Nuclear Shape Transition Between Spherical U(5) and γ-Unstable O(6) Limits of the Interacting Boson Model

Abstract

The interacting boson model (IBM) with intrinsic coherent state (characterized by and ) is used to describe the nuclear second order shape phase transition (denoted E(5)) between the spherical oscillator U(5) and the -soft rotor O(6) structural limits. The potential energy surfaces (PES's) have been derived and the critical points of the phase transition have been determined . The model is examined for the spectra of even-even neutron rich xenon isotopic chain. The best adopted parameters in the IBM Hamiltonian for each nucleus have been adjusted to reproduce as closely as possible the experimental selected numbers of excitation energies of the yrast band, by using computer simulated search program.Using the best fitted parameters , the energy ratios for the  levels are calculated and compared to those of the O(6) and U(5) dynamical symmetry limits.¹²²Xe and ¹³²Xe are considered as examples for the two O(6) and U(5) dynamical symmetry limits