Collective states of even-even nuclei in gamma-rigid quadrupole Hamiltonian with Minimal Length under the sextic potential

TL;DR

This paper develops a novel model combining sextic potential and Minimal Length formalism within the Bohr Mottelson framework to better describe collective states of even-even nuclei, achieving improved agreement with experimental data.

Contribution

It introduces a new approach integrating sextic potential with Minimal Length formalism to enhance nuclear structure predictions.

Findings

Improved agreement with experimental energy levels, reducing rms errors by up to 63%.

Demonstrated the impact of Minimal Length on energy ratios and transition rates.

Analyzed shape phase transitions in key isotopic chains.

Abstract

In the present paper, we study the collective states of even even nuclei in gamma rigid mode within the sextic potential and the Minimal Length (ML) formalism in Bohr Mottelson model. The eigenvalues problem for this latter is solved by means conjointly of Quasi-Exact Solvability (QES) and a Quantum Perturbation Method (QPM). Numerical calculations are performed for 35 nuclei:(98 108)Ru, (100 102)Mo, (116 130)Xe, (180 196)Pt, (172)Os, (146 150)Nd, (132 134)Ce, (154)Gd, (156)Dy and (150 152)Sm. Through this study, it appears that our elaborated model leads to an improved agreement of the theoretical results with the corresponding experimental data by reducing the rms with a rate going up to 63% for some nuclei. This comes out from the fact that we have combined the sextic potential, which is a very useful phenomenological potential, with the formalism of the ML which is based on the generalized uncertainty principle and which is in turn a quantum concept widely used in quantum physics. Besides, we investigate the effect of ML on energy ratios, transition rates, moments of inertia and a shape phase transition for the most numerous isotopic chains, namely Ru, Xe, Nd and Pt.