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October 5, 2025Open Access

Next highest weight and other lower SU (3) irreducible representations with proxy-SU (4) symmetry for nuclei with 32 Z, N 46

Key Points

The analysis identifies lower su(3) irreps crucial for understanding triaxial shapes in specific nuclei.
Results show that nuclei within range 32 ≤ Z,N ≤ 46 exhibit both proxy-su(3) and proxy-su(4) symmetry.
A method for determining su(3) irreps is provided, aiding future investigations into nuclear shapes.
This framework supports ongoing studies into isotopes of Ge, Se, Kr, and other elements concerning their nuclear configurations.

Abstract

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 30, it is seen that one needs not only the highest weight (hw) or leading SU (3) irreducible representation (irrep) (λH, μH) but also the lower SU (3) irreps (λ, μ) such that 2λ+ μ=2λH + μH-3r with r=0, 1 and 2 Bonatsos et al. , Symmetry 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 Z, N 46, there will be not only proxy-SU (3) but also proxy-SU (4) symmetry Kota and Sahu, Physica Scripta 99, 065306 (2024). Following these developments, presented in this paper are the SU (3) irreps (λ, μ) with 2λ+ μ=2λH + μH-3r, r=0, 1, 2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 N 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.

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