Various aspects of the Deformation Dependent Mass model of nuclear structure

TL;DR

This paper explores a deformation-dependent mass model in nuclear physics, providing new analytical solutions and addressing the moment of inertia issue in the Bohr Hamiltonian, with applications to shape/phase transitional nuclei.

Contribution

It introduces a novel deformation-dependent mass model with analytical solutions and applies it to describe nuclei at shape/phase transitions.

Findings

The DDM model yields moments of inertia that grow slower than in the traditional model.

Analytical solutions are obtained using supersymmetric quantum mechanics techniques.

The model effectively describes nuclei at critical shape/phase transition points.

Abstract

Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the Kratzer potentials, by employing techniques from supersymmetric quantum mechanics. Apart from the new set of analytic solutions, the newly introduced Deformation-Dependent Mass (DDM) model offered a remedy to the problematic behaviour of the moment of inertia in the Bohr Hamiltonian, where it appears to increase proportionally to the square of beta. In the DDM model the moments of inertia increase at a much lower rate, in agreement with experimental data. The current work presents an application of the DDM-model suitable for the description of nuclei at the point of shape/phase transitions between vibrational and gamma-unstable or prolate deformed nuclei and is based on a method that was successfully applied before in the context of critical point symmetries.