Nature of $γ$-deformation in Ge and Se nuclei and the triaxial projected shell model description

Abstract: Recent experimental data have demonstrated that $^{76}$Ge may be a rare example of a nucleus exhibiting rigid $\gamma$-deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and $\gamma$-vibrational bands in $^{76}$Ge, a rigid-triaxial deformation parameter $\gamma\approx 30^\circ$ is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published results from the spherical shell model. The occurrence of a $\gamma\gamma$-band in $^{76}$Ge is predicted with the bandhead at an excitation energy of $ \sim$ 2.5 MeV. We have also performed TPSM study for the neighboring Ge- and Se-isotopes and the distinct $\gamma$-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states.