Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

Abstract

Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate γ-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.

arXiv comment17p, 9 figs, 2 tables (accepted for publication in Annals of Physics)

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Cited by in corpus (4)

• Collective states of even-even nuclei in gamma-rigid quadrupole Hamiltonian with Minimal Length under the sextic potential
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• Probing DDM and ML quantum concepts in shape phase transitions of $\gamma$-unstable nuclei
• Coriolis contribution to excited states of odd-mass nuclei with different deformation-dependent mass coeffcients