The proxy-SU(3) approximation to the shell model, which restores the SU(3) symmetry of the 3-dimensional harmonic oscillator beyond the sd shell, predicts the collective deformation variables β and γ of even–even atomic nuclei in a parameter-free way based on the most symmetric irreducible representation (irrep) of SU(3) allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interaction, which in group theoretical language is the highest-weight (hw) irrep. In the few cases in which the hw irrep turns out to be completely symmetric, thus being able to accommodate only the ground-state band, the next hw (nhw) irrep becomes indispensable. In the present article, complete tables of the hw and nhw irreps are given for all atomic nuclei ranging from Z=28, N=28 to Z=82, N=126, along with the corresponding parameter-free predictions for the deformation variables β and γ. A few examples using the tabulated results to provide microscopic insight for specific effects in various regions of the nuclear chart are also given.
Bonatsos et al. (Mon,) studied this question.