Shape phase transitions in algebraic nuclear models

Abstract

A review of the shape phase transitions within the IBA, is presented. This nuclear model depends on two control parameters, (r(2), r(1)), and two order parameters, (beta, gamma). In the control parameter space, the accesible shapes and stability properties of the Consistent-Q nuclear model are established. The procedure of coherent states plus catastrophe formalisms to determine the shape phase diagram of an algebraic nuclear model is illustrated by considering the Meshkov-Glick-Lipkin nuclear model. The relevance of the separatrix to organize the classical orbits and the structure of the quantum energy levels is established.