Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

TL;DR

This paper reviews how attractive nucleon-nucleon interactions favor the most symmetric SU(3) irreps in nuclear models, predicting shape transitions and analyzing binding energies within a simplified SU(3)-symmetric framework.

Contribution

It demonstrates the significance of highest weight SU(3) irreps in nuclear structure and introduces their effects on shape transitions and energy calculations using a simplified Hamiltonian.

Findings

Favoring of symmetric SU(3) irreps by NN interactions

Prediction of prolate to oblate shape transition beyond mid-shell

Analysis of binding energies within proxy-SU(3) scheme

Abstract

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only the three dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.