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 β shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first β-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.

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

“…Here, we recall that, within the ML formalism, the collective quadrupole Hamiltonian of Bohr-Mottelson has the following form [20,48,49] :…”

“…which is a valid approximation owing to the smallness of the parameter α. However the above differential equation was solved exactly with an infinite square well like potential within the standard method [20], and approximately with a scaling Davidson potential [48] by means conjointly of Asymptotic Iteration Method (AIM) [51] and a quantum perturbation method. Also the Coulomb and Hulthen potentials were also studied [49] in this context.…”

“…Correction to the energy spectrum of system by QPM Before the treatment of perturbation term, it is important to mention that Eq. ( 19) was previously solved for an ISWP [20], Davidson potential (D) [48], Hulthèn and Coulomb potentials [49]. All these potentials are presented in Table 1 in order to be compared with our model.…”

“…As the energy levels in quantum mechanical problems, the wave function is an important mathematical object. So, by using the same method, the corrected wave function in first-order approximation can be calculated by [48]:…”

“…In the same context, the probability density distribution can be also evaluated via the following formula [48] :…”