Rotational bands beyond the Elliott model

TL;DR

This paper investigates nuclear rotational bands beyond the traditional Elliott model by decomposing wave functions into symmetry subspaces, demonstrating that the symplectic extension $ ext{Sp}(3,R)$ offers a more consistent description of band structures in certain nuclei.

Contribution

The study extends the understanding of nuclear rotational bands by applying $ ext{Sp}(3,R)$ symmetry analysis to no-core shell-model wave functions, highlighting its advantages over $ ext{SU}(3)$ in describing band structures.

Findings

$ ext{Sp}(3,R)$ provides a more consistent description of band structures.

Strong $B(E2)$ values delineate the band structure.

Connected upper and lower bands share the same symplectic structure.

Abstract

Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed a discrete nucleon representations of $\mathrm{SU}(3)$ from fermionic creation and annihilation operators. Ever since, Elliott's model has been foundational to descriptions of rotation in nuclei. Later work, however, suggested the symplectic extension $\mathrm{Sp}(3,R)$ provides a more unified picture. We decompose no-core shell-model nuclear wave functions into symmetry-defined subspaces for several beryllium isotopes, as well as $^{20}$Ne, using the quadratic Casimirs of both Elliott's $\mathrm{SU}(3)$ and $\mathrm{Sp}(3,R)$. The band structure, delineated by strong $B(E2)$ values, has a more consistent description in $\mathrm{Sp}(3,R)$ rather than $\mathrm{SU}(3)$. {In particular, we confirm previous work finding in some nuclides strongly connected upper and lower bands with the same underlying symplectic structure.