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

TL;DR

This paper provides model-independent evidence of rigid triaxial deformation in $^{76}$Ge, crucial for understanding its role in neutrinoless double-beta decay, through Coulomb excitation and shape parameter analysis.

Contribution

It presents the first model-independent evidence for low-spin, rigid triaxial deformation in $^{76}$Ge using a statistical analysis of quadrupole asymmetry.

Findings

Both ground-state and $eta$ and $ ext{gamma}$ bands share the same deformation parameters.

Compelling evidence for low-spin, rigid triaxial shape in $^{76}$Ge.

Shape parameters serve as constraints for nuclear matrix element calculations.

Abstract

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 $0\nu\beta\beta$.