Rotational bands beyond the Elliott model

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