Symmetry and shape coexistence in ¹⁰Be

Within the low-lying spectrum of ¹⁰Be, multiple rotational bands are found, with strikingly different moments of inertia. A proposed interpretation has been that these bands variously represent triaxial rotation and prolate axially-deformed rotation. The bands are well-reproduced in ab initio no-core configuration interaction (NCCI) calculations. We use the calculated wave functions to elucidate the nuclear shapes underlying these bands, by examining the Elliott $\mathrm{SU}(3)$ symmetry content of these wave functions. The ab initio results support an interpretation in which the ground-state band, along with an accompanying $K=2$ side band, represent a triaxial rotor, arising from an $\mathrm{SU}(3)$ irreducible representation in the $0\hbar\omega$ space. Then, the lowest excited $K=0$ band represents a prolate rotor, arising from an $\mathrm{SU}(3)$ irreducible representation in the $2\hbar\omega$ space.