Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

TL;DR

This paper derives exact analytical solutions for the Bohr Hamiltonian with Manning-Rosen potential, applying them to model gamma-unstable and axially symmetric nuclei, achieving good agreement with experimental data.

Contribution

It provides the first closed-form analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with Manning-Rosen potential for specific nuclear shapes.

Findings

Accurate modeling of heavy nuclei with known bandheads.

Good agreement between theoretical predictions and experimental data.

Analytical solutions facilitate understanding of nuclear structure.

Abstract

In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for {\gamma}-unstable nuclei as well as exactly separable rotational ones with {\gamma}=0. Some heavy nuclei with known \b{eta} and {\gamma} bandheads have been fitted by using two parameters in the {\nu}-unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.