  An extensive, model-independent analysis of the nature of triaxial
deformation in $^{76}$Ge, a candidate for neutrinoless double-beta
($0\nu\beta\beta$) 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 $\gamma$ bands. Both sequences were
determined to be characterized by the same $\beta$ and $\gamma$ 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 $0\nu\beta\beta$.

Nuclear Experiment;Nuclear Theory