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

Abstract

The consequences of the attractive, shortrange 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.

Resolution of the spin paradox in the Nilsson model

“…The use of asymptotic quantum numbers for deformed nuclei is just an example of choosing a basis as close as possible to the dynamics of the physical system under study [32,33]. It should be noted that the Nilsson model is still in wide use, 65 years after its introduction [11], either in the framework of Nilsson mean-field plus pairing calculations [34,35], cranking shell model calculations based on the Nilsson potential with pairing correlations [36], or in relation to approximate SU(3) symmetries [37] like the pseudo-SU(3) symmetry [38][39][40][41][42][43][44][45][46][47], the quasi-SU(3) symmetry [48,49], the proxy-SU(3) symmetry [50][51][52][53][54][55][56][57], and the recovery of SU(3) symmetry at superdeformation [58].…”