Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

Abstract

The quantum phase transition studies we have done during the last few years for odd-even systems are reviewed. The focus is on the quantum shape phase transition in Bose-Fermi systems. They are studied within the Interacting Boson-Fermion Model (IBFM). The geometry is included in this model by using the intrinsic frame formalism based on the concept of coherent states. First, the critical point symmetries E(5/4) and E(5/12) are summarized. E(5/4) describes the case of a single j=3/2 particle coupled to a bosonic core that undergoes a transition from spherical to γ-unstable. E(5/12) is an extension of E(5/4) that describes the multi-j case (j=1/2,3/2,5/2) along the same transitional path. Both, E(5/4) and E(5/12), are formulated in a geometrical context using the Bohr Hamiltonian. Similar situations can be studied within the IBFM considering the transitional path from UBF(5) to OBF(6). Such studies are also presented. No critical points have been proposed for other paths in odd-even systems as, for instance, the transition from spherical to axially deformed shapes. However, the study of such shape phase transition can be done easily within the IBFM considering the path from UBF(5) (spherical) to SUBF(3) (axial deformed). Thus, in a second part, this study is presented for the multi-j case. Energy levels and potential energy surfaces obtained within the intrinsic frame formalism of the IBFM Hamiltonian are discussed. Finally, our recent works within the IBFM for a single-j fermion coupled to a bosonic core that performs different shape phase transitional paths are reviewed. All significant paths in the model space are studied: from spherical to γ-unstable shape, from spherical to axially deformed (prolate and oblate) shapes, and from prolate to oblate shape passing through the γ-unstable shape. The aim of these applications is to understand the effect of the coupled fermion on the core when moving along a given transitional path and how the coupled fermion modifies the bosonic core around the critical points.

Quantum phase transitions in algebraic and collective models of nuclear structure

“…Other candidates as examples of the critical point symmetries in odd nuclei are 129 Xe (by Harissopulos, see discussion in Ref. [85]), the Ir-Au region, where the U(6/4) supersymmetry shows up, and 63 Cu.…”

“…Some of the topics of this section have recently been covered in Ref. [129], therefore material will be drawn from that source. Previously, this topic has been reviewed by Petrellis and coauthors [130].…”

“…Arias for our long-standing collaboration on the topics of this review paper and I'd like to thank M. Böyükata for having recently taken care of Ref. [129] and for the preparation of several figures for our works, that have been included in the present article. I also thank Gagandeep Singh for helping with the task of proofreading.…”

The Rotor-Vibrator Plus Multi-Particle-Hole Description of 154Gd

“…As is well known, both the collective model and the interacting boson model (IBM) are very successful in describing spectroscopy of medium and heavy mass nuclei in low-energy regime [1,2]. Shape phase evolution in these nuclei has also been extensively studied [3][4][5][6][7][8]. Shell model description of deformed nuclei has also been studied extensively [9][10][11] based on the pseudo SU(3) model [12][13][14].…”