Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry

TL;DR

The paper investigates how the attractive short-range nucleon-nucleon interaction influences the preference for highest weight irreducible representations in fermionic SU(3) symmetry, impacting nuclear shape predictions.

Contribution

It demonstrates that the NN interaction favors the most symmetric SU(3) irreps, leading to new insights on nuclear shape transitions and symmetry properties.

Findings

Highest weight irreps are most favored by NN interactions.

No SU(3) irrep is more symmetric than the highest weight irrep.

Predicts prolate to oblate shape transition beyond mid-shell.

Abstract

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3) symmetry are discussed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation, which corresponds to the maximal spatial overlap among the fermions. The percentage of the symmetric components out of the total in an SU(3) wave function is introduced, through which it is found, that no SU(3) irrep is more symmetric than the highest weight irrep for a certain number of valence particles in a three dimensional, isotropic, harmonic oscillator shell. The consideration of the highest weight irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region.