Triaxiality and shape coexistence in $^{72,76}$Ge: A model independent analysis.

An exploration of the structure of Ge isotopes is important for understanding the microscopic origin of collectivity, the nature of deformation and modifications of shell structure in nuclei of the $N\sim40$ mass region. The present study focuses on the electromagnetic properties of low-lying states in $^{72,76}$Ge obtained via sub-barrier multiple Coulomb excitation with GRETINA and CHICO2. In the case of $^{72}$Ge, the extracted matrix elements agree with a shape coexistence interpretation between the $0_1^+$ and $0_2^+$ states, but require significant mixing between the $0^+$ wavefunctions as well as triaxiality in order to reproduce the data. Similarly, the invariant sum-rule analysis of the $^{76}$Ge data indicates that both the ground state and gamma bands are characterized by the same deformation parameters, with triaxiality $(\gamma \sim 30^\circ)$ being important for a complete description. A summary of these results and data highlighting the nature of gamma deformation in $^{76}$Ge - whether rigid or soft - will be presented.