Collective motion in prolate {\gamma}-rigid nuclei within minimal length concept via a quantum perturbation method

TL;DR

This paper develops an analytical model for nuclear collective motion using minimal length quantum concepts and a perturbation approach, providing a flexible framework to describe vibrational nuclei with new insights into parameter bounds.

Contribution

It introduces a novel analytical solution for prolate gamma-rigid nuclei incorporating minimal length effects via a quantum perturbation method with a scaled Davidson potential.

Findings

The minimal length parameter has a physical upper bound.

The model accurately describes ground and beta bands of nuclei.

Scaling parameters improve the potential's physical relevance.

Abstract

Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate {\gamma}-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method (QPM), by considering a scaled Davidson potential in \b{eta} shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first \b{eta}-band are all studied as a function of the free parameters. The fact of introducing the minimal length concept with a QPM makes the model very flexible and a powerful approach to describe nuclear collective excitations of a variety of vibrational-like nuclei. The introduction of scaling parameters in the Davidson potential enables us to get a physical minimum of this latter in comparison with previous works. The analysis of the corrected wave function, as well as the probability density distribution, shows that the minimal length parameter has a physical upper bound limit.