标题： 下一个最高权和其他低于$SU(3)$的不可约表示，具有代理-$SU(4)$对称性的核的$32 \le \mbox{Z,N} \le 46$ 显示英文标题

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

摘要： 在代理-SU(3)模型应用于确定周期表中核素的$(\beta,\gamma)$值以及理解具有$Z \ge 30$的核素中三轴形状的主导现象的应用中，可以看出，不仅需要最高权 (hw) 或主要$SU(3)$不可约表示 (irrep)$(\lambda_H, \mu_H)$，还需要较低的$SU(3)$不可约表示$(\lambda ,\mu)$，以便$2\lambda + \mu =2\lambda_H + \mu_H-3r$与$r=0,1$和$2$[Bonatsos 等，Symmetry{\bf 16}，1625 (2024)]。 这些给出了下一个最高权 (nhw) 不可约表示，下一个下一个最高权不可约表示 (nnhw) 以此类推。最近，研究表明对于具有$32 \le \mbox{Z,N} \le 46$的核素，不仅存在代理-$SU(3)$对称性，还存在代理-$SU(4)$对称性 [Kota 和 Sahu，Physica Scripta{\bf 99}，065306 (2024)]。 在这些发展之后，本文介绍了$SU(3)$的不可约表示$(\lambda ,\mu)$，带有$2\lambda + \mu =2\lambda_H + \mu_H-3r$，$r=0,1,2$，用于各种 Ge、Se、Kr、Sr、Zr、Mo、Ru 和 Pd 同位素（带有$32 \le \mbox{N} \le 46$），假设具有良好的代理-$SU(4)$对称性。描述了一种获得 SU(3) 不可约表示的简单方法并加以应用。本文提供的代理-$SU(3)$不可约表示的表格将有助于进一步研究这些核的三轴形状。 显示英文摘要

摘要： 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 $32 \le \mbox{Z,N} \le 46$, 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 $32 \le \mbox{N} \le 46$) 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.