Parameter-free deformation variables of the proxy-SU(3) symmetry in even-even atomic nuclei with Z=28-82, N=28-126

TL;DR

This paper presents parameter-free predictions of nuclear deformation variables beta and gamma using the proxy-SU(3) symmetry, providing comprehensive tables of irreps for nuclei with Z=28-82 and N=28-126.

Contribution

It introduces complete tables of highest weight and next highest weight irreps for a wide range of nuclei, enabling parameter-free deformation predictions based on group theory.

Findings

Predicted deformation variables beta and gamma for all nuclei in the specified range.

Provided comprehensive tables of irreps for nuclei Z=28-82, N=28-126.

Demonstrated the use of these tables for microscopic insights into nuclear structure.

Abstract

The proxy-SU(3) approximation to the shell model, which restores the SU(3) symmetry of the 3-dimensional harmonic oscillator beyond the sd shell, predicts the collective deformation variables beta and gamma of even-even atomic nuclei in a parameter-free way, based on the most symmetric irreducible representation (irrep) of SU(3) allowed by the Pauli principle and the short-range nature of the nucleon-nucleon interaction, which in group theoretical language is the highest weight (hw) irrep. In the few cases in which the hw irrep turns out to be completely symmetric, thus being able to accommodate only the ground state band, the next hw (nhw) irrep becomes indispensable. In the present article complete tables of the hw and nhw irreps are given for all atomic nuclei ranging from Z=28, N=28 to Z=82, N=126, along with the corresponding parameter-free predictions for the deformation variables beta and gamma. A few examples using the tabulated results for providing microscopic insight for specific effects in various regions of the nuclear chart are also given.