Shell model structure of proxy-SU(3) pairs of orbitals

TL;DR

This paper demonstrates that Nilsson orbitals used in the proxy-SU(3) scheme have a simple, shell-model basis structure at all deformations, facilitating the integration of proxy-SU(3) into the shell model framework.

Contribution

It reveals the shell model basis structure of Nilsson orbitals in proxy-SU(3), enabling their use within the shell model approach.

Findings

Nilsson orbitals correspond to single shell model eigenvectors.

The simple structure holds at all deformations for these orbitals.

Nilsson 0[110] pairs match specific shell model pairs.

Abstract

The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis |N l j Omega>, with each Nilsson orbital corresponding to a single shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to |1 1 1 0> pairs in the spherical shell model basis, paving the way for using the proxy-SU(3) approximation within the shell model.