Shape Phase Transitions in Geometrical and Algebraic Nuclear Collective Models

Abstract

Phase transitions in finite systems sound Greek to many and κινζικα (Chinese) to Greeks. In fact, evidence for phase transitions as function of nucleon number has been lurking for over 30 years, when early measurements of two nucleon transfer cross-sections and isotope shifts in Sm and Gd nuclei [1] gave clear evidence of dramatic changes in the shape of nuclei across an isotopic chain. Later theoretical investigations [2] within the framework of the interacting boson approximation (IBA) model [3] found that the transition from spherical to deformed shapes exhibits features of a first- or second-order phase transition, depending on the trajectory taken within the parameter space. These are quantum phase transitions (QPT) in the equilibrium shape of nuclei [4], occurring at zero temperature. Over the past several years, the idea of QPT has found a renewed interest, stemming from the development of critical point symmetries (CPS) [5,6], which provide very simple descriptions of behavior at the critical point of QPT, and the discovery of their empirical realizations [7,8].