ’ Ex=267$ IIOV 10- L=0+2 10'1' 10'2; c.m. ongle[degr‘ees] Figure 11 Figure 12. 71 Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)36Cl re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the an- gular range from 30 to 35°. The dotted curves show the contribution of the first indicated i-value for mixed-8 distributions. 102 - . - . - , Ex=2799 Rev 1 (L=3) 10E 1? E 10.1; I. E 0 -2’ . - 1° 0 20 80 L- 2 10 e - - . e m 5 Ex=2995 85v 2 10» L=1+3 ‘5’ 1' C2 . ‘0 10" -2 b 10 0 .0 1 fi fi Ex=3‘+70 the); L=0+2 72 éx=I28183fike h D p , O h 1 F I > 4 A éx§64§o 1917 L=1+3 E 1 E 1 11 10-1%}1 9, 1 ’ LA ‘ l A 10.2} 1 0 20 90 80 lb 25 E6 30 c.m. ongle[degrees] Figure 15 Figure 16. 79 Experimental angular distributions for states in 36C1 as observed in the 37C1(p,d)36C1 re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contribution of the first in- dicated z-value for mixed-i distributions. éx=18530 191} L=0+2 [mb/sr] éx='66'83 'uex} L=1+3 .T #:1196856 3.99 l;=2 80 102 102 it s r , ’ Ex=6596 keV . L=1+3 10! 1 10'1 lo‘ZIf 102 . . , f. ’ Ex=6750 keV » L=0+2 10E éx='eeé3 'm} 1 L=0+2 Figure 16 ; éxésefe Iev' L=2 10 2‘0 ‘ L+0 e 102 , . . . r _ Ex=6774 kev i r L=2 1 1o:! 3 1 1 10‘1' ‘ E 1 -2’ 47 4A . ‘ . « 1° 0 20 1+0 102 e. . , . : Ex=7088 keV : >- L:2 I E 1 g 1 m: g 1 ‘ 2i) ‘ 4‘0 ‘ c.m. ongle[degr‘ees] Figure 17. 81 Experimental angular distributions for states in 36C1 as observed in the 37Cl(p,d)35C1 re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the contribution of the first in- -dicated z—value for mixed—2 distributions. 82 102 , 1 f 1 . 102 v 1 .1 1 .1 102 r 1 , . v : Ex=7512 keV . Ex=75$7 keV : Ex=7685 keV » L=0+2 « » L=0+2 1 » L=0+2 10 1 10 10 1 E 1 E b 1 . ”C 1! 1 1 (r) ’ ‘ lE \ 10 1 .r) : 1 -2’ k L L yéi 1° l 20 HO so (:3 102 . r . . - 102 . 1 , r 11 102 is . v 1 . 'O 5 Ex=7755 keV 1 ’ Ex=7870 keV 1 : Ex=8189 koV » L=1+3 1 1 L=0+2 1 1 (L=0+2) \E; 101 1 101 1 101 1 -O ’ ‘ 1 1.1 1 1 1 1 : _ : 10'1F 1 10'1 . 1 1‘ i . , , : lo'zm 10"? W‘ 1 20 H0 80 1 *20 so so c.m. ongle[degrees] Figure 17 83 Minimization of the quantity do 2 23' 3'5 (Oi)2j,DWBA " _ 1 do 2 X 7 fi’ -<'i'$'2'(ei)exp)flmi:I [(A IIMZ 1 l 2 j the appropriate isospin Clebsch—Gordon coefficient and spectroscopic factor, respec- tively, was required for all fits. g%(ei)£j DWBA' 3%(ei)exp' I and A01 are the DWBA calculated differential cross-section th where A2j=2.29 C Szj' With C and $2 at the 1 experimental angle, the experimental value of the , differential cross-section at angle i and the total (statis- tical plus estimated systematic) error in the appropriate experimental number, respectively. N is the number of data points within the 30-350 angular range. All fits were per- formed over this subset of experimental points in order to allow comparisons of the resulting Spectroscopic factors which are reasonably independent of the great differences found at larger angles for the three calculations used in the present analysis. Table 7 lists the spectroscopic factors and 2-values for all states for which useful angular distributions could be extracted from the present data. Attempts to fit two zj come binations were made for each distribution, except where known final state spins precluded a possible mixed-2 transition; for example, the known J",1?- 0+,2, 4299 keV level was fit only with a pure 2,j=2,3/2 calculation. In other cases where only one z-value is assigned to a transition, the addition of a 84 Table 7. Experimental values of 1 and C28, for the 3791(p,d)36C1 reaction as observed in the present investigation. All assignments are based on the DFRNL analysis} with the spectroscopic factors normalized to yield C 8; =1.10 for the transition to the 3501 ground state. 2 a 2 a Ex(keV) g C S2 Ex(keV) l C 58 000 2 1.10 5299 (1,3) <0.01,0.01 789 2 1.66 5517 1,3 <0.0l,0.02 1165 0,2 0.05,0.36 5605 0,2 0.02,o.ou 1600 0,2 0.16.0.11 5702 1,3 0.02,0.02 1958 0,2 0.23,0.2u 5730 3 0.09 2867 l 0.01 5913 0,2 0.01.0.ou 2991 0,2 0.17,0.l9 5957 0,2 0.01,0.05 2517 (3) 0.05 5986 (1,3) <0.01,0.02 2675 0’2 0'07,0031 6095 0,2 0002,0015 2799 (3) 0.05 6196 0,2 0.01,0.05 2863 2 0.05 6188 0,2 0.01.0.07 289“ (0.2) <0-01.0.03 sasu 0,2 0.02.0.ou 2995 1.3 <0.01.0.01 6379 0.2 0.03.0.18 3208 1 <0.01 6923 1,3 <0.01,0.08 3331 l 0.01 sueo 1,3 0.02,0.15 3970 0,2 0.05,0.07 6550 0,2 0.01,0.01 3566 0’2 000130001 6596 1,3 (0001,0002 3598 (1,3) <0.01,o.02 5513 2 ‘0.15 3722 3 0.0“ 6683 1,3 <0.01,0.07 3962 1,3 <0.01,0.01 6750 0,2 0.0l,0.05 3990 1 <0.01 677k 2 0.31 #030 1 <0.01 6826 2 0.36 4205 0.2 0-0190-0“ 6893 0,2 0.02.0.ou M299 2 0.29 7088 2 0.22 uszu 1,3 0.01.0.ou 7512 0,2 0.01.0.06 «551 0,2 - o.ou,o.os 7557 0,2 0.18,0.18 9830 1,3 0.01,0.02 7665 0,2 0.01.0.02 #852 1,3 <0.01,0.01 7755 1,3 <0.01,o.ou 9889 0,2 0.05,0.05 7870 0,2 0.02,0.02 5198 1,3 <0.01,0.01 8189 (0,2) <0.01,o.ou a Values for i=0 1,2,3 are for 2s 2p 1d and 1f calculations, respectively. 1’2, 3’2, 3’2 7’2 85 second failed to improve the overall fit significantly. In Table 8, a comparison of DFRNL, FRNL, and ADIABATIC results with those of other single neutron pick-up experiments is presented for previously observed transitions only. III.5. Discussion III.5.A. Energy Levels 36 To date, the excitation energies of levels in C1 have not been reported to the precision of states in other s-d 70-77 shell nuclei. Table 5 serves to illustrate the existing disparity in energy assignments for even the low-lying levels. Nearly all of the levels observed in the (n,y) studies7o'71 are observed in the present experiment. We observe only 24 of the 41 levels reported by Alves, et al.,72 but several states not observed in that investigation are reported here 63-65 and in other single neutron transfer experiments. Much the same situation exists with regard to the (d,p) studies of Hoogenboom, et al.73 and Decowski.74 The doublet at 1958 keV is not resolved in the present or previous single neutron pick-up works, but the negative-parity state is in all pro- bability very weak, compounding the experimental problem but simplifying interpretation of the resulting "doublet". The assigned excitation energy of 4299 keV for the + 36 0 , T82 analog of the S ground state agrees very well with the 4297 and 4295 keV assignments of Refs. 65 and 78, 86 respectively. The energy levels extracted from the present work generally allow a reasonable correlation with those ob- served in previous studies, particularly for levels below 4 MeV excitation, and many states have been observed for the first time via a single neutron pick-up reaction. 111.5.B. 2 and n Assignments Orbital angular momentum quantum numbers (2) for the 36Cl via neutrons transferred in the formation of 61 states in single neutron pick-up can be at least tentatively assigned on the basis of the DFRNL fits to angular distributions ob- 37 served in the present work. Since the Cl ground state is known to have J"=3/2+, transitions involving even-2 transfers 36Cl with positive parity. Likewise, odd-2 pOpulate states in transfers lead to negative parity states. Assignments of 2=O+2 were generally evidenced by a definite forward rise in the experimental angular distribution, characteristic of the DWBA 230 shape. Separate fits involving Ids/2 and ld3/2 neutron transfer calculations yielded only slightly different chi-squared per point values over the prescribed angular range for the distributions of positive parity states. Consequently, the 35 positive parity assignments below 8.2 MeV excitation are made on the basis of fits to i=0 and/or i=2 DWBA cal- culations with j=1/2 and j=3/2, respectively. 87 As a result of the i=2 spin-orbit splitting for the neu- tron bound-state, any i=2, j=3/2 spectroscopic factor may be converted to the appropriate i=2, j=S/2 value via multi- plication by ~0.85. Transfers involving i=1 neutrons yield experimental an- gular distributions with a characteristic "dip" at very for- ward angles. This is clearly evident in both lpl/2 and 2p3/2 DWBA calculations for this mass region and bombarding energy. 63,73,74 As in previous charged particle work we observe evidence of £=3 transfers leading to states in 36 C1. The 1337/2 trans- fer calculations appear somewhat similar to i=2 DWBA shapes for forward angles but do not fall off as quickly. Therefore, 36C1 on the basis we assign negative parities to 25 levels in of the i=1 forward angle fall-off and/or the relatively high 2=3 cross-section around 30°. For all levels, single 2-values are assigned when the addition of a second 2 either resulted in a negative contribution to the cross-section or failed to produce a significant improvement in chi-squared per point values, or when known final state J values excluded mixed- transitions. The 3 assignments made on the basis of the present study are shown in Table 7. Parentheses denote levels for which the fit was only slightly preferable to one involving opposite parity z-values. Our parity assignments agree with those made from previous single neutron pick-up experiments, except for 88 the n=(+) observation for the 5.76 MeV level made by Rosin, 64 We assume a correSpondence with the negative parity 5734 keV state observed in this work. The recent 35C1(p,d)36C1 et al. study by Decowski74 assigned at least tentative negative parities to the 2675, 2863, and 2894 keV levels. However, previous pick-up experiments“)-65 have observed positive parity transitions to these levels. The characteristic forward angle i=0 shape for the 2675 keV state and the excellent i=2 fit to the 2863 keV level observed in the present work confirm the positive parity assignments to each of these levels and limit their J" values to (1,2)+ and (0-3)+, respectively. The pre- sent data also indicates a rise in cross-section at forward angles for the 2894 keV state, again indicative of a positive parity transition. Also based on the forward angle data, we assign positive parities to the 3470, 5605, 5906, and 6095 keV states as opposed to the n=(') assignments of Hoogenboom, 73 All other present parity assignments for levels et a1. showing reasonable energy correspondences agree with those based on previous (d,p) works. III.5.C. Experimental C28 Values In Table 8 we present a comparison of the spectroscopic factors obtained from the DFRNL, FRNL, and ADIABATIC fits and from the previously performed single neutron pick-up experiments 36 leading to states in C1. Only previously observed levels are 89 «nag .mm 00cmhmuwmv and” cam QOCUQOHQZO .NN oocuhmmuxm .mo oocohowomn .mo monogamomo .xso: anemones NN.o Ho.ev eH.o N eN.o mH.o eH.o eH.o o N.+N NmmN ms.e as. oN.o em.e N H.+xmuov oNeo smN.o eo.o No.o oo.o m H.1AmuNo smNm oo.o No.o No.o mo.o N - se.o se.o eo.o me.o o H.+AN.HV seer om.o ms.o Hm.o NN.o sN.o oN.o N N.+o ooNs me.o woe.o mo.o mo.o so.o n H.1AmnNe NNNm oo.o so.ov oo.o mo.o so.o N ma.o mo.o HH.e so.o eo.e me.o o H.+AN.HV eNem em.o Nm.e Ns.e H:.o em.o ms.o N No.o e H.+xsueo moeN Nm.o H:.o sm.o Nm.o NN.o Hm.o N No.0 No.0 No.o o H.+Aao mNoN He.o mN.osHN.o sH.ov «N.o NH.e oH.o N meo.o mm.o oH.est.o sm.o sa.o oN.e NH.o o H.+AN.HV HosN Ns.o Hm.e-ma.o oH.ov Hm.o eH.e sN.o N oN.o NH.o Ns.e eN.o-Nm.o Ns.o oN.o NN.o MN.o e H..N emoe Ns.e mH.ov Ha.ev mH.o oo.o HH.o N Hm.o Hoe.o ee.o HH.oueN.e eN.e 2H.o me.o oe.o o H..AN.HV some os.o Ns.o Nm.o mm.e mm.o mm.o mm.o om.o N oN.o mNe.o me.ov so.o oo.o mo.e mo.o o H..H mode mo.H oN.H Ne.H Nm.H em.e Ne.H em.H mo.a N e..m meN oH.H oe.H oH.H OH.H oe.H eH.H OH.H oH.H N H..N coo Aoo.oe “oe.ae xom.He xNo.oe Aeo.Ne Amm.ee Aom.Ne «3.3 1.3.3 63.21% eateries 23:: $335? $5: oszmmo or ease ogoxexm .opcum ocaonw wnu pom oa.au ammo umnu £03m noanMEhoc one mocam> umcuo HH< .momocucwsca cw ooucwmowa one oumum 0:509» ecu how mosam> ou2H0mA< .Homm 0» Huh» scam mcofluwm:Mpu sou mmo no mo=Hm> Houcoawnoaxm .m dance 90 included. Relative to the DFRNL values, the FRNL calculations yield somewhat lower i=2 spectroscopic factors in the 2=0+2 mixtures, that disparity increasing with excitation energy. In contrast, the ADIABATIC i=2 values tend to be higher in these mixtures. These deuteron parameter and calculational differences appear to be a direct result of the basic 2:0 Q-dependences, i.e., the FRNL and ADIABATIC shapes retain less and more of the first minimum, respectively, with increasing excitation energy. The DFRNL spectrosc0pic factors are generally in good agreement with those obtained from previous studies. However, significantly more total strength is assigned to the 1165, 1600, and 1958 keV states by Vignon, g£_21.,22 and to several of the low-lying levels in the (d,t) study by Puttaswamy and Yntema.62 The present experiment also allows the observation of mixed i=0 and £22 contributions to several levels for which pure 220 or 2:2 transfers have previously been assigned. A particularly interesting example is the 2675 keV state. The previous pick-up experiments in which this level was ob- 63-65 assigned a pure 2=2 transfer to the transition. served However, the present data for O<10°, a region not explored in any of those works, definitely indicates the characteristically 2:0 forward angle rise (see Fig. 13). The inclusion of an i=2 contribution to several previously assigned pure i=0 transitions seems justified on the basis of DWBA i=0 shape comparisons dis- cussed in Sec. IV. 91 we observe only one strongly populated positive parity state in the 4 MeV excitation region, with CZS2 3/2=0.29. I 3 79 The and Puttaswamy and 7Cl(d,3He)368 work of Gray, et al. Yntema80 yield values of 0.27 and 0.33, respectively, for the transition to the 0+ ground state. Therefore, we concur with Refs. 63-65 in the assignment of J",T=0+,2 for the 4299 keV 36 3 S ground state. The two (d, He) level, as the analog of the works also show considerable spectroscopic strength for the 3.3 MeV, 2+ level in 36$. The 7557 keV state in 3 6c1(czs(z=0)= 0.18, CZS(2=2)=0.18) appears to be the most likely candidate for the analog of that level, based on its total strength relative to the other levels observed in that energy region and the Spectroscopic factors of CZS(2=0)=0.22, and 36 C25(g=0)=0.30 for the 3.3 MeV 8 state reported in Refs. 79 and 80, respectively. III.5.D. Comparison with Shell-Model Calculations The spectrosc0pic factors extracted from the present data (DFRNL) and those calculated from various shell-model Hamilton- ians are presented in Table 9. The results of the Tabakin 59 interaction calculations have been renormalized to facilitate a relative comparison with the present results. The MSDI and 12.5 pA studies conducted by Wildenthal, et al.3 tend to be less successful for upper s-d shell nuclei and have been omitted. £92 0 0 oPXUF 00m mam\m Nm 0 mmoouvm\m NW 0 N m .u 0o xaucmcwsoompm o .20 mocopuuom c0 nausea Ion mm ouswpowwx mo mcoflpUCDM o>m3 on» mean: mCOHHMHsoauo «\mva .~\Hn~v .muu so vaESm meowusnwsucoo nxmo ocu «\mv 0:0000¢ 300 you couwaussocua coon «>0: mosau> 00o moumum vcsosm pom mo.ou~m~o ousaomau 0mm uocohouomo .wCOdPHmfidfiP MW“ HON Uflfiaflm flfifl mcowusnwsucoo «Vmoa can v0 «9 vocohouoxn .xno: ucowosmm 0.0 «00.0 000.0v 000.0 0 00.0 00.0 00.0 0 0.+0 0000 00.0 00.0 00.0 00.0 00.0 0 0.+0 000: 00.0 00.0 00.0 0 00.0 00.0 00.0 0 0.+000 0000 000.0 000.0 000.0 0 0.+000 0000 0.0 000.0 00.0 00.0 0 00.0 00.0 00.0 0 0.+000 0000 00.0 00.0 000.0 000.0 0 00.0 00.0 00.0 00.0 0 0.+000 0000 00.0 000.0 000.0 000.0 000.0 0 0.0 00.0 00.0 00.0 00.0 0 0.+0 0000 00.0 00.0 00.0 00.0 00.0 0 00.0 00.0 00.0 00.0 00.0 0 0.+000 0000 00.0 00.0 00.0 00.0 00.0 0 00.0v 00.0 00.0 00.0 00.0 0 0.+0 0000 00.0 00.0 00.0 00.0 00.0 0 0.+0 000 00.0 00.0 00.0 00.0 00.0 0 0.+0 000 v00onmu0 020x<0<0 00+00.00 000<+:0.00 0000000 00 0.00 00>mxoxu .mCOwHMHfionU H0608 HHOSM m30w9fl> EOQH 0m0£u 5PM»; >U=Pm chmaa TCU Sun UwCMwaO MOSHU> AuvaU MO COmthQEOO < .m ”Anna. 93 Nine T=1 levels have been included in Table 9, with firm spin assignments having been made to four. The other spins have been tentatively assigned on the basis of the neutron orbital angular momentum transfers observed in this work (the presence of i=0 components limiting final state spins to 1 or 2) and the general trends of recent shell- model level sequencing. It is evident that the ground state and 789 keV level spectrosc0pic factors for all of the cal- culations are in good agreement with present results. This is not surprising since, in isospin formalism, the wave functions for these two levels are dominated by a (dB/2)12(sl/2)4(d3/2)4 configuration, the simplest of shell- 36 model pictures for C1. The agreement is also good for the second excited state, although the Tabakin calculations59 exhibit only about one-half the observed i=2 strength. For higher excited states, the predicted spectroscopic factors are very sporadic, with no clear choice of a preferred set of wave functions. However, there is some indication of an over-estimation of the 282 strength and the 2=0 strength for transitions to the second 3+ level and the fourth l+ level, respectively. The full s-d shell calculations of Wildenthal, gt_al.3 predict a weakly populated 3+ level near 4 MeV excitation, but no pure £32 transitions of appropriate strength are observed in that region. A 3+ level populated by predominatly dS/Z transfer is predicted for the 5-6 MeV 94 region (CZS(2=2)=0.2), which may correspond to the ob- served 6618 keV level (CZS(2=2)=0.13). The only other T=1 state predicted to carry significant pick-up strength is a 4+ level at approximately 7 MeV excitation (CZS(£=2)=1.24). Three levels with significant pure £=2 strength are ob- served near 7 MeV (6774, 6826, and 7088 keV) with total c25(2=2)=o.77. The spectroscopic factors extracted from the present data for the 4299 and 7557 keV levels agree with the 2 and 3 orbital shell-model predictions except for the experiment- ally observed £=2 strength of the transition to the latter state. Since they are the only strongly populated levels in the appropriate energy regions and exhibit the cor- respondingly correct z-values, we concur with previous pick-up works in their identification as the analog states of the (J",T)=(0+,2) ground state and (2+,2) 3.30 MeV levels in 36S, but assign the excitation energies in 36 Cl much more accurately. Single-shell sum rules for spectroscopic factors dictate a T=1 contribution to the total d3/2 strength of 3.75 with the T=2 levels adding 0.25 for a total (113/2 shell- model limit of 4.0. The summed 2=2,j=3/2 spectroscopic strength observed for transitions to the ground state, 789, 36 1165, 1600, 2675, and 3470 keV levels in C1 is 3.61. These states indeed show a majority of the predicted d3/2 95 strength for the T=1 levels in recent shell-model studies. The observed £=2 spectroscopic factor for the 4299 keV level would indicate that appropriate transitions to that state carry essentially all of the <13/2 strength for the A:36,T=2 system. A total d5/2 spectroscopic strength of 2.61 may then be assigned to the single neutron transfers 36Cl below 8.2 MeV. after the £=2 values in to states in Table 7 have been properly normalized to correspond to d5/2 transitions. Erne60 has predicted 24 T=1, negative parity levels in 36C1 between 2.0 and 6.5 MeV excitation. In the present study, 25 levels between 2.0 and 8.2.MeV are assigned at least a tentative negative parity, in excellent agreement with theory. The summed observed spectroscopic strengths are 0.15 and 0.69 for 2p3/2 and 1f.”2 neutron transfers, re- spectively. III.6. Summary Excitation energies have been assigned to many levels in 36C1 with a precision heretofore unmatched in many previous studies of that nucleus. Spectroscopic factors for single neutron pick-up leading to many negative parity states in 36C1 have been reported for the first time. Essentially all of the <13/2 strength and nearly one-half the expected total d5/2 transition strength have been observed below 8 MeV 96 excitation, with the approximate distributions among the T=1 and T=2 levels agreeing well, in total, with recent shell-model calculations. Approximately 60% of the shell- model limit for i=0 strength is also observed in this energy region. The summed negative parity (£=l,3) spectroscopic factors indicate small but significant f-p shell components 37 in the Cl ground state wave function. A level-by-level comparison of the present results with recent predictions indicates a need for the inclusion of f—p shell excitations 36 in any attempt to fully describe the levels in C1 above 2 MeV excitation. Iv.’ THE 39K(p,d)38K REACTION IV.l. Introductory Remarks In the simplest shell-model picture, the lowest energy 38 5 states of K should arise from the couplings of two d3/2 holes, yielding J",T values of 3+ and 1+, T=0, and 0+ and 2+, T=1. The incorporation of sl/Z-hole excitations into this picture is the most logical first improvement, a step taken 56 by Glaudemans, Wiechers, and Brussaard. Their shell-model provides a description for many aspects of the low-lying positive parity states in 38K. However, much as appears to be the case for the two-particle nucleus in the s-d shell, 18F, the mixing of the d3/2 and dS/Z orbits may be important even in the lowest few energy levels. Several calculations O which consider excitations in all three s-d shell orbits 3,59,81 have been reported, and appear to yield still fur- ther improvement in the agreement between theory and experi- 18 ment. Finally, again in analogy with F and excitations 38K cannot be explained from the p shell, the structure of in final detail without recourse to excitations from the s-d shell to the f-p shell. Some initial investigations along these lines have also been reported. We attempt in the present work to provide an accurate and complete experimental summary of two aspects of the structure of 38K. The first of these involves making a catalog of as many of the levels in the low-energy region 97 98 as possible, and assigning them precise excitation values. To this end, we have measured multiple spectra, using the 39 (p,d) reaction on K, with a resolution (10 keV, FWHM) that is at least three times better than that achieved in any of the previous particle-detection work on this 82’83 and ten times better than that achieved in 64,84-86 nucleus previous single-neutron transfer experiments leading to 38K. The second aspect of our study involves measuring the 2-values of the neutron transfers which populate these states, and the associated spectroscopic factors. This has been done by a carefully cross checked DWBA analysis of the experimental angular distributions of the observed transitions, which were measured all the way in to eL=3°. We will dis- cuss our results in their relation to the previous experi- mental situation and in their implications for the current theoretical pictures for this and neighboring nuclei. IV.2. Experimental Procedure Thin (~70 ugm/cmz) targets were made by evaporating 39K, 7% 41K) onto thin carbon natural potassium metal (93% backings (30 ugm/cmz). These targets were kept under vacuum throughout the experiment and thicknesses were estimated from the (p,d) yields and scattering chamber geometry. The targets were bombarded with 35 MeV protons from the MSU Cyclotron, and reaction products were analyzed in an Enge-type split-pole 99 magnetic spectrograph. Deuteron spectra were obtained both 32 and with 25 micron- with a single-wire proportional counter thick nuclear emulsion plates. The counter data yielded angular distributions at closely spaced angles from 30 to 550 for the strongly populated levels separated from their neighbors by more than the counter resolution of 50 keV, FWHM. The spectrograph acceptance aperture was 0.6 msr for angles than 300 and 1.4 msr for angles greater than 30°. Particle identification and data acquisition in this part of the experiment were accomplished in the MSU Sigma—7 computer. An appropriate change of the spectrograph magnetic field allowed observation of protons elastically scattered from 39K in an experimental configuration otherwise identical to that used for the (p,d) measurements. Data for 39K(p,po)39K were taken at angles from 250 to 450 and the cross-section normalization for the (p,d) data was taken relative to these elastic cross-sections, after an appropriate adjustment of the measured proton yields accounting for the 7% 41K target contamination. The measured proton elastic scattering cross- sections were assumed to have the values predicted from an optical-model calculation using the Becchetti-Greenlees37 parameters (see APPENDIX B). We estimate an uncertainty of 10% in the optical model prediction for this mass and an- gular range, and an additional 10% uncertainty in the mechanics of our normalization procedures. 100 Spectra were also taken with nuclear emulsions at laboratory angles from 40 to 42°. A typical example is shown in Fig. 18. The average resolution obtained for the deuteron groups here was approximately 10 keV, FWHM. The spectro- graph acceptance apertures were the same as those used for 38K up to 6 MeV of excitation the counter data and levels in were recorded. For each angle, the deuteron spectrum to approximately 4.5 MeV’was collected on one 25 cm-long emulsion plate, with the remainder of the deuteron groups and the proton groups from scattering on 12C, 16O, and 39K falling on a second abutting plate. The upper limit of 6 MeV for the energy range presented here was determined by the position of the elastic proton groups at forward angles. Relative normalization of all deuteron and proton spectra was accomplished by the use of a NaI monitor detector which recorded elastic protons scattered at 900 to the beam. A beam-current integrator was also used to check normalization consistency. 1V.3. Excitation Energies Centroids of the deuteron and proton groups which were used in the analysis and assignment of excitation energies were extracted from the spectra recorded with nuclear emulsions at 14°, 18°, and 20°. The analysis involved the fitting of selected reference peak energies to precisely Figure 18. 101 A spectrum from the 39K(p,d)38K reaction, measured at 35 MeV and 300, as recorded on nuclear emulsion plates. The resolution of the deuteron groups is 10 keV, FWHM. All 38K excitation energy values are from the present work. 39K[p,d]38K F I 1482 T 0882 "-= BhSZ HSZ ll, {,th —-=: - (\l H '1 ‘I O 0 0-4 0 m 669! r u .1 0 Cd . . " co > w E . LO 0’) ”Bdrm“: ll 4 ('0 0.- —- LlJ ‘4 69¢» --==——-_~;1T NZZX‘€(§'6])|§€—.c13 OE! 3’ O F. Lynn: 1 Inn“; 1 Inn“ 1 1M‘O m N O O C.) H 1-4 9-4 102 :1“ O H 'uuuu 9101'0 Jed s+un03 O "IIITT [Hurt I I [unrrr '- 9469-1669 ’ '* (Y) 010189 ‘ 1689 03589 82 =: (849 “—— 0889 -— a) 9289 ‘—— N ShSS —— sms ——-- H189 — 8909 - *‘C 866*: ‘— __ 3" ESBh (\J 811*: —- 829+. 86 h — 69». -= N Jr £12): 94“: O 0868 sees 0” Gage Z 2% e 8028 -="-"“ ASS ‘ (D H 28 {,8 ---=: “.88 4188 (.0 0 H _J "09!“.th C m N C) O O H H c—4 Plate Distonce[cm.] Figure 18 103 34'67'87-89 via a least-squares iteration of known values the beam energy, the scattering angle, the small gap between the abutting plates, and the parameters appropriate to a quadratic Bp vs. focal-plane-distance relationship.67 The reference peaks chosen for this analysis (used only at those angles for which they yielded accurate, unambiguous centroids) are shown in Table 10. In all cases, apprOpriate target-loss corrections were taken into account. We found it impossible to obtain a good fit to the reference energies if we used the accepted 39K(p,d)38K Q-value of 34 -10860i8 keV. An equal-weight, minimum chi-squared fit to all reference peaks was obtained by adjusting this accepted value by +9 keV. This same adjustment was required if all levels from 39K(p,d)38K except the ground state were omitted from the calibration data set. In all fits, the chi-squared- per-point value was ml. The greatest adjustments to the nominal beam energy and scattering angle which the fits re- quired were 8 keV and 0.20, respectively. These changes are compatible with the accuracy with which we set up the cyclotron beam line and the scattering chamber-spectrograph geometry. 38 The assignment of any given level to K was made on the basis of a series of angle-to-angle comparisons of mea- 40 sured excitation energy. A level in K (from 41K(p,d)4oK) 38 misidentified at 140 as belonging to K would, at 20°, 104 Table 10, States used in the energy calibration for the 39K(p,d)38K reaction data. Excitation Energy (keV) Reaction in Residual Nucleus .39K(P,d)38K ground statea u59.631.2b 1599.u11.3b 2u03.311.2b 2871.oii.2b 160(p,d)150 ground statec 12C(p,d)llC ground statec 1.999211.od 39K(p,P)39K ground state 2522.710”?e 3019.310.2e 160(p,p)160 ground state 12C(p,p)12C ground state uuuo.oto.sf aAdjusted as described in text. b Reference 87. 0 Reference an. d Reference 67. e Reference 88. f Reference 89. 105 show a shift in assigned excitation energy of almost 4 keV because of the incorrect assumption made for the target mass. Shifts of this type, easily observed in the present high re- solution data, naturally increase for larger angular dif- ferences, lighter nuclei and (p,t) reactions, allowing the unambiguous assignment of the various particle groups to specific residual nuclei. The present analysis allowed the assignment of excita- 40 tion energies to several levels in K which fall close to the 38K in the spectrograph focal plane. Two lowest few levels of of these levels, to which we make assignments of 2258 and 2575 keV, are known to have excitation energy values of 2260.6:l.0 keV and 2574.7:l.0 keV from Ge-Li detector studies of their gamma ray decays.90 Since the Q-value for 41K(p,d)40K is known {-787l.3:l.4 keV) to good accuracy34 and our analysis indicates that Q[41K(p,d)4OKJ-QE39K(p,d)38K]#2980:2 keV, we can assign Q[39K(p,d)38KJ=-1085112 keV either on the basis of this "local" comparison, which is essentially independent of the overall focal-plane calibration, or on the basis of the systematic calibration of 50 cm of the focal plane as des- cribed above. 38 The excitation energies we assign to levels of K ob- served in the present study are presented in Table 11. The 38K82,83,85-87,9l,92,64 results of other studies of are also presented in this table. It can be seen that almost all levels 38 of K observed in other reactions are found in the present 1()6 'falilt' Lin-rjgy lc'vc'lu ()1 "8K t-x¢'ilc:d in the- prw-cvunt ilnqusti;{dt iOII of thv (p,d) reaction and in previous studies of other reactions. Excitation Energy (keV) (H.I.,Y)C - (p,d)a (d,0,Y)b and (d,c)° (d,s)f (d,t)g (3He,o)h (3He,a)l (8,1)9 000 000 000 000 000 000 000 13021 131.u:1.2 130c luu 119 128 138 13(0) “5921 “59.621.2 059 “3(0) “56 “66 05(0) 169921 1699.821.3 1702 169(0) 1700 170(0) 170(0) 280021 2HO3.821.2 2N03 281(0) 2M05 200(0) 2M0(0) 261022 2518.121.“ 2628 261(0) 268821 2689.821.8 26'46C 263(0) 2639 263(0) 260(0) 283021 2831.521.3 281(0) 287121 2871.021.2 2860 280(0) 285(0) 287(0) 2995 22 3000 297(0) 305(0) 331721 3319 22 3327 333(0) 33u122 33u7 :3 3337d 3u200 3H2(0) 3M3221 3032 22 3UHO 3UH(0) 3001 302(0) 308(0) 31458C 361721 360(0) 3670 22 365(0) 370323 3691 367(0) 370(0) 371(0) 381922 379(0) 388223 381(0) 385923 3865 383(0) 393822 391(0) 398022 3980 398(0) 3989 397(0) “00(0) “17622 818(0) 920(0) #21722 “18(0) 032123 833823 “36(0) “005:3 unssia 050(0) u59822 u6u633 067322 0660 866(0) 867(0) Q71323 u85323 099823 505823 508(0) 520923 523(0) 525(0) S3ulz3 suuszz suu(0) 5u5(0) 55u92u 562622 562(0) 568023 573722 57782u $80923 578(0) $85623 585(0) 589123 590023 597623 599123 f Reference 83. 8Reference 85 (115 keV). h aPresent Work. bReference 87. cReference 91. dReference 92 (110 keV). eReference 82 (quoted to only the nearest 10 keV). Reference 86 (quoted to only the nearest 10 keV). 1Reference 60 (quoted to only the nearest 10 keV). 107 work. Below 4 MeV excitation there appear to be six levels 82'83 particle-detection experiments or in observed in (d,a) (d,a)87 and heavy-ion initiated91 gamma-detection experiments which we do not see in the (p,d) spectra. Reasonably sure correspondences can be established between the nineteen levels we do observe in this region and previously reported levels. Of the six levels we do not observe, three are seen by at least two other investigations, while two are reported only 83 91 by Jinecke and one only by Engelbertink. There is reason to think91 that the 3420 keV and 3458 keV levels have J15, which is consistent with their being very weakly populated via the (p,d) reaction. There are no such simple explanations available for our non-observance of the other four levels. In the 4-5 MeV region of excitation JEnecke again reports two or three more levels than we observe, but the discrepancies be- tween his and our energy calibrations make it difficult to be sure which levels are which in that region. Of the forty-six levels below 6 MeV excitation observed in the present study, only twenty have been observed in the various previous studies of single-nucleon transfer reactions leading to 38K. All of the levels reported in these earlier investigations are observed in the present work. The excitation energy assignments made in the present study agree well with the results of the most precise previous 82,87,91,92 investigations. The only significant discrepancy is the 6 keV gap between the (p,d) recorded energy of 334li2 keV 108 and the (d,ay) recorded energy of 334713 keV. Some of the energies quoted in Ref. 93 differ widely from our values, but these discrepancies are probably not outside the uncertainties, arising from lack of resolution, in that particular study. The uncertainties quoted for our excitation energies are the total estimated probable errors, compounded from the re- producibility of peak positions inherent in the scanning of the emulsions, uncertainties in the calibration energies, and uncertainties in the details of the spectrograph calibration. They are consistent with the scatter observed in analyzing several different spectra with several variations of the way in which the energy-analysis program is applied. Values of the differences in excitation energy between pairs of states 50 to 1000 keV apart should always be good to 1-2 keV as long as both were populated with reasonable strength. IV.4. Angular Distributions IV.4.A. Discussion of DWBA Calculations 49 The DWBA calculations we discuss here were all made with the proton optical-model parameters of Ref. 37. Although an- other parameter set50 produces discernibly different proton elastic scattering predictions for s-d shell nuclei at Ep-35 MeV, the DWBA (p,d) predictions are quite insensitive to the dif- ferences between these two proton potentials. 109 There is a lack of extensive deuteron elastic scattering data for the mass region of the s-d shell at energies appro- priate to the present experiment. This necessitated an ex- tensive survey of the relevant literature in an attempt to find a suitable set of such parameters. The criterion of suitability was, of course, a reasonable reproduction of our observed angular distribution shapes. The criterion for a good i=2 prediction was a match to known pure i=2 distributions I obtained in the present work and in simultaneously performed 3 measurements of the 5Cl(p,d)34Cl reaction.7 Correspondence to the pure i=0 transitions leading to the 0.842 HeV and 33 5.49 MeV levels in S, observed via the 34S(p,d)33s reaction at Ep-35 MeV, was used as the criterion for a good 220 DWBA shape. We have investigated the efficacy of deuteron potentials proposed by Hinterberger, et al.,51 Perey and Perey,53 Newman, I et al.,52 Schwandt and Haeberli,S4 Mermaz, et al.,55 and 98 in both the local, zero-range (LZR) and the Cowley, et al. finite-range, non-local (FRNL) versions of the DWBA. The non- locality parameters used for the proton and deuteron channels 49 values 0.85 and 0.54. The were, respectively, the standard geometry of the neutron bound-state wave function had the standard Woods-Saxon form, ro=1.24 fm, a=0.65 fm, and a Thomas spin-orbit term with A=25. The depth of the bound-state potential well was always adjusted to match the experimental neutron separation energies corresponding to the various ex- cited states of 38K. The finite-range parameter was 0.621.49 110 All calculations were carried out with no lower cut-off in the radial integration. In addition, we investigated the "adiabatic" prescription for deuteron-proton transfer reactions, as proposed by Johnson andSoper43 and shown to yield good results for reactions on 45 44 46-48 lead, f-p shell, and oxygen, targets, and a ”density- dependent" damping of the an interaction as proposed by Freedom.48 51-55'98 deuteron optical- When any of the conventional model potentials was used, the calculated shapes of i=0 and 2-2 distributions were in much better agreement with our experi- mental test cases in the FRNL approximation than in the LZR approximation. The best results obtained with any of the vari- ous potentialsSI"55 appear to be obtained with the "Set I" parameters of Hinterberger, et al.51 (see Table 12), which is gratifying, since this potential set is probably the best grounded in terms of mass and energy dependence. The Hinter- berger, §£_gl. "Set II" and the Newman, g£_21. potentials yielded results not too different from those of "Set I". The critical success of the Hinterberger ”Set I" para- meters, relative to potentialslof different origins, lies in its correct reproduction of the forward angle (0cm<20°) 24) and 222 shapes. Its principle failing, shared by all the others to a greater or lesser extent, is its overestimation of cross- sections at larger angles (ecm>30°), a failing which grows more pronounced as the Q-values become more negative (excitation 111 .0m.mom c0 cw>0w mm mocmpcmawouo 0x0co >0: ooo.ouxm sou use czosm mos0m>o .3 .0030 59.0.0 9.000.008.0800 couosa paw compass m... .uomo .00 we .nowsonpwucwm mo 0 pew nmumamnmd oowmso>mi00.wumn . 0. 0 000090000 mm s muses» 10.0 0000 00.0 30.0 c00wmsodom nouns auspm ocsom o» poumsnvc cosusmz AUHH mmm 009 was >0v erN >3 mm as m> . .sumo xmmAp000xmm 050 Mo mwm>0mcm on» :0 com: mumumEmsma 0mpOEo0mowuao .00 m0nme 112 energies get higher, binding energies of transferred neutrons become larger). Experience led us to expect that both the 43 48 alterations to "abiabatic" and the "density-dependent" the conventional DWBA procedure would improve the predictions at these larger angles. The "adiabatic" potential, designed to account for effects resulting from disassociation of the deuteron, is not related to actual deuteron elastic scattering data but is constructed from proton and neutron optical-model potentials (taken from Ref. 37 in the present instance) ac- 43,47 cording to a particular prescription. The adiabatic- potential calculations were carried out in the LZR approximation, since the FRNL corrections did not yield significantly dif- ferent results. The "density-dependent damping" of the Vfin interaction,48 motivated by a paper by Green,69 provides an alternate means to reduce DWBA cross-sections at larger angles. We have ‘ chosen the damping factor F(r)=(l.0—l.845p(r)2/3), where 1/3 )/a and "r " and "a" are the p(r)-0.l7[l+exp(x)]-1, x(r-roA o radius and diffusivity of the neutron bound-state well. The density-dependent an damping was studied in conjunction with FRNL calculations which used the Hinterberger, et al. "Set I" deuteron potential. We have analyzed our data in detail with the following DWBA calculations (see Table 12): (l) The Becchetti-Greenlees37 proton parameters and Hinterberger, gg_gl.51 "Set I" deuteron parameters, using the FRNL approximation. These calculations, 113 henceforth referred to as FRNL, are thus completely orthodox and unadjusted. (2) This same combination of proton and deu- teronparameters and computational approximations, but with the addition of the density-dependent damping of the Vbn interaction, henceforth referred to as DFRNL, and (3) The Becchetti-Greenlees proton parameters and the adiabatic deu— teron parameters in the LZR approximation, henceforth referred to as ADIABATIC. The results of these three types of DWBA calculations are compared with each other and with some of our experimental data in Figs. 19 and 20. The general characteristics of these cal- culations, relative to the experimentally observed i=2 and 280 transfer distributions, are as follows. The FRNL calculations fit the pure i=2,j=3/2 observed shapes from 30 out to 500 quite well; the indications are that from 500 on out, the theoretical differential cross sections are too large. For i=0 transitions, the observed shapes are reasonably well reproduced out over the second maximum, but from there on, the theoretical predictions are much too large. In addition, the structure of the theoret- ical distributions begins to be flattened out for states at higher excitation energies, while the observed shapes seem al- most independent of the Q-value involved. The DFRNL calculations fit the 2-2 observed shapes essentially perfectly throughout the experimental angular range covered. I The agreement with the observed 280 shapes is considerably im- proved over the FRNL predictions, but cross-sections are still Figure 19. 114 A comparison of fits to representative angular distributions from the 39K(p,d)38K reaction at 35 MeV with the three chosen types of DWBA cal- culations. All fits were performed over the 30 to 35° angular region. The curves are identified as follows: ———DFRNL, ---—FRNL, and — —ABIABATIC. 115 102 e 102 6x; 000 keV 6x=r2‘+0‘+ rkeq L=2 L=0+2 10 10 /-—\ 1 L (r) \ 10‘1 .Q E 10‘2 031022.22- 1022.222. ‘0 E Ex=3980 keV Ex=5856 keV » L=0+2 L=0+2 \\\ 10! 10 “O ‘2? . J 10 0 20 L+0 c.m. ongle[degrees] Figure 19 116 Figure 20. A comparison of ADIABATIC, FRNL, and DFRNL cal- culations (see text and Table 12) with i=0 transitions in the 3“S(p,d)33S reaction at 35 MeV. differeniiol cross seciion[or‘bi+r‘or‘g uni+s] 117 103 r 1 T l I : 3L*8[p,d]3'=3s; 50:35 Mevi zn=0 +r0nsi+ions j 2 — DFRNL 10 L— - , 5 ----- FRNL 5 : ——-— ADIABATIC i L \ " ‘\Ex=0.8L+ MeV-- 10;:- /// \\ \\\ I 0000 \ '1' b: . \ \\_’,’ \‘E t I, \ _ I s 1 I, /"‘\ 0 .- l 0 J . z 4 , E 10:- :1 t 1 )-p -4 1:- ‘ I .0 E \ [I \ Ill 5 r \ ’ ‘ / 3 L- t (I \" j g. u . _ II 10 1 1 U1 1 l 1 0 20 L+0 80 c.m. ongle[degr‘ees] Figure 20 118 somewhat too large beyond 30°, and the undesired trend of shape with Q-value persists. Finally, the ADIABATIC calculations do not match the forward angle (ecm<15°) behavior observed for the £82 distri- butions, although for 0cm215°, the fits to the data are as good as the FRNL results (but still not as good as the DFRNL results). The differential cross sections predicted for ecm§20° for the £80 diStributions are indeed lower than those obtained with the FRNL and DFRNL calculations, but over the _3°-40° region, the agreement with experiment is worse for states at high excitation energy and only comparable for lower ex- cited levels. IV.4.B. Analysis of Experimental Angular Distributions Our measurements of the angular distributions of the in- tensities with which states in 38K are populated in the 39K(p,d)38K reaction at Ep-35 Mev are presented in Figs. 21—24. Some states included in the table of excitation energies are not shown because they were not observed at a sufficient number of angles. The solid curves through the data points are fits of the DFRNL calculations described above. These fits, and the resulting spectroscopic factors, were obtained by minimizing the quantity do 2 1 afimi’i DWBA do 2 x " N 1,51 “An —731i‘—— " 35(01)exp)/A°i] 119 through the adjustment of the coefficients A2j' Here, 3%(Gi)ij,DWBA are the numbers output from the DWUCK program for angles ei’%%(ei)exp are the experimental differential cross-sections and A01 are the statistical plus estimated re- lative systematic errors in the experimental numbers. Values of i=0 plus 2, or 1 plus 3, were used except in special cases where known spin assignments precluded mixing. The number of data points, N, included all observations in the angular range 30-350. The spectroscopic factors, weighted by the isospin Clebsch-Gordon factors, are then obtained from the relation 2 A = 2.29 C S .. £3 2:] In Table 13 we list the excitation energies, z-value assign- ments and spectroscopic factors for all the states whose an- gular distributions we considered analyzable. The DFRNL DWBA calculations were used in extracting these numbers. We carried out the same fitting procedure, again with the DFRNL predictions, including all data points out to 60°. The maximum changes in the resulting spectroscopic factors were 10%. we also carried out the fitting procedure for all dis- tributions, in the 3o_350 angular range, with the FRNL and ADIABATIC DWBA predictions. The DFRNL results are compared to the FRNL and ADIABATIC results and to results of previous experiments and analyses in Table 14. Only those states pre- viously observed are included in this table, to keep the size 120 Figure 21. Experimental angular distributions for states in 38K, as observed in the 39K(p,d)33K reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the amount of the i=0 component in mixed 2=0-z=2 distributions. 121 102 2 - - 2 102 . 1 v .2 2, 102‘ Ex= 000 keV . I Ex= 130 keV : L=2 4 * L=2 6x; 959 rueV L=0+2 10’ 10 g 10’ $1022.---102-2,i.102,22,- \ Ex=1699 keV : Ex=2‘+0‘+ keV E Ex=281'+ keV : L=0+2 L=0+ . ' = 1 y; 10 10* 2 10 L 3 1 E a 3 I . . ' I! l 20 ‘ 9b 60 102 .. . 1 V , 102 v Y - , - 102 - , . .0 v 5 Ex=2698 keV 3 : Ex=2830 keV 3 : Ex=287l keV ~ L=3 « » L=1+3 0 i L=1+3 1: a 1: a 1: a . : : : : ; -1’ 0 ‘ -1’ ‘ -1' ‘ 1° E. 1 1°! 3 1° N I § I I I U 1 10'2' - . . . A 10'2 0; . ‘7 10‘? . r . . . ‘ ID 20 so 0 l o u .0 0 20 HO 0 c.m. ongle[degrees] Figure 21 Figure 22. 122 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K re- action at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the amount of the 2:0 component in mixed 2=0-2=2 distributions. 123 102 V if v to v 102 is r ,s 7 Y 102 , 1 t to r ‘ ; Ex=33'-+l keV Ex=3H32 keV : Ex=3617 keV a » L=0+2 3 L=0+2 1 i L=3 1 10: 3 10 10_ 3 3 II. 1‘: N1 . J ‘ 2b ‘ 4b “80 102 i,'r f 1, - 1o2 - v . r - 102 or r v r r. _ Ex=3703 keV Ex=3819 keV a . Ex=3859 keV i » (L=0+2) L=l+3 3 i L=0+2 3 10 1 10F 1 10r 1 1. 1 1E a I; a -fi ‘ 1 3 10 t 1. 1 20 I+0 010 l 4 01° 1 20 90 o 102 T . - e r 102 re f v , T 102 - . - e f : Ex=3938 keV 3 Ex=3980 keV i Ex=Hl76 keV : L=1+3 < L=0+2 1 i L=0+2 1 ; t . . o 0 2b ‘ Rb ‘ o c.m. onqle[degr‘ees] Figure 22 Figure 23. 124 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 3° to 35°. The dotted curves show the amount of the i=0 component in mixed 2=0-2=2 distributions. ' dG/dQ [mb/sr‘] 102 v , i, , v : Ex=q217 keV é » (L=1+3) 1 10? a 1E a fi: : 10 E 3 1 ‘2’ l . A 0 0 20 so 60 102 , 7 vs , . : Ex=4713 keV i » L=0+2 I 10F ( ) 1 éx¥5249'ue0 L=0+2 ‘ so 125 102 v , V. l v ’ Ex=%598 keV i , L=1+3 I 10{ E 1r a 10*? g ’ ? 10‘27‘2.'jr.j“E“7~ 0 20 H0 80 102. T , v , v Ex=%998 keV i L=0+2 3 60 102 - , 2' r a L Ex=SHH9 keV i . L=0+2 : 10E E 1! a -1 1 10 > 3 10‘2’ I: A A ..- I 0 20 %0 60 102 - r Y , , 5 Ex=H673 keV 10» L=0+2 ( 10'1 -2: ‘ Li ‘ _ 1 10 o 20 L+o so 102 , . . , f : Ex=5058 keV : L L:3 : 1o:F 3 1E 1 _fi : 10 E 3 -2’ "U . \>__ I 10 o 20 HO 0 102 V r v . - _ Ex=5599 keV : > L=0+2 I 1E a o c.m. ongle[degr‘ees] Figure 23 Figure 24. 126 Experimental angular distributions for states in 38K, as observed in the 39K(p,d)38K reaction at 35 MeV. The solid curves are fits of the DFRNL calculations to the data in the angular range from 30 to 35°. The dotted curves show the amount of the i=0 component in mixed £=0~£=2 distributions. 127 102 To 3 r T V. 102 - is- r v 3 102 - 3 f r Y Ex=5626 keV 3 g Ex=5680 keV a E Ex=5737 keV 3 L=0+2 3 . (L=1+3) 10 L=0+2 3 AAAAAJ A A‘AJAL‘ A A 10’27’::‘T_‘T\;T\::~‘ 102 r t r , v 102 , r 3 V , 102 - , r . . Ex=5809 keV Ex=5856 keV 3 5 Ex=5891kev 3 L=0+2 L=0+2 3 » L=0+2 3 10-2 A" 1A L A 10 13 10g 1 1 3 a 10‘1 ‘3 a ‘. 1o‘2Le 3 . e e ‘ 10‘2' A A A: A so 0 20 L+o so 1 2 2 2 3o 10-32-. 10-le,i t? Ex=59w keV 3 E Ex=5978 keV 3 Ex=5991 keV : 3 L=3 3 » L=0+2 1 i L=0+2 ‘ 10 3 10E 3 10E 3 1 ‘ 1 ‘ 1 ‘ 1 3 E 3 F 3 lo“ ‘ 10‘1’ ‘ 10'l ‘ 3 {ififl’fik“L_\\§ 3 13'? ‘ 10'2“ . A A A L ‘ 10'2 ‘ ‘80 o 20 so so 0 "20 HO c.m. ongle[degrees] Figure 24 .128 Table 13. Experimental values of z and 0282 , obtained from the DFRNL analysis for transitions from 39K to 38K as observed in the present investigation. All values are normalized so that 028‘ for the ground state is 1.75. The assumed j-values are 3/2 for i=2, 3/2 (n=2) for 1:1, and 7/2 for 1:3. Ex(keV) 0",?“ 1 0233 Ex(keV) J”,Ta 2 0733 000 3‘,0 2 1.75 0217 (1,3) 0.02 ,0.01 130 0*,1 2 0.31 0593 1,3 0.005,0.00 059 1‘,0 0,2 0.13 ,0.32 0673 (l,2)*,l 0.2 0.19 ,0.25 1699 1*, 0,2 0.02 ,0.57 0713 (0,2) 0.005,0.05 2000 2*, 0,2 0.03 ,1.26 0993 0,2 0.005,0.02 2610 3 0.05 5053 3 0.03 2603 (2,3)' 3 0.03 5209 (l,2)’,1 0,2 0.16 ,0.17 2330 (0,3)' 1,3 0.02 ,0.01 5009 0,2 0.000,0.15 2371 (0,3)’ 1,3 0.01 ,0.05 5509 0,2 0.003,0.03 3301 l‘,0 0.2 0.01 ,0.02 5626 0,2 0.06 ,0.05 3032 2‘,0 0.2 0.03 ,0.03 5630 (1,3) 0.003.o.00 3617 3 0.00 5737 0,2 0.009,0.26 3703 (0,2) 0.003,o.02 5309 (1,2)+ 0.2 0.17 ,0.16 3319 1,3 0.01 ,0.02 5356 (1,2)+ 0,2 0.11 ,0.12 3359 0,2 0.005,0.03 5391 (1,2)+ 0,2 0.06 ,0.00 3933 1,3 0.01 ,0.02 5900 3 0.03 3930 (2)‘,l 0,2 0.10 ,0.02 5976 0,2 0.001,0.lo 0176 0,2 0.02 ,0.03 5991 0,2 0.006,0.0l ‘Refepences 30, 35, 37, 92, 93, 90. 129 manageable, but these suffice to indicate the trends and scatter of the spectroscopic factors as functions of the de- tails of the DWBA calculations. IV.4.C. Assignment of g-values 38K levels observed in the present in- Of the forty-six vestigation, thirty-six can be assigned at least tentative values for the orbital angular momentum quantum numbers of the neutrons transferred in the process of their formation (see Table 13). Twenty-four levels are assigned pure £22 or a combination of 180 and i=2 transfers. The basis for these assignments is typically an excellent and unambiguous fit to the the experimental distribution with a mixture of calculated 2:0 and 2:2 shapes. Most of the transitions having significant i=0 strength are also easily recognized simply on the basis of the differential cross-sections for this type of transfer, which is clearly evident in the 3o_13o portion of our angular distributions. Assignments of negative-parity o-values (2=l and 3) could not, in general, be made with the assurance possible for the positive parity cases. This was because the experimental dis- tributions were rather featureless (except for a few examples dominated by 2=1) and because the calculated £=3 shape does not appear to fit the data as well as those for i=0, 1 and 2. Con- sequently, it is possible in many cases to get as reasonable 130 a fit to the data with 2=2+4 shapes as it is with 2=1+3 shapes. In addition, there is the uncertainty as to whether some of the weakest, flattest distributions observed are even characteristic of a single-step direct transfer. we have assigned a negative parity (223 and/or 1) to twelve of the levels observed. Many of these assignments, however, are dependent upon an assumption which rules out the possibility of significant £=4 transfer strength in the present experiment. Questions involving the agreement of the present assign- ments with previous results, their relationship to theoretical studies, and the degree of certainty with which the presence or absence of a particular z-value component can be detected in a given transition will be discussed in the following sections. 2 IV.4.D. Discussion of Values Extracted for C S In the present study, we are not concerned with extracting the absolute magnitude of the single nucleon transfer spectro- scopic factors. We are interested primarily in trying to get some measure of the reliability of relative spectroscOpic factors for a particular l-transfer as a function of Q—value (or the separation energy for the picked-up neutron), and of the relative values for different (i=2 vs. 2=0) 2-transfers. The latter point reduces, in the limit, to the question of the certainty with which a weak component of one mode of z-transfer can be identified in a transition dominated by the other. This, 131 of course, is important beyond just the spectroscopic factor, since the presence of a particular 2 often has direct im- plications for the spin of the residual state. The accuracy with which the Q-dependent effects on over- all cross-section magnitudes are reproduced by DWBA calculations is difficult to pin down, but serious difficulties have been 79'94 we mentioned in a previous section that details noted. of the angular distributions as a function of Q-value are not well handled in all cases. We have merely tried rather dif- ferent sets of optical-model parameters and examined the consistency of the results. This was also the tack used to examine the accuracy (really only the consistency) of the relative magnitudes of the peak cross-sections for different 3£transfers. The results of these studies, covering not only the three types of DWBA calculations already discussed here in some detail, but also a good many others, indicate that most reasonable DWBA formulations for the (p,d) reaction yield consistent results within the domain of the residual nuclear states studied here. The extent to which these re- sults are "correct" can be further explored by comparing ex- tracted spectroscopic factors with those obtained from other reactions, as will be done in a following section. The spectroscopic factors extracted from a fit to (generally) mixed-1 angular distributions contain Q-dependent and £-dependent uncertainties arising from errors and lack of completeness in the data set, and from failures of the 1232 N\0.N .00: 0.N oaonn 0N0 NN0.N 0:0 .>o: 0.N 30000 0N0 00.: 00. u 000 0000000000 N\N.m0uog .au 0.Nuouo-u=u 000003 000 cocoa-ooze .oouuoaon Oman no.0" mauu .mo ouconouomn .so oucokouomo sou osouoou owaooaOLMOOAa «nu Add 0x903 acouOde No.0 00.0 00.0 N . 00.0 00.0 00.0 0 oxN No 0000 00.0 00.0 NN.0 N N0.0 00.0 00.0 00.0 00.0 o ..N.00 0000 0N.0 00.0 00.0 N 00.0 00.0 00.0 0 .NN.00 0000 00.0 00.0 00.0 00.0 N No.0 00.0 00.0 00.0 o 0...N.0o 0000 0N.0 00.0 NN.0 00.0 NN.0 N NN.0 00.0 0N.0 00.0 00.0 00.0 00.0 o 0..NN.00 00N0 NN.0 00.0 :00.0 0N.0 No.0 0N.o N 0N.0 00.0 0N.0 NN.0 00.0 0N.0 00.0 0 0...N.00 0N0: 00.0 H0.0 00.0 00.0 0N.0 No.0 N 00.0 00.0 0N.o 0N.0 00.0 00.0 00.0 00.0 0 0..NN.00 0000 NN.0 No.0 0N.0 00.0 00.0 00.0 N 00.0 00.0 N0.0 00.0 00.0 00.0 0 0.+N N000 00.0 00.0 00.0 00.0 0 00.0 No.0 00.0 0 0. oooN 0N.N 0N.0 N.N 00.0 00.0 00.0 00.0 0N.N N 00.00 NN.0 00.0 00.0 00.0 00.0 o 0..N oooN 00.0 00.0 NN.0 N0.0 00.0 00.0 N 00.00 00.0 00.0 . 00.0 No.0 No.0 0 0..N 0000 NN.0 NN.0 00.0 00.0 0N.o 00.0 N 00.0 00.0 00.0 NN.0 00.0 00.0 0 0..H 000 0N.0 0N.0 00.0 0N0.o 00.0 00.0 00.0 00.0 N . 0..0 002 .0.00 x00.0o x00.00 “00.00 “00.00 AN0.00 a o 00.0 00.0 00.0 00.0 00.0 00.0 N o..0 000 c x Noz0.0o 0x.$o:0o oxa.ox0o 0.0.00 oooo uozuo 00¢ .mononucosoa cm voucumona one euoum oesop- ou x Iosu acOHumucchu any sou am m0.HumN any Low nonuu> «unwound 0:9 .1 0 ho «0:01) mausolahooxu .30 «dock on on N 133 DWBA curves to exactly reproduce the shapes of pure -£ dis-~ tributions, as well as from the more fundamental uncertainties in cross-section trends mentioned above. By measuring the experimental distributions in to 3° we have insured that the £80 spectroscopic factors are free from the extra uncertainties chronic in many previous studies, in which the data extends in to cover only the second maximum of the £=O shape. The intrinsic cross-section of the DWBA-calculated i=0 transition at 3° is ~20 times the magnitude of the i=2 prediction at its 2S(£=0) are ex- maximum. Hence, our extracted values for C tremely secure in an experimental sense. That is, there is no way to reproduce the shape of an experimental distribution which has a significant peaking at 00 without putting in essentially the total amount of i=0 strength obtained in our fits. The exact amount of 3-0 admixture in a predominantly i=2 distribution can be given to an accuracy sufficient for any meaningful comparison with theoretical predictions. The more interesting question, involving weak to non-existent 2:0 components, concerns the limit to which their presence can definitely be assigned. The better the quality of the data and the better the theoretical fit to pure £32 shapes, the more stringent a criterion may be employed. We think that in the present work the presence of an 1=0 component is un- ambiguously established if c25(2=0)20.005. The problem of extracting accurate 1-2 spectroscopic factors from shapes displaying significant 380 character is 134 much more difficult than the converse problem. Since the intrinsic magnitudes of the i=2 DWBA cross-sections are so much smaller than those of the 2=O predictions, and are also relatively unstructured, the amount (and the uncertainty thereof) of observed i=2 strength in an apparently i=0 experi- mental shape can be quite significant in terms of nuclear structure predictions. Unless one has perfect 1:0 DWBA pre- dictions and essentially perfect data, this problem seems impossible to overcome. An objective, integrating-fit criterion such as we have used is probably not the best ap- proach to extracting i=2 components unless the theoretical g-O fits are quite good. It is quite possible that the 1-2 strength assigned by the fit serves predominantly to compen- state for the principle defect in the £20 predicted shapes. we think that the fits of the DFRNL predictions to the data are good enough to justify an automatic, non-subjective analysis procedure. Some of the lack of consistency which crOps up in the comparison between spectroscOpic factors extracted with the three different calculations surely arises from deficiencies in the FRNL and ADIABATIC 2:0 shapes. IV.5. Discussion of Results IV.5.A. Comparison with Previous Experimental Results 38 All levels in Ar (T-Tz-l) should have analogues in the 38K spectrum which have essentially the same properties. 135 79,94 Experiments with the 39K(d,3He)38Ar reaction show that the O+ ground state and the 2+ first excited state at 2.167 MeV are 4. strongly populated with 2=2 transfer and that 2+, 2+, 2 , and (1,2)+ levels at 3.937, 4.565, 5.157, and 5.552 MeV, respec- 95 are strongly populated via 2=0 transfer. It was ex- tively, plained in Ref. 94, before unique spins for the higher states were known, that the spectroscopic factors for states below 6 MeV excitation observed in the 39K(d,3He)38Ar reaction could be . -1 39 '2 understood in terms of a (d3/2)J=3/2 model for K: (d3/2)J=0 and 2 wave functions for the ground and first excited states (<13/2 pickup) and (d3}251}2)J=1’2 wave-functions for the higher lying £=0 strength. Since only one 1+ and one 2+ state can be formed from the Sl/2-d3/2 coupling and four i=0 states are observed, it is obvious that fragmentation of the 220 strength into states arising from other configurations occurs. It was argued in Ref. 94 that the fragmentation most probably involved 2+ states (since confirmed), and that the extra two 2+ states had their origins in f-p shell configurations rather than in d5/2 hole ex- citations. The state at 5.55 MeV was suggested to have Jfl=1+. 38 All of these strongly excited levels in Ar should be observed, with similar relative strength, in the 39K(p,d)38K 38Ar states presently known to spectra. The total number of exist below 6 MeV excitation is 21. Our present high re- solution data may allow the observation of others. The analogues of the first five strongly excited 38Ar levels are observed at 130, 2404, 3980, 4673, and 5249 keV. Relative to the lowest 0+,T=l state, the energy shifts of these five 136 38 38K, relative to Ar, are +107, -87, -22, excited states in and -42 keV, respectively. The analogue of the 5.552 (”5.85") MeV level in 38Ar 3 38 observed in (d, He) is not clearly identifiable in K. We observe three 280 transitions in the 5800-5900 keV region in the present experiment which would not have been resolved in the (d,3He) study. However, only one (at 5.552 MeV) 95 positive-parity level is known to exist in the appropriate 38 energy region of Ar, implying that the i=0 transition ob- served in (d,3He) proceeds to a single state. All this implies 38 that two of the three i=0 states we observe in K near 5.85 MeV excitation have T80. However, the 280 spectroscopic strength observed in (d,3He) is significantly greater than that of any one of the 5.85 MeV states in 38K. The consistency between the spectroscopic factors ex- tracted from the (d,3He) data and the (p,d) data can be in- spected in Table 14. The apparent analogues of the first 38Ar have 39K(p,d)38K spectro- 3 five strongly excited levels in scOpic factors consistent with the (d, He) values, the largest deviation occuring for the 4.673 MeV state. Thus, it seems likely that the failure to find a single state in the 5.85 38K which has spectroscopic strength comparable to the (l)+,T-l state at the corresponding energy in 38Ar, MeV region of together with the other features of the situation just dis- cussed, is evidence of almost complete mixing of the 1+,T-l 137. state which must occur in this region in 38K with one, and probably two, close lying Tbo neighbors. Indeed, the sum- 38 med spectroscopic strength of the three K levels at 5.85 nicely equals the strength of the (presumed) single state in ”Ar. It is not possible to establish further isospin assign- 38 38 38Ar level ments in K via correspondence between the K and schemes because the level densities are high relative to the average Coulomb shifts and because proton pick-up data com- parable to the present neutron pick-up work does not exist. The agreement between the present results and those of previous neutron pick-up studies of 38K seems quite good, considering the limitations of the older data. It is perhaps interesting that, on the average, all of the neutron pick-up results exhibit the same deviations from the proton pick-up results, namely a larger CZS(2=2)for the first 0+,T=l state and a smaller CZS(£=0) for the 4.67 MeV, 2+ state. IV.5.B. Comparison of Results with Structure Theory Pick-up spectroscopic factors predicted for 39K+38K transitions are compared with the present experimental results in Table 15. The listed theoretical numbers are averages of the predictions derived from the two most successful Hamiltonians presented in Ref. 3, Kuo-type Hamiltonians 17 12.5p+ O and ll.0h+ASPE. The agreement appears quite 138 Table 15. Experimental and theoretical values of C28 for single neutron pick-up from 9K. Ex (keV)a J",T 3 DFRNLa THEORYb 000 3*,0 2 ,1.75 ,1.72 130 0+,1 2 ,0.31 ,0.23 059 1‘,0 0,2 0.13.0.32 0.13.0.00 1699 1*,0 0,2 0.02.0.57 0.00,0.06 2000 2*,1 0,2 0.03.1.26 0.01.1.20 3032 2‘,0 0,2 0.03.0.03 0.03.0.15 3930 <1,2)*,l 0,2 0.10.0.02 0673 (l,2)*,1 0,2 0.19.0.25 0.53.0.05 5209 (1,2)*,l 0,2 0.13.0.17 5309 (1,2)+ 0,2 0.17,0.16 5355 (1,2)* 0,2 0.11.0.12 0.37.0.00 5391 (1,2)+ 0,2 0.06.0.00 aPresent Work. b Reference 3. 139 impressive, and seems to confirm the essential validity of this particular approach to calculating low-lying positive parity states at the top of the s-d shell. While the com- parison definitely confirms the success of the Kuo matrix elements relative to the other interactions studied, the .differences between the individual predictions of these two interactions were too small to be resolved. Indeed, it would seem to be almost beyond the scope of single nucleon pick-up experiments to meaningfully discriminate between the two sets of wave-functions. 38K is far in excess The density of states observed in of what is predicted by the dS/Z-sl/z-dB/z shell-model cal- culations just discussed, which so successfully predict the observed apportionment of i=0 and 2-2 (mostly but not all, d3/2) strength among the low-lying levels. The drastic frag- mentation of the i=0 spectroscopic strengths to ”extra" T=1 levels provides another view of the existence and significance of states which should arise from f-p shell configurations. All s-d shell calculations firmly exclude any reasonable sup- position that the extra T-l states below 6 MeV excitation, which cannot be contracted from d3/2-31/2 couplings, arise from dS/Z excitations. The (d,3He) data support this view, indicating that the next 1-2 level above the 2+ first excited state falls at 7 MeV excitation. 140 IV.6. Conclusions we have found that the angular distributions of the (p,d) 39K, using a proton energy of 35 MeV and covering reaction on 6 MeV of excitation in the residual nucleus, can be success- fully analyzed with DWBA calculations which employ the most broadly based proton and deuteron optical-model potentials available. The finite-range, non-local DWBA calculations which use these parameters fit both i=0 and 2=2 distributions quite well in the 30-250 range. At larger angles, the pre- dicted cross-sections do not drop off as rapidly as do the data. Use of a deuteron potential constructed by folding neutron and proton potentials, or use of a damped Vfin inter- action serve to improve agreement at larger angles. The density-dependent damping procedure yields the best fits to the present data. Any of these DWBA prescriptions yields stable and theoretically sensible spectroscopic factors if only the 30-200 data are used. Many new levels have been observed in the present experi- ment and assigned excitation energies accurate to 1-3 keV. The detailed angular distribution measurements permitted the assignment of a positive parity and spin limits to many of the observed levels, and tentative negative parity to many others. The spectroscopic factors extracted for the more strongly populated states are, in general, consistent with re- sults of previous neutron and proton pick-up experiments. The 141 results for the low-lying positive parity levels provide con- clusive verification for the relevant predictions of recent shell-model calculations. The details of structure observed above 3 MeV excitation are evidence of extensive effects of f-p shell configuration states, but aside from energy level schemes, no predictions from extended (s-d-f-p) shell-model calculations are yet available to compare to our results. We observe what appears to be very strong mixing between T=0 and T=l,J-l+ states at 5.85 MeV excitation. LIST OF REFERENCES REFERENCES l. E.C. Halbert, J.B. McGrory, B.H. Wildenthal, and S.P. Pandya, Advances in Nuclear Physics, Vol. IV, Ed. by M. Baranger and E. ngt, (Plenum Press, New York, 1971). 2. B.H. Wildenthal, J.B. McGrory, E.C. Halbert, and H.D. Graber, Phys. Rev. 91, 1708(1971). 3. B.H. Wildenthal, E.C. Halbert, J.B. McGrory, and T.T.S. Kuo, Phys. Rev. 91, 1266(1971). 4. B.H. Preedom and B.H. Wildenthal, Phys. Rev. 96, 1633(1972). 5. T.T.S. Kuo and G.E. Brown, Nucl. Phys. 3;, 40(1966). 6. D.L. Show, J.A. Nolen, E. Kashy, and B.H. Wildenthal, Bull. Am. Phys. Soc. 11, 533(1972). 7. J.A. Rice, B.H. Wildenthal, and B.H. Freedom, Bull. Am. Phys. Soc. 11, 485(1972). 8. B.H. Wildenthal and J.A. Rice, Bull. Am. Phys. Soc. 11, 534(1972). 9. J.W. Olness, W.R. Harris, P. Paul, and E.R. Warburton, Phys. Rev. 91, 958(1970). lO. J.B. Garrett, H.T. Fortune, and R. Middleton, Phys. Rev. 91, 1138(1971). ll. J.D. Garrett, R. Middleton, D.J. Pullen, S.A. Andersen, 0. Nathan, and Ole Hansen, Nucl. Phys. A164, 449(1971). 12. J.N. Hallock, H.A. Enge, A. Sperduto, R. Middleton, J.D. Garrett, and H.T. Fortune, Phys. Rev. 96, 2148(1972). 13. S. Hinds, H. Marchant, and R0 Middleton, Nucl. Phys. 21, 427(1964). l4. J.D. Garrett, R. Middleton, and H.T. Fortune, Phys. Rev. 21, 165(1971). 15. H.D. Graber and G.I. Harris, Phys. Rev. 188, 1685(1969). 16. .A.K. Hyder and G.I. Harris, Phys. Rev. 91, 2046(1971). l7. J.R. Erskine, D.J. Crozier, J.P. Schiffer, and W.P. Alford, Phys. Rev. g3, 1976(1971). 142 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 143 P.M. DeLuca, J.C. Lawson, E.D. Berners, and P.R. Chagnon, Nucl. Phys. A173, 307(1971). R.N. Horoshko and M.H. Shapira, Nucl. Phys. A180, 37(1971). H. Brunnader, J.C. Hardy, and J. Cerny, Nucl. Phys. A137, 487(1969). H.A. Snover, J.M. McDonald, D.B. Fossan, and E.K. warburton, Phys. Rev. 94, 398(1971). B. Vignon, J.P. Longequeue, and I.S. Towner, Nucl. Phys. A189, 513(1972). H. Nann, L. Armbruster, and B.H. Wildenthal, Nucl. Phys. A198, 11(1972). w. Kutschera, D. Pelte, and G. Schrieder, Nucl. Phys. A111, 529(1968). B.H. Wildenthal and E. Newman, Phys. Rev. 175, 1431 (1968). J.G. van der Baan and B.R. Sikora, Nucl. Phys. A173, 456(1971). P.J. Mulhern, G.D. Jones, 1.6. Main, H.T. McCrone, R.D. Symes, M.F. Thomas, and P.J. Twin, Nucl. Phys. A162, 259(1971). H.G. Blosser and A.I. Galonsky, IEEE Trans. on Nuclear Science, NS-B, No. 4, 466(1966). J.B. Spencer and H.A. Enge, Nucl. Instr. and Methods 33, 181(1967) . D.L. Cohen, Rev. Sci. Instr. 30, 415(1959). H.G. Blosser, G.M. Crawley, R. deForest, E. Kashy, and B.H. Wildenthal, Nucl. Instr. and Methods 91, 61(1971). W.A. Lanford, unpublished. R. Au, G. Stark, R. deForest, and R. Dumit, unpublished. A.H. Wapstra and N.B. Gove, Nuclear Data Tables, Vo1. 9, Numbers 4-5, July 1971. ‘ R.C. Haight, Ph.D. Thesis, Princeton University, 1969. 144 36. 8.6. Nilsson, Kgl. Danske Videnskab Selskab, Mat. Fys. Medd. 29, No. 16(1955). 37. E.D. Becchetti and G.w. Greenlees, Phys. Rev. 182, 1190(1969). 38. R.J. Philpott, W.T. Pinkston, and G.R. Satchler, Nucl. Phys. A119, 241(1968). 39. C.A. Whitten, N. Stein, G.E. Holland, and D.A. Bromley, Phys. Rev. 188, 1941(1969). 40. J.L. Snelgrove and E. Kashyu IPhys. Rev. 187, 1246(1969). 41. R. Sherr, B.F. Bayman, E. Rost, M.E. Rickey, and C.G. Hoot, Phys. Rev. 139, 31272(1965). 42. P.J. Plauger and E. Kashy, Nucl. Phys. 5152, 609(1970). 43. R.C. Johnson and P.J.R. Soper, Phys. Rev. 91, 976(1970). 44. J.D. Harvey and R.C. Johnson, Phys. Rev. 93, 636(1971). 45. G.R. Satchler, Phys. Rev. 94, 1485(1971). 46. B.M. Preedom, Phys. Rev. g5, 587(1972). 47. G.M..McAllen, W.T. Pinkston, and G.R. Satchler, Particles and Nuclei l, 412(1971). 48. B.M. Preedom J.L. Snelgrove, and E. Kashy, Phys. Rev. 91, 1132(1970). 49. P.D. Kunz, unpublished. 50. M.F. Fricke, E.E. Gross, B.J. Morton, and A. Zucker, Phys. Rev. 156, 1207(1967). 51. F. Hinterberger, G. Mairle, U. Schmidt-Rohr, G.J. Wagner, and P. Turek, Nucl. Phys. A111, 265(1968). 52. E. Newman, L.C. Becker, B.H. Preedom, and J.C. Hiebert, Nucl. Phys. A100, 225(1967). 53. C.M. Perey and F.G. Perey, Phys. Rev. 152, 923(1966). 54. P. Schwandt and W. Haeberli, Nucl. Phys. A123, 401(1969). 55. M.C. Mermaz, C.A. Whitten, J.w. Champlin, A.J. Howard, and D.A. Bromley, Phys. Rev. 94, 1778(1971). 56. P.w.M. Glaudemans, G. Wiechers, and P.J. Brussaard, Nucl. Phys. 56, 548(1964). 145 57. I. Lovas and J. Revai, Nucl. Phys. 52, 364(1964). 58. P.W.M. Glaudemans, P.J. Brussaard, and B.H. Wildenthal, Nucl. Phys. A102, 593(1967). 59. A.H.L. Dieperink and P.J. Brussaard, Nucl. Phys. A128, 34(1969). 60. E.C. Erne, Nucl. Phys. 81, 91(1966). 61. G.A.P. Engelbertink and P.W.M. Glaudemans, Nucl. Phys.' A123, 225(1969). 62. N.G. Puttaswamy and J.L. Yntema, Bull. Am. Phys. Soc. 11, 12, 1123(1967): results reported in Ref. 64. . 63. Lars Broman, C.M. Fou, and Baruch Rosner, Nucl. Phys. A112, 195(1968). 64. G. Ronsin, M. Vergnes, G. Rotbard, J. Kalifa, and I. Linck, Nucl. Phys. A187, 96(1972). 65. J. Kroon, B. Bird, and G.C. Ball, Nucl. Phys. A204, 609(1973). 66. E.E. Warburton, J.W. Olness, and A.R. Poletti, Phys. Rev. 160, 938(1967). 67. J.A. Nolen, E. Kashy, I.D. Proctor, and G. Hamilton, to be published. 68. H.J. Maier, J.G. Pronko, and C. Rolfs, Nucl. Phys. A146, 99(1970). 69. A.M. Green, Phys. Letters 248, 384(1967). 70. w. Rudolph and H.U. Gersch, Nucl. Phys. 11, 221(1965). 71. J. Honzatko, J. Kajfosz, and z. Rosina, Nucl. Phys. A174, 668(1971). 72. R.N. Alves, J.M. Kuchly, J. Julien, C. Samour, and J. Morgenstern, Nucl. Phys. A135, 241(1969). 73. A.M. Hoogenboom, E. Kashy, and W.W. Buechner, Phys. Rev. 128, 305(1962). 74. P. Decowski, Nucl. Phys. A169, 513(1971). 75. L. Meyer, Nucl. Phys. 52, 213(1964). 76. G. van Middelkoop and P. Spilling, Nucl. Phys. 11, 267(1966). 77. 78. 79. 80. 31.' 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 146 J. Kopecky and E. warming, Nucl. Phys. A127, 385(1969). J.C. Hardy, H. Brunnader, and J. Cerny, Phys. Rev. 91, 561(1970). w.S. Gray, P.J. Ellis, T. Wei, R.M. Polichar, and J. Jinecke, Nucl. Phys. A140, 494(1970). N.G. Puttaswamy and J.L. Yntema, Phys. Rev. 111, 1624(1969). R.D. Lawson, reported in Ref. 85. I.J. Taylor, Nucl. Phys. 41, 227(1963). J. JAnecke, Nucl. Phys. 48, 129(1963). L.M. Blau, W.P. Alford, D. Cline, and H.E. Gove, Nucl. Phys. 16, 45(1965). H.T. Fortune, N.G. Puttaswamy, and J.L. Yntema, Phys. Rev. 185, 1546(1969). J.A. Fenton, T.H. Kruse, N. Williams, H.E. Williams, R.N. Boyd, and w. Savin, Nucl. Phys. A187, 123(1972). W.R. Collins, C.S.C., D.S. Longo, and L.A. Alexander, University of Notre Dame Nuclear Structure Laboratory, Annual Report, 1971. S. Maripuu, Nucl. Phys. A151, 465(1970). J.J. Kolata, R. Auble, and A. Galonsky, Phys. Rev. 162, 957(1967). A.N. James, P.R. Alderson, D.C. Bailey, P.E. Carr, J.L. Durell, M.w. Greene, and J.P. Sharpey-Schafer, Nucl. Phys. A172, 401(1971). G.A.P. Engelbertink, private communication. A. Gallmann, E. Aslanides, F. Jundt, and E. Jacobs, Phys. Rev. 186, 1160(1969). H. Hasper, Ph.D. Smith, and P.J.M. Smulders, Phys. Rev. 25, 1261(1972). B.H. Wildenthal and E. Newman, Nucl. Phys. A118, 347(1968). P.M. Endt and C. van der Leun, to be published. 96. 97. 98. 147 G.E. Trentelman, unpublished. D.D. Duncan, K.H. Buerger, R.L. Place, and B.D. Kern, Phys. Rev. 185, 1515(1969). 'A.A. Cowley, G. Heymann, and R.L. Keizer, Nucl. Phys. g_6_, 363(1966). APPENDIX A MONSTERZ APPENDIX A MONSTER2 MONSTER2 is the computer code used to analyze all of the nuclear emulsion plate and position-sensitive proportional counter data taken for this thesis using the MSU split-pole magnetic spectrograph. The code accepts input in the form of experimental parameters (beam energy, scattering angle, spectrograph magnetic field strength (in terms of the field- sampling NMR frequency) and focal-plane-position settings), reactions appropriate to the experiment and spectral peak specifications (excitation energy, or centroid and total counts). Relativisitic reaction kinematics are calculated 96 MONSTER2 with a modified version of the function KINE. is multi-functional with options to perform the following tasks: (1) transform cross-sections from laboratory to center-of-mass (CM) coordinates, (2) perform spectrograph calibration and evaluate excitation energies, (3) predict positions of particle groups in the spectrograph focal plane, (4) identify contaminant peaks and (5) perform multi-angle excitation energy averaging and cross-section compilation. l. CROSS-SECTION TRANSFORMATION: When particle group yields are input, they are multiplied by a useresupplied normalization factor to yield an absolute cross-section in the laboratory. They are converted to a CM cross- section by multiplying by OCM/OLAB as calculated in KINE A-l A-2 for the particular reaction and Q-value under con- sideration. The statistical error in the CM cross- section is automatically calculated. EXCITATION ENERGIES: Nuclear reactions are typically designated as A(a,b)B, where A is the target nucleus, a the projectile, b the outgoing particle, and B is the residual nucleus. B may be left in any of its states for which the transition is energetically and quantum mechanically allowed. Accurate observation of the momentum of particle b, (p), allows a precise excitation energy assignment to the appropriate level in B via reaction kinematics. In an Enge-type split-pole spectrograph, the radius of curvature (p) of the outgoing particle is roughly proportional to the position in the focal plane at which it is detected. Since pap, a p vs. position calibration allows the determination of the particle momentum and, hence the excitation energy of the corresponding level in the residual nucleus. The MSU spectrograph focal plane is assumed to be described by the relation67 _ 2 BO _ BpKINE+ABp B(p°+aD+BD +00) A.l with the following definitions: A-3 B - spectrograph magnetic field (kilo-gauss), deter- mined from NMR frequency. 89 - "real" particle rigidity (p=qu, where q is the charge of the outgoing particle). BpKINE - particle rigidity calculated from relativistic kinematics based on the reaction, Q-value and nominal beam energy and scattering angle. D - absolute focal plane peak position relative to a designated reference position, Do' usually 9-13 inches from the high energy end. 0 - radius of curvature corresponding to Do' 0,8 - linear and quadratic coefficients of the ex- pansion about Do(~-0.4 and 510-4/inch, re- spectively). 6 - a first-order estimation of the gap between abutting plates when a single spectrum is re- corded on two consecutive plates in the focal plane; 6 is non-zero only for particle groups falling on the second (low energy) plate. 080 - a correction to BDKINE necessitated by small, but real, variations in the nominal experimental parameters. To first order, JE—AE «pp—3.2.139 A2 AEbeam beam AOL L ABp 8 ABp where E— beam is evaluated for a 50 keV change in the beam A-4 energy and AEQ-= A-B--"-'§--'£—-with«45E— calculated in KINE AGL AT AOL 00k 0 I I ’ B = (T=part1cle kinetic energy) and KTE ETOT/Bp (ETOT=T+partlcle rest mass). 35, When sufficient particle groups from known energy levels (reference peaks-RP) are present, one may perform a complete energy calibration on the given spectrum. Once these RP and their associated reactions and ex- citation energies are input, MONSTER2 calculates BpKINE and the coefficients of po, 0, 8, 06, AEbeam’ and AeL (see equations A.l and A.2) from the nominal input beam energy and scattering angle. 0 a, B, AEbeam' 00L, 0' and 33 (when 6 is not constrained to be zero) are then calculated via a least-squares fit to the RP energies. Any of the variables may be held constant and error messages are issued if the data is insufficient, or incorrect (AEbeam>loo keV or AeL>2°). If the fit is reasonable, i.e., no error flags, the appropriate cor- rections to the beam energy, scattering angle and plate gap are made and the entire spectrum is analyzed, re- sulting in excitation energies for all peaks and reactions. If particle group yields are also input, lab-to-CM cross- section conversion takes place automatically. 22, If the number and/or type of known reference levels is not sufficient to perform a complete calibration for a given spectrum, the user may opt to use the approximate 67 parameters stored in MONSTER2. In this case, 6, AEbeam' A- 5 and 00 are assumed to be zero, i.e., all kinematics are L calculated using input beam energy and scattering angle values, and a plate gap is specified by the user. a and B are calculated as a function of focal plane orientation (input as the parameters DS and DL), Do is assumed to be 10 inches, and pc is calculated on the basis of the first reference peak position. When operating in this mode, insertion of one re- ference level forces all other peaks to be analyzed re- lative to it using the available calibration parameters. If more than one RP is specified from the same or dif- ferent reactions, MONSTER2 also performs a linear particle momentum match to obtain a best fit to all reference energies. This results in an effective adjustment of a. Table A1 shows the extent to which this fitting procedure can compensate for errors in the nominal experimental and calibration parameters. The trial errors in Table A1, except AB, were chosen as approximate maximum uncertainties usually associated with the respective parameters. At present, 3 appears to be the most important single para- meter for spectra covering more than ~10 inches of focal plane distance. Unfortunately, it is also the most poorly known, the values for B currently stored in MONSTER2 are based on theoretical predictions and prove to be very different from those calculated in several individual cali- bration runs on actual spectra. The change in 8 considered A-6 Table A1. Extrapolations from the MONSTER2 momentum matching fits to known energy levels. Nominal energies and calibration parameters were obtained from a complete calibration run on the test spectrum. All other energies (MeV) are obtained from a fit to the first three (0.000, 0.130, 0.459 MeV) levels after the indicated shift the given parameter had been as- sumed. Nominal AEbeams+35 keV AeL=+O.3° Aa=-1% .38=3x10-5 Afs=+1% 0.000 0.000 0.000 0.000 0.000 0.000 0.130 0.130 0.130 0.130 0.130 0.130 0.459 0.459 0.459 0.459 0.459 0.459 1.699 1.698 1.698 1.698 1.698 1.699 2.403 2.402 2.402 2.402 2.402 2.402 3.431 3.430 3.430 3.430 3.429 3.430 3.977 3.978 3.977 3.977 3.976 3.978 5.249 5.248 5.248 5.248 5.245 5.248 5.890 5.891 5.890 5.891 5.887 5.891 7.115 7.114 7.113 7.113 7.107 7.113 8.236 8.235 8.233 8.234 8.226 8.234 9.118 9.117 9.116 9.116 9.106 9.116 A-7 in Table A1 serves to indicate the effect of uncertainties in this parameter. The fitting procedure compensates for the other uncertainties to <0.5 keV/MeV to 9 MeV above the fitting region and can handle 8 uncertainties reasonably well over shorter extrapolation ranges. Accuracies can be significantly improved using the option to manually adjust a and B or by the use of contaminant peaks (see 4.) as additional reference levels in "unknown" regions of the spectrum. PARTICLE GROUP POSITIONS: A knowledge of particle group placement in the spectrograph focal plane is useful not only for experimental set-up, but also in preliminary data analysis. Peak positions for specified reactions may be predicted with MONSTER2 from the experimental parameters and appropriate excitation energies. The positions are predicted, and listed in order, using the internal cali- bration parameters and the inverse of the excitation analysis process. Although uncertainties in beam energy and precise scattering angle impose the main limitation on the absolute position accuracy, relative spacings of known levels from the same and different reactions have been reproduced to 50.2 mm in test case comparisons with actual plate data. CONTAMINANT IDENTIFICATION: Reaction products from target impurities often fall on the focal plane in the same re- gion as the specific particles-under investigation. The A-8 specification of any "reasonable" reaction requires that MONSTER2 analyze every peak as though it were produced by that reaction in the pertinent experimental con- figuration. Comparison of the output excitation energies with known impurity levels may allow one to identify contaminants or particle groups in the spectrum which are different from those being studied. From example, the 16O(p,d)1500.000, the 12C(p'd)11CO.OOO' and the 39K(p,t)37K peaks seen in the present studies were all identified in this manner, usually within 1:3 keV when the fitting procedure was used with known levels from target nuclei. MULTI-ANGLE AVERAGING: Excitation energies are generally assigned on the basis of 2 or more spectra. MONSTER2 can search on up to 10 spectra input on the same job and perform an average of appropriate excitation energies, weighted by the raw yield for the appropriate peaks. One can also punch corresponding differential cross-sections, yielding angular distributions for specific energy levels in given residual nuclei. APPENDIX B ELASTIC SCATTERING DATA APPENDIX B ELASTIC SCATTERING DATA All of the (p,d) data presented herein has been normalized by comparison with proton elastic scattering data. The (p,d) and (p,po) spectra for each target were recorded with a single- wire proportional counter under identical experimental con- ditions, except for an appropriate adjustment of the spectro- graph magnetic field. Consequently, with proper relative data normalizations, a knowledge of the absolute cross-section to observed proton ratio for the (p,po) data allows the observed deuteron cross-sections to be expressed in an absolute manner. Figure Bl shows the spectra recorded from proton scat- 23Na-35c1, 23Na-37c1, and 39 tering on the K targets at 40°. Angular distributions were recorded from 25° to 50° at 5° intervals. The distributions are shown in Figs. BZ, B3, and B4 normalized to Optical-model calculations using the 37 parameters for the appropriate masses. Becchetti-Greenlees The Na and Cl experimental cross-sections for the two sodium- chloride targets are presented in the observed relative con- figuration at each angle. Figure Bl. Proton elastic scattering spectra recorded at 40° with a single-wire proportional counter. B-3 ”IT? I I I TITIITITT IIIIIII I I IIIIIII I I IIIIIII I r 800 700 800 L9 Z H CC LLJ F.— +— b < [11111114 lunlll 1 11111111 J [Hill LJI>> L (n a) 3 2 l3 L.) ‘8 D r H L0 N82 48 or) 09“ '\ 1" (“ht )- m |l DZI d < O— ‘ __J LU g __ LL] [”1le 1 1 Inn]: 1 1 11111114 1 11111111 (0 L. Z .. C3 p_ >4es t C) 28 P\ m 091mm 0— C—f’J—D " 381 ‘ ' E8 111111 1 1111111 1 1 JJLlllJ l 1 1114114 1 J [111111 (,0 m N (.0 C3 e—4 C) 0—3 3" C.) O O 1—4 H leuuouo Jed s+unoo number channel Figure Bl Figure 82. Measured proton elastic scattering differential cross-sections for the 23Na-35Cl target. da/dQ [mb/sr) 10” 1 I 1 I r .0 ; \ PROTON ELASTIC SCATTERING: - \ a1 35 Nov 0 " \ Becchetti - Greenlees Proton ‘ 7 ‘\ 0p+ical Model Parameters ‘ 3. ‘ ———3SC|[p,p°]35CI theory 0 IascIIp.po)3SCI data 103? —--23Na[p,p°]23Na +heorg: E v23Na[p,p°]23Na data : r- j .. \w -w \\ I- \4 1010 J 1 l L L .1 10 20 30 '30 50 80 c.m. angle[degrees] Figure 82 Figure BB. Observed proton elastic scattering cross- sections for the 23Na-37Cl target. 10" 10 ' I 1 I T I I .3 I \ PROTON ELASTIC SCATTERING: .— ‘ 01’ 35 NOV .1 h ‘\ Becchetti - Greenlees Proton .. P \\ 0P+ical Model Parameters ~ I \\\ 37Cl[PoPo)°7C| theory 0 \‘ I 37C|[P»Po]°7CI dOIO " ""'23N0[P.Po]23Na theory_ 5 \ '23N0(P.po]23Na 330 3 E : b 9 - \1 i I L l L C'm- onQIGIdegr‘ees] Figure B3 Figure B4. Measured proton elastic scattering cross- sections for the 39K target. do/dQ [mb/sr] H O N 0—5 C) (D 10 c.m. angle[degrees] Figure B4 T I I I I : PROTON ELASTIC SCATTERING: ~ 01‘ 35 MeV -+ ’ Becchetti - Greenlees Proton ‘ 1 Optical Model Parameters .. _. 38K[p,p,,]39K theory 0 I39K[p,p°]39l< data . E '2 I .1 l- -l t 0 )- -l 7 'l g 1 3— -l " -l l l l L 1 0 10 20 30 Lt0 '50 80 AN ”'lllll 31 lllllllllllllllsllllllllll“