Quadrupole properties of the eight $SU(3)$ algebras in $(sdgi)$ space

TL;DR

This paper analyzes the quadrupole properties of eight $SU(3)$ algebras in $(sdgi)$ space, revealing shape preferences and differences in quadrupole moments using algebraic, shell, and deformed shell models.

Contribution

It provides a detailed comparison of quadrupole properties across eight $SU(3)$ algebras in $(sdgi)$ space using multiple modeling approaches.

Findings

Six $SU(3)$ algebras generate prolate shapes.

Two $SU(3)$ algebras generate oblate shapes.

One algebra produces small quadrupole moments.

Abstract

With nucleons occupying an oscillator shell $\eta$, there are $2^{\eta/2}$ number of $SU(3)$ algebras; $\eta/2$ is the integer part of $\eta/2$. Analyzing the first non trivial situation with four $SU(3)$ algebras in $(sdg)$ space, demonstrated recently is that they generate quite different quadrupole properties though they all generate the same spectrum. More complex situation is with eight $SU(3)$ algebras in $(sdgi)$ space. In the present work, quadrupole properties generated by these eight algebras are analyzed first using the more analytically tractable interacting boson model. In addition, shell model and the closely related deformed shell model are used with three examples of nucleons in $sdgi$ space. It is found that in general six of the $SU(3)$ algebras generate prolate shape and two oblate shape. Out of all these, one of the $SU(3)$ algebra generates quite small quadrupole moments for the low-lying states.