Nucleon-pair coupling scheme in Elliott's SU(3) model

TL;DR

This paper demonstrates that Elliott's SU(3) symmetry in nuclear shell models can be realized using a truncated space of collective pairs with optimized structures, accurately reproducing rotational spectra and properties.

Contribution

It introduces a method to realize SU(3) symmetry with collective pairs in a truncated shell-model space, improving understanding of nuclear rotational motion.

Findings

Exact reproduction of level energies and quadrupole properties for a specific nucleus

SDG pairs effectively capture SU(3) collectivity, unlike SD pairs

Mapping to bosonic systems offers insight into collective subspaces

Abstract

Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective $S$, $D$, $G$, $\dots$ pairs (i.e., with angular momentum zero, two, four, $\dots$) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for 6 protons and 6 neutrons in the $pf$ ($sdg$) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with $SDG$ ($SDGI$) pairs. The $SD$-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with $s$, $d$, $g$, $\dots$ bosons provides insight into the existence of a decoupled collective subspace in terms of $S$, $D$, $G$, $\dots$ pairs.