Collective states of even–even nuclei in γ-rigid quadrupole Hamiltonian with minimal length under the sextic potential

Abstract

In the present paper, we study the collective states of even–even nuclei in γ-rigid mode within the sextic potential and the minimal length (ML) formalism in Bohr–Mottelson model. The eigenvalues problem for the latter is solved by combined means of quasi-exact solvability and a quantum perturbation method. Numerical calculations are performed for 35 nuclei: 98−108Ru, 100−102Mo, 116−130Xe, 180−196Pt, 172Os, 146−150Nd, 132−134Ce, 154Gd, 156Dy and 150−152Sm. 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 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. In addition, 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.