Robustness of the proxy-SU(3) symmetry in atomic nuclei and the role of the next highest weight irreducible representation

Abstract

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables beta and gamma in even-even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the most symmetric irreps allowed by the Pauli principle and the short-range nature of the nucleon-nucleon interactions. The special cases in which the use of the next highest weight irrep of SU(3) becomes necessary are pointed out and numerical results are given for several regions of the nuclear chart, which can be used as input for irrep-mixing calculations.