Investigation of $^{76}$Ge structure via inelastic scattering studies*

The search for neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of $^{76}$Ge has led to renewed interest in the structure of this mass region, as structural information helps constrain calculations of the $0\nu\beta\beta$ nuclear matrix elements. The structure of many of the even-even Ge isotopes, including $^{76}$Ge, show interesting features, such as low-lying $0^+$ states that have been interpreted as evidence for shape coexistence, as well as indications of triaxiality. Of fundamental importance in understanding the nature of the excited states in $^{76}$Ge is the determination of transition strengths, which has been obtained through $^{76}$Ge(n,n$^{\prime}\gamma)$ studies at the University of Kentucky and the $^{76}$Ge$(\gamma,\gamma^{\prime})$ reaction at the High Intensity $\gamma$-Ray Source at Duke University. The measured transition strengths support the identification of band structure in $^{76}$Ge, a newly observed mixed-symmetry state, and the M1 scissors mode.