A $\gamma$-rigid solution of the Bohr Hamiltonian with deformation-dependent mass term for Kratzer potential and $\gamma = 30^\circ$

TL;DR

This paper introduces a deformation-dependent mass model for the Bohr Hamiltonian with a Kratzer potential, providing analytical solutions and improved agreement with experimental nuclear spectra for Pt isotopes.

Contribution

It develops a new Z(4)-DDM model with an analytical solution for the Kratzer potential in a gamma-rigid framework, enhancing nuclear structure predictions.

Findings

Good agreement with experimental spectra for Pt isotopes

Analytical expressions for spectra and wave functions derived

Improved accuracy over previous models

Abstract

In this work, the Davydov-Chaban Hamiltonian, describing the collective motion of $\gamma$-rigid atomic nuclei, is amended by allowing the mass parameter to depend on the nuclear deformation. Further, Z(4)-DDM (Deformation-Dependent Mass) model is proposed by considering the Kratzer potential for the $\beta$ variable, and solving the problem by techniques of asymptotic iteration method (AIM). The results of the calculated spectra and $B(E2)$ transition rates for series of $^{192-196}$Pt isotopes are compared with the corresponding experimental data as well as with other theoretical models. Exact analytical expressions are derived for spectra and normalized wave functions of the Kratzer potential. The obtained results show an overall good agreement with the experimental data and an important improvement in respect to other models