Connecting the proxy-SU(3) symmetry to the shell model

TL;DR

This paper establishes a rigorous connection between the proxy-SU(3) symmetry approximation and the spherical shell model, demonstrating that proxy-SU(3) effectively replaces intruder orbitals with their partners, thus enabling its use in shell model calculations.

Contribution

The paper provides a formal mapping between proxy-SU(3) symmetry and the shell model, validating the approximation through basis transformation and orbital replacement.

Findings

Proved the mapping of Elliott SU(3) basis onto the shell model basis.

Showed proxy-SU(3) corresponds to replacing intruder orbitals with de Shalit-Goldhaber partners.

Confirmed the connection within the Nilsson model framework.

Abstract

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, proving that the proxy-SU(3) approximation corresponds to the replacement of the intruder orbitals by their de Shalit-Goldhaber partners, paving the way for using the proxy-SU(3) approximation in shell model calculations. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.