Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32\le \text{mbox}Z,N\le 46$

Abstract

In the applications of proxy-SU(3) model in the context of determining $(\beta ,\gamma )$ values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with $Z\ge 30$, it is seen that one needs not only the highest weight (hw) or leading $SU(3)$ irreducible representation (irrep) $({\lambda }_H,{\mu }_H)$ but also the lower $SU(3)$ irreps $(\lambda ,\mu )$ such that $2\lambda +\mu =2{\lambda }_H+{\mu }_H-3r$ with $r=0,1$ and $2$ [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with $32\le \text{mbox}Z,N\le 46$, there will be not only proxy-$SU(3)$ but also proxy-$SU(4)$ symmetry [Kota and Sahu, Physica Scripta {\bf 99}, 065306 (2024)]. Following these developments, presented in this paper are the $SU(3)$ irreps $(\lambda ,\mu )$ with $2\lambda +\mu =2{\lambda }_H+{\mu }_H-3r$, $r=0,1,2$ for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with $32\le \text{mbox}N\le 46$) assuming good proxy-$SU(4)$ symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-$SU(3)$ irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.

Comments: 24 pages, 10 tables