Review of critical point symmetries and shape phasetransitions within algebraic and collective models

Abstract

Several aspect of shape phase transitions and critical point symmstries are reviewed inthis contribution within the frameworks of the Interacting Boson Model(IBM) and theInteracting Boson Fermion Model(IBFM) for even and odd sysstems respectively andcompared with collective geometric models. We discuss in particular the case of an oddj= 3/2 particle coupled to an even-even boson core that undergoes a transition from thespherical limitU(5) to theγ-unstable limitO(6). The spectrum and transition rates atthe critical point are similar to those of the even core and they agree qualitatively with theE(5/4) boson-fermion symmetry. We discuss also theUBF(5) toSUBF(3) shape phasetransition in which the allowed fermionic orbitals arej= 1/2,3/2,5/2. The formalismof the intrinsic or coherent states is used to describe in details the ground state as wellas the excitedβ−andγ−bands. This formalism is also used to calculate the PotentialEnergy Surface of the cubic quadrupole operator that leads to traixiali