Approximate Solution of Bohr-Mottelson Hamiltonian with Minimal Length Effect for Hulthen Potential Using Asymptotic Iteration Method

TL;DR

This paper presents an approximate analytical solution to the Bohr-Mottelson Hamiltonian with minimal length effects for the Hulthen potential, using the Asymptotic Iteration Method, revealing how the energy spectrum varies with parameters.

Contribution

It introduces a novel application of the Asymptotic Iteration Method to solve the Bohr-Mottelson Hamiltonian with minimal length effects for the Hulthen potential.

Findings

Energy spectrum increases with minimal length parameter.

Energy spectrum increases with the range of the potential.

Wave functions are expressed in hypergeometric form.

Abstract

The approximate solution of Bohr-Mottelson Hamiltonian in rigid deformed nucleus case for Hulthen potential with minimal length effect was investigated using Asymptotic Iteration Method. Asymptotic Iteration Method was used to solve approximately the Bohr-Mottelson Hamiltonian to obtain energy spectrum and un-normalized wave function. The energy spectrum was calculated numerically using the Matlab software. The un-normalized wave function was expressed in the hypergeometric term. The results showed that the energy spectrum increased due to the increasing minimal length parameter. The energy spectrum also increased by the increasing range of potential.