Bohr Hamiltonian with an energy dependent $\gamma$-unstable Coulomb-like potential

TL;DR

This paper presents an exact analytical solution to the Bohr Hamiltonian with an energy-dependent Coulomb-like potential, revealing spectral similarities to vibrational nuclei and potential links to shape coexistence in certain nuclei.

Contribution

It introduces a novel energy-dependent Coulomb-like potential within the Bohr Hamiltonian and derives closed-form solutions, connecting theoretical predictions with experimental nuclear shape phenomena.

Findings

Spectrum resembles spherical vibrator with different degeneracy

Closed-form energy levels and transition rates are obtained

Model wave functions suggest shape coexistence phenomena

Abstract

An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in the asymptotic limit of the slope parameter resembles the spectral structure of the spherical vibrator, however with a different state degeneracy. The parameter free energy spectrum as well as the transition rates for this case are given in closed form and duly compared with those of the harmonic $U(5)$ dynamical symmetry. The model wave functions are found to exhibit properties that can be associated to shape coexistence. A possible experimental realization of the model is found in few medium nuclei with a very low second $0^{+}$ state known to exhibit competing prolate, oblate and spherical shapes.