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

TL;DR

This paper develops an analytical model for deformed nuclei using a Bohr Hamiltonian with a deformation-dependent mass, applying SUSYQM techniques to improve spectral predictions and match experimental data.

Contribution

It introduces the Deformation Dependent Mass (DDM) Davidson model, incorporating deformation-dependent mass into the Bohr Hamiltonian using SUSYQM, enhancing the description of nuclear spectra.

Findings

The model accurately reproduces experimental spectra.

Deformation-dependent mass reduces the overestimation of moment of inertia.

The approach improves transition rate predictions.

Abstract

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the beta variable, in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the Deformation Dependent Mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. 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, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.