Relativistic configuration-interaction density functional theory: Nonaxial effects on nuclear $\beta\beta$ decay

The relativistic configuration-interaction density functional theory is developed for even-even and odd-odd nuclei and is used to predict the nuclear matrix element of the neutrinoless $\beta\beta$ ($0\nu\beta\beta$) decay in nucleus $^{76}$Ge, amongst the most promising $\beta\beta$-decay candidates. The nonaxial deformation, i.e., triaxiality, which poses severe challenges in evaluating the nuclear matrix element of $^{76}$Ge, is incorporated within a full model space for the first time. The spectroscopic properties of the $\beta\beta$-decay partners $^{76}$Ge and $^{76}$Se, and the nuclear matrix element governing the two-neutrino $\beta\beta$ ($2\nu\beta\beta$) decay in $^{76}$Ge are well reproduced, providing solid examinations for the validity of theoretical calculations. The inclusion of the triaxial degree of freedom enhances the nuclear matrix element of the $0\nu\beta\beta$ decay significantly by a factor around two. The present results indicate that the goals of next-generation experiments searching for the $0\nu\beta\beta$ decay in $^{76}$Ge can be achieved using only a quarter amount of the experimental materials.