Bohr Hamiltonian with deformation-dependent mass term for the Kratzer potential

TL;DR

This paper develops a deformation-dependent mass model within the Bohr Hamiltonian framework using the Kratzer potential, deriving analytical spectra and transition rates, and comparing them with experimental data to improve nuclear structure descriptions.

Contribution

It introduces a novel deformation-dependent mass term in the Bohr Hamiltonian with the Kratzer potential, solved via SUSYQM, enhancing the model's physical realism.

Findings

Mass dependence moderates moment of inertia increase

Analytical spectra and wave functions derived

Model shows good agreement with experimental data

Abstract

The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Analytical expressions for spectra and wave functions are derived for separable potentials in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, moderates the increase of the moment of inertia with deformation, removing a main drawback of the model.