# $\gamma$-rigid triaxial nuclei in the presence of a minimal length via a quantum perturbation method

## TL;DR

This paper derives a solution to the Schrödinger equation for $eta$-rigid triaxial nuclei within a minimal length framework, using a combined AIM and QPM approach, and compares results with experimental data.

## Contribution

It introduces a novel application of minimal length formalism to the Bohr model of nuclei, solving the Schrödinger equation with a perturbation method for the first time.

## Key findings

- Theoretical results agree well with experimental data.
- The method effectively describes phase transitions in nuclei.
- Provides a new approach for modeling $eta$-rigid triaxial nuclei.

## Abstract

In this work, we derive a closed solution of the Shr$ \ddot{o} $dinger equation for Bohr Hamiltonien within the minimal length formalism. This formalism is inspired by Heisenberg algebra and a generlized uncertainty principle (GUP), applied to the geometrical collective Bohr- Mottelson model (BMM) of nuclei by means of deformed canonical commutation relation and the Pauli-Podolsky prescription. The problem is solved by means conjointly of asymptotic iteration method (AIM) and a quantum perturbation method (QPM) for transitional nuclei near the critical point symmetry Z(4) corresponding to phase transition from prolate to $\gamma$-rigid triaxial shape. A scaled Davidson potentiel is used as a restoring potential in order to get physical minimum. The agreement between the obtained theoretical results and the experimental data is very satisfactory.