Evolution of shape phase transitions as functions of energy, spin, and boson number in the Interacting Boson Model

Shape phase transitions from spherical to deformed nuclei have been a subject of recent interest because explorations of such behavior have led to a greater understanding of the evolution of collectivity throughout the nuclear landscape. Two critical points in particular, X(5), a first order phase transition, and E (5), a second order phase transition, were identified in the geometrical model. Recent work within the context of the Interacting Boson Model (IBM) has explored these regions in the finite N limit corresponding to realistic nuclei. IBM calculations extending to large boson numbers provide powerful tools for relating transitional behavior observed in nuclei to phase transitions in macroscopic systems. A study of first and second order phase transitions in the large boson limit as functions of N, spin, and energy has been undertaken with the use of a variety of observables, including both electromagnetic transitions, and energies. The results of this investigation will be presented. Work supported by US DOE grant number DE-FG02- 91ER-40609.