Evidence for rigid triaxial deformation in ${}^{76}$Ge from a model-independent analysis

Abstract

An extensive, model-independent analysis of the nature of triaxial deformation in ${}^{76}$Ge, a candidate for neutrinoless double-beta ($0\hat{I}½{\hat{I}}^2{\hat{I}}^2$) decay, was carried out following multi-step Coulomb excitation. Shape parameters deduced on the basis of a rotational-invariant sum-rule analysis provided considerable insight into the underlying collectivity of the ground-state and ${\hat{I}}^3$ bands. Both sequences were determined to be characterized by the same ${\hat{I}}^2$ and ${\hat{I}}^3$ deformation parameter values. In addition, compelling evidence for low-spin, rigid triaxial deformation in ${}^{76}$Ge was obtained for the first time from the analysis of the statistical fluctuations of the quadrupole asymmetry deduced from the measured $E2$ matrix elements. These newly determined shape parameters are important input and constraints for calculations aimed at providing, with suitable accuracy, the nuclear matrix elements relevant to $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$.

6 pages, 5 figures