Collective motion in triaxial nuclei within minimal length concept

TL;DR

This paper explores how the minimal length concept influences the collective motion in triaxial nuclei, deriving a modified Hamiltonian and analyzing its effects on energy levels, with applications to specific nuclei and comparison to experimental data.

Contribution

It introduces a minimal length-modified Hamiltonian for triaxial nuclei within the Bohr model and identifies new quasi-dynamical critical point symmetries in nuclear structure.

Findings

Minimal length has a low effect on energy levels at low angular momentum.

Significant effects of minimal length appear at higher angular momentum.

Numerical results for specific nuclei show qualitative agreement with experimental data.

Abstract

The concept of minimal length, inspired by Heisenberg algebra, is applied to the geometrical collective Bohr- Mottelson model (BMM) of nuclei. With the deformed canonical commutation relation and the Pauli-Podolsky prescription, we have derived the quantized Hamiltonian operator for triaxial nuclei as we have previously done for axial prolate $\gamma$-rigid ones (M. Chabab et al., Phys. Lett. B 758 (2016) 212-218). By considering an infinite square well like potential in $\beta$ collective shape variable, the eigenvalues of the Hamiltonian are obtained in terms of zeros of Bessel functions of irrational order with an explicit dependence on the minimal length parameter. Moreover, the associated symmetry with the model that we have constructed here can be considered as a new quasi-dynamical critical point symmetries (CPSs) in nuclear structure. The theoretical results indicate a dramatic contribution (Low effect) of the minimal length to energy levels for lower values of the angular momentum and regular (significant effect) for higher values. In fact, these features show that the minimal length scenario which is useful in recognizing the properties of real deformed nuclei having high spins or strong rotations. Finally, numerical calculations are performed for some nuclei such as ${}^{124,128,130}$Xe and ${}^{114}$Pd revealing a qualitative agreement with the experimental data.