New analytic solutions of the collective Bohr Hamiltonian for a β-soft, γ-soft axial rotor

Abstract

New analytic solutions of the quadrupole collective Bohr Hamiltonian are proposed, exploiting an approximate separation of the β and γ variables to describe γ-soft prolate axial rotors. The model potential is a sum of two terms: a β-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a γ-dependent term taken as a harmonic oscillator. In particular, it is possible to give a one-parameter paradigm for a β-soft, γ-soft axial rotor that can be applied, with considerable agreement, to the spectrum of 234U.