V.K.B. Kota
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 {\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≤\mboxZ,N≤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=2λH+μH−3r, r=0,1,2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32≤\mboxN≤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.
nucl-th1 citation