# Rotational bands beyond the Elliott model

Published in *Journal of Physics G: Nuclear and Particle Physics*, 2021

DOI: 10.1088/1361-6471/abdd8e | arXiv: 2011.08307

Recommended citation: R. Zbikowski, C. W. Johnson, A. E. McCoy, M. A. Caprio, and P. J. Fasano, J. Phys. G: Nucl. Part. Phys. 48, 075102 (2021). __(download)__

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 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 $\mathrm{Sp}(3,\mathbb{R})$ 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 $\mathrm{Sp}(3,\mathbb{R})$. The band structure, delineated by strong $B(E2)$ values, has a more consistent description in $\mathrm{Sp}(3,\mathbb{R})$ 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.