COLLECTIVE NUCLEAR STRUCTURE STUDIES IN THE OSMIUM NUCLEI by Richard F. Casten B. S. , College of the Holy Cross, 1963 M. S. , Yale University , 1964 A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy 1967 T o m y father, m y mother, and to Jo-Ann ABSTRACT Collective nuclear structure studies on the four even-even isotopes of o^gaiuxn, Os'®8 . 188, 190, 192 have been pursued using Co u l o m b excitation induced by O ions with incident energies between 42 and 80 M e V obtained from the Yale M P T a n d e m V a n de Graaff accelerator. The o s m i u m isotopes span the important transition region from highly deformed to nearly spherical nuclei located at the high mass extremity of the rare earth region of collectivity and they have therefore long been the center of mu c h theoretical and experimental interest. The deexcitation radiation has been observed singly, in coincidence with o'6 ions backscattered from the target, and in coincidence with other y-rays representing the 2+ -* 0+ and 4+ -* 2+ transitions in each isotope. In Os'®8 ’ '®®> '®8 all levels through the 6+ state of the ground state rotational band as well as the 2+I and 4 ' levels of the so-called y-vibrational band have been excited. In Os'®® an additional 0+ level at 1086 kev w a s observed while in Os'®^ all kn o w n states except the unnatural parity 3+ level were detected. Furthermore, in Os'®®, Os'®®, and Os'®^ ne w states at 780, 840, and 855 kev, respectively, are tentatively proposed with J71-assignments of 2+ or 3~ ascribed as likely and not inconsistent with any of our measurements. The m ain emphasis has been on the extraction of absolute reduced transition probabilities (B(E2) values). These have been obtained, for the excitation of all states previously known, by both model-dependent and model-independent analyses. The results have been compared with several macroscopic and microscopic nuclear models, with particular attention to that of Ku m a r and Baranger. The latter has proved the most complete and successful of any in predicting both absolute B(E2) values and the variations of these with neutron nu m b e r in the o s m i u m isotopes. The trend toward the spherical or vibrational limit in Os'®2 is calculated to be somewhat sharper than is observed experimentally. Suggestions are made for possible improvements in the pairing-plus-quadrupole model of these authors. A n interpretation of the o s m i u m isotopes as typified by shallow potential m i n i m a for moderately prolate deformations (and slightly axially asymmetric equilibrium configurations in Os'®®> '®^) and by extreme softness to vibrations in both /3 and y em e r g e s from this comparison and is actually confirmed by both the successes and failures of the other models with which comparisons are made. Discussion is also m a d e of the possible existence and implications of finite excited state quadrupole moments predicted in osmium by Ku m a r and Baranger and in other spherical nuclei by other authors. Finally, suggestions for future experimental tests of the theoretical calculations in this transition region are offered. ACKNOWLEDGEMENTS It is a great pleasure to acknowledge m y appreciation to Dr. J. S. Greenberg and to Prof. D. A. B r o m l e y wh o supervised the research performed here. I would like to thank Dr. Greenberg for his advice and participation in all phases of this work and for the guidance in the data analysis provided by his probing questions and suggestions. I a m very deeply indebted to Prof. B r o m l e y not only for making available the facilities of the A. W . Wright Nuclear Structure Laboratory of Yale University but also especially for numerous invaluable discussions concerning this work and for his generous support and counsel in so many matters. I a m indebted to Dr. K. K u m a r for discussions concerning his calculations and for communication of certain results of those calculations prior to their publication. I a m grateful to Dr. G. A. Burginyon for his extensive cooperation and advice in the collection and analysis of the data presented herein, for his help with the c o m ­ puter pr o g r a m s and for innumerable discussions concerning ma n y facets of this work. Thanks are also extended to S. Sie for help in the later phases of data acquisition. I would like to thank the entire faculty of the Nuclear Structure Laboratory, as well as m y fellow graduate students there, for the m a n y interesting discussions dealing with all aspects of nuclear physics. I would also like to express m y appreciation to the entire operating and support staffs of the accelerator for their continual assistance and ready cooperation during the course of these measurements and during the preparation of this final manuscript. I would like to thank m y wife, Jo-Ann, for her constant encouragement and, in particular, for typing the various drafts and the final manuscript of this thesis. N o aspect of this work would have been even remotely possible were it not for the singularly unfailing lifelong support, encouragement, guidance and stim­ ulation of m y father to w h o m I can in no wa y express sufficient gratitude and appreciation. T h e inspiration and example he has provided will never be forgotten. I a m indebted to the Danforth Foundation for its abiding interest in all aspects of m y graduate education and for its grants which supported that education in particularly tangible fashion. Finally, I would like to thank the United States Atomic Energy Co m m i s s i o n for financial support of this research. TABLE OF CONTENTS ABSTRACT ACKNOWLEDGEMENTS ORIENTATION ....................................................... I THEORETICAL CONSIDERATIONS ..................................... 5 A. Macroscopic Models .............................................. 5 B. Microscopic M odels............................................... 14 C. Coulomb Excitation Theory......................................... 29 EXPERIMENTAL CONSIDERATIONS ................................... 40 A. Methods of Me a s u r e m e n t ........................................... 40 B. Accelerator...................................................... 43 C . Scattering Chamber and Particle and G a m m a Ray Detection Apparatus.................................... 45 D. Targets........................................................... 48 E. Electronics....................................................... 50 DATA PRESENTATION AND DECAY SCHEMES ......................... 52 A. Orientation....................................................... 52 B. O s 186............................................................. 55 C. O s 188............................... * ............................ 58 D. O s 19°............................................................. 62 E. O s 192............................................................. 64 DATA ANALYSIS ..................................................... 66 A. Data Reduction.................................................... 66 B. Extraction of Nuclear Information.................................. 75 C. Perturbation Theory Analysis...................................... 79 D. Model Dependent Calculations...................................... 82 E. Complete Calculation via the Coupled Schrodinger Equations..................................... 84 F. Err o r s ........................................................... .86 PRESENTATION AND INTERPRETATION OF EXPERIMENTAL RESULTS. 88 VII. SUMMARY AND SUGGESTIONS ............................................ 112 VUI. APPENDICES ...................................... 119 Appendix 1................................................................ 119 Appendix II............................................................... 125 IX. REFERENCES ........................................................... 139 I. ORIENTATION There is as yet no exact mathematical technique for the complete calcu­ lation of the properties of a many-body quantum mechanical system. Except for its lightest representatives, the atomic nucleus in general constitutes such a system. In addition, even if such a mathematical apparatus were available, the nuclear (or nucleon-nucleon) force is only very imperfectly known. In order to m a k e progress in the elucidation of nuclear structure one must therefore m a k e certain mathematical and physical assumptions and approximations. The recent history of nuclear structure physics has consisted largely of a succession of such nuclear models and has been characterized by a steadily improving accord between them and the experimental facts which encourage and test them. Broadly speaking, there are two striking features revealed by the data of nuclear physics: the nearly independent motion of the nucleons in the nucleus and the strong correlations a m o n g the motions of ma n y nucleons resulting in apparently collective behaviour. These two seemingly contradictory aspects have given rise to two general models of nuclear structure, the shell model and the collective model. Both of these, of course, have m a n y variants. The earliest collective models were "phenomenological" in that they pos­ tulated, without derivation, that the nucleus possessed certain gross properties implied by the data. Thus, for example, in order to explain certain features of the data recognizable as similar to those of a rotating symmetric, quantum m e ­ chanical top, the nucleus was consequently assumed to be deformed and to rotate. No accounting