# Comparaison between Coulomb and Hulth\`en potentials within Bohr Hamiltonian for $\gamma$-rigid nuclei in the presence of minimal length

## TL;DR

This paper derives analytical solutions for the Schrödinger equation with Coulomb and Hulthén potentials in the Bohr Hamiltonian considering minimal length effects, and compares theoretical predictions with experimental data for γ-rigid nuclei at critical shape phase transition.

## Contribution

It introduces a novel analytical approach to solve the Bohr Hamiltonian with specific potentials under minimal length formalism, providing new insights into nuclear structure at critical points.

## Key findings

- Analytical energy eigenvalues and wave functions derived.
- Theoretical excitation energies match experimental data at X(3) critical point.
- Transition rates are calculated and compared with observations.

## Abstract

In this work we solve the Schr\"odinger equation for Bohr Hamiltonian with Coulomb and Hulth\'en potentials within the formalism of minimal length in order to obtain analytical expressions for the energy eigenvalues and eigenfunctions by means of asymptotic iteration method. The obtained formulas of the energy spectrum and wave functions, are used to calculate excitation energies and transition rates of $\gamma$-rigid nuclei and compared with the experimental data at the shape phase critical point X(3) in nuclei.