Nature of triaxial deformation in $^{76}$Ge: A model-independent analysis

The low-lying structure of $^{76}$Ge has become a subject of intense scrutiny ever since it was first suggested as a possible example of rigid triaxiality at low spin [1]. For decades, the experimental observation of such rigid structures has remained elusive and indeed, there has been a longstanding issue associated with whether axially asymmetric nuclei retain rigid-triaxial deformation in their ground-state configuration. In this study, an extensive, model-independent analysis of the nature of triaxial deformation in $^{76}$Ge has been performed following a high-statistics Coulomb excitation measurement with GRETINA and CHICO2. 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. Compelling evidence for low-spin, rigid-triaxial deformation in $^{76}$Ge based on the analysis of the statistical variance of the quadrupole asymmetry deduced from the measured $E2$ matrix elements will be presented. The relevance of these results for calculations aimed at providing, with suitable accuracy, the nuclear matrix elements relevant to neutrinoless double-beta decay will also be highlighted. [1] Y. Toh {\it et al.}, Phys. Rev. C87, 041304 (2013).