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EPJ Web of Conferences

The prolate-oblate shape phase transition in the interacting boson model

Yu Zhang, J. Xu, Si-Han Li, Y. An

Published Jan 1, 2013• 2 citations
Publisher

Abstract

The prolate-oblate shape phase transition in the the interacting boson model is revisited by adopting the transitional Hamiltonian with a linear dependence on the control parameter. The analysis of the shape phase transition in both the large-N limit and finite N case shows that the O(6) symmetry is robust as the critical point symmetry of the prolate-oblate shape phase transition.

DOI
10.1051/epjconf/20136301014

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The prolate-oblate shape phase transition in the the interacting boson model is revisited by adopting the transitional Hamiltonian with a linear dependence on the control parameter. The analysis of the shape phase transition in both the large-N limit and finite N case shows that the O(6) symmetry is robust as the critical point symmetry of the prolate-oblate shape phase transition.
We examine a quantum phase transition in $\ensuremath{\gamma}$-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,ds,ds,d boson system.
Quantum phase transitional patterns in the whole parameter space of the consistent- Q Hamiltonian in the interacting boson model are studied based on an implemented Fortran code for the numerical computation of the matrix elements in the SU (3) Draayer–Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior in a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate–oblate shape phase transition.
Quantum phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model with a description based on the concept of intrinsic states. We consider the case of a single j=9/2 odd-particle coupled to an even-even boson core that performs a transition from spherical to deformed prolate and to deformed gamma-unstable shapes varying a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core is discussed along the shape transition and, in particular, at the critical point.
Quantum phase transitional patterns in the whole parameter space of the consistent-Q Hamiltonian in the Interacting Boson Model are studied based on an implemented Fortran code for numerical computation of the matrix elements in the SU (3) Draayer-Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior under a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate-oblate shape phase transition.
Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.