Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32 \le \mbox{Z,N} \le 46$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908571818524672 |
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| author | Kota, V. K. B. |
| author_facet | Kota, V. K. B. |
| contents | In the applications of proxy-SU(3) model in the context of determining $(β,γ)$ 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) $(λ_H, μ_H)$ but also the lower $SU(3)$ irreps $(λ,μ)$ such that $2λ+ μ=2λ_H + μ_H-3r$ 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 $(λ,μ)$ with $2λ+ μ=2λ_H + μ_H-3r$, $r=0,1,2$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32 \le \mbox{Z,N} \le 46$ Kota, V. K. B. Nuclear Theory In the applications of proxy-SU(3) model in the context of determining $(β,γ)$ 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) $(λ_H, μ_H)$ but also the lower $SU(3)$ irreps $(λ,μ)$ such that $2λ+ μ=2λ_H + μ_H-3r$ 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 $(λ,μ)$ with $2λ+ μ=2λ_H + μ_H-3r$, $r=0,1,2$ 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. |
| title | Next highest weight and other lower $SU(3)$ irreducible representations with proxy-$SU(4)$ symmetry for nuclei with $32 \le \mbox{Z,N} \le 46$ |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2510.00800 |