The Variable Moment of Inertia (VMI) Model and Theories of Nuclear Collective Motion

CONTENTS FOREWORD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 1 HISTORICAL INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 1.1 Atomic hyperfine structure and nuclear quadrupole moments.. ... .. . . . . . 241 1.2 Packing fraction, the charged liquid drop, and early clues to nuclear shell structure 242 1.3 Search for rotational bands. . . . . . . . . . . . . . . . . . . . . 242 1.4 Slow neutron capture,fission, and dynamiCS of the liquid drop. . . 243 1.5 The individual particle shell-model. 243 1.6 Relation between energy and transition rate for single particle transition. 243 1.7 Odd-A quadrupole moments, enhanced E2 transitions in even-even nuclei, and rotational bands. The Bohr-MotteIson collective model alld the expan:sion of rotational energies in terms of J(J + 1) . . 244 1.8 Relation between moment of inertia and transition quadrupole moment: the hydrodynamical model leads to discrepancy .... ," ',. . ... , , . 246 1.9 First 2 + state energies in even-even nuclei: energy gap and pairing force. 246 1.10 Analogy with a superconductor: pairing-plus-quadrupole model and moment of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 1.11 First 2 + state energy treated as a scale factor: the vibrational model. . 249 1.12 "Transitional" level schemes in even-cven as nuclei and Mailmann curves. 252 1.13 Electric quadrupole moments of 2 + states in spheriCal nuclei and energies of extended ground state bands imply increase of moment of inertia with angular momentum. . . . . . . . . . . . . . . . . . 255 1.14 Beta-stretching model and self-consistent.fourth-order cranking modelfit bands ill strongly deformed nuclei. . . . . . . . . . . . . . . . . 25 7 2 THE VMI MODEL. , , , , , , , , ....... , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ... , , , , 258 2.1 An analytical expression for the Mal/mann curves in terms of an effective variable moment of inertia. . . . . . . . . . . . . . . . . . . . . . . . . . . 258