Analytical solutions for the Bohr Hamiltonian with the Woods-Saxon potential

TL;DR

This paper derives approximate analytical solutions for the Bohr Hamiltonian using the Woods-Saxon potential, successfully modeling certain nuclear states but with limitations for others due to potential shape constraints.

Contribution

It introduces a novel analytical approach to solving the Bohr Hamiltonian with the Woods-Saxon potential, incorporating the Pekeris approximation for improved nuclear modeling.

Findings

Accurately describes ground and gamma-1 bands of prolate nuclei

Fails to model beta-1 bands due to lack of a hard core

Inadequate for gamma-unstable nuclei with small well size

Abstract

Approximate analytical solutions in closed form are obtained for the 5-dimensional Bohr Hamiltonian with the Woods-Saxon potential, taking advantage of the Pekeris approximation and the exactly soluble one-dimensional extended Woods-Saxon potential with a dip near its surface. Comparison to the data for several gamma-unstable and prolate deformed nuclei indicates that the potential can describe well the ground state and gamma-1 bands of many prolate deformed nuclei corresponding to large enough "well size" and diffuseness, while it fails in describing the beta-1 bands, due to its lack of a hard core, as well as in describing gamma-unstable nuclei, because of the small "well size" and diffuseness they exhibit.