Conjunction of $\gamma$-rigid and $\gamma$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes

TL;DR

This paper introduces a two-parameter model combining gamma-rigid and gamma-stable motions in nuclei, bridging the X(5) and X(3) models, and explores their effects on nuclear energy spectra and wave functions.

Contribution

A novel exactly separable Bohr Hamiltonian model that interpolates between gamma-stable and gamma-rigid nuclear shapes using two parameters.

Findings

Model recovers X(5) in the lower limit of parameters.

Model tends to X(3) in the upper limit of parameters.

Numerical results for selected nuclei demonstrate the model's ambiguous behavior.

Abstract

Based on the competition between $\gamma$-stable and $\gamma$-rigid collective motions mediated by a rigidity parameter, a two-parameter exactly separable version of the Bohr Hamiltonian is proposed. The $\gamma$-stable part of the Hamiltonian is restricted to stiff oscillations around the $\gamma$ value of the rigid motion. The separated potential for $\beta$ and $\gamma$ shape variables is chosen such that in the lower limit of this parameter, the model recovers exactly the ES-$X(5)$ model, while in the upper limit it tends to the prolate $\gamma$-rigid solution $X(3)$. The combined effect of the rigidity and stiffness parameters on the energy spectrum and wave function is duly investigated. Numerical results are given for few nuclei showing such ambiguous behaviour.