Symmetries as a framework for understanding signatures of collectivity and shape coexistence*

Ab initio nuclear theory provides not only a microscopic framework for quantitative description of the nuclear many-body system, but also a foundation for deeper understanding of collective behavior. To gain insight into the structure and correlations which give rise to emergent collective behavior in no-core shell model (NCSM) predictions of p-shell nuclei, we decompose the calculated wave functions by symmetries.  In particular, we consider the  Elliott's SU(3) and Sp(3,R) symmetries, which are tied to nuclear rotation, deformation and giant resonances.  These decompositions demonstrate that Elliott's SU(3) rotational model provides a natural framework for understanding the emergence of rotational bands throughout the p-shell.  In some nuclei,  rotational bands with vastly different structure appear within the low lying spectrum of the same nucleus hinting at shape coexistence.