Relativistic configuration-interaction density functional theory: Nonaxial effects on nuclear $ββ$ 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 $ββ$ ($0νββ$) decay in nucleus $^{76}$Ge, amongst the most promising $ββ$-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 $ββ$-decay partners $^{76}$Ge and $^{76}$Se, and the nuclear matrix element governing the two-neutrino $ββ$ ($2νββ$) 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 $0νββ$ decay significantly by a factor around two. The present results indicate that the goals of next-generation experiments searching for the $0νββ$ decay in $^{76}$Ge can be achieved using only a quarter amount of the experimental materials.