A solvable model which has X(5) as a limiting symmetry and removes some inherent drawbacks

TL;DR

This paper introduces a solvable nuclear shape model that extends X(5) symmetry, addressing its limitations and providing improved agreement with experimental data for certain isotopes.

Contribution

A new solvable model for nuclear shape coordinates that removes key drawbacks of X(5) and offers better data agreement, especially for gamma band energies.

Findings

Model reduces to X(5) in small gamma limit

Eigenfunctions are spheroidal and generalized Legendre polynomials

Numerical results match experimental data well

Abstract

Solvable Hamiltonians for the $\beta$ and $\gamma$ intrinsic shape coordinates are proposed. The eigenfunctions of the $\gamma$ Hamiltonian are spheroidal periodic functions, while the Hamiltonian for the $\beta$ degree of freedom involves the Davidson's potential and admits eigenfunctions which can be expressed in terms of the generalized Legendre polynomials. The proposed model goes to X(5) in the limit of $|\gamma|$-small. Some drawbacks of the X(5) model, as are the eigenfunction periodicity and the $\gamma$ Hamiltonian hermiticity, are absent in the present approach. Results of numerical applications to $^{150}$Nd, $^{154}$Gd and $^{192}$Os are in good agreement to the experimental data. Comparison with X(5) calculations suggests that the present approach provides a quantitative better description of the data. This is especially true for the excitation energies in the gamma band.