Connection between Elliott SU(3) and spherical shell model bases

TL;DR

This paper establishes a transformation linking the Elliott SU(3) basis, derived from the harmonic oscillator in Cartesian coordinates, with the spherical shell model basis, facilitating the inclusion of spin-orbit coupling.

Contribution

It provides a clear method to connect Elliott SU(3) states with spherical shell model states, enhancing the understanding of nuclear structure models.

Findings

Derived transformation between Elliott SU(3) and spherical shell model bases.

Simplified inclusion of spin-orbit coupling in nuclear models.

Clarified the relationship between different nuclear basis representations.

Abstract

In the Elliott SU(3) symmetry scheme the single particle basis is derived from the isotropic harmonic oscillator Hamiltonian in the Cartesian coordinate system. These states are transformed into the solutions of the same Hamiltonian within the spherical coordinate system. Then the spin-orbit coupling can be added in a straightforward way. The outcome is a transformation between the Elliott single particle basis and the spherical shell model space.