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

TL;DR

This paper develops a relativistic density functional theory incorporating nonaxial (triaxial) effects to accurately predict nuclear matrix elements for neutrinoless double beta decay in $^{76}$Ge, significantly impacting experimental sensitivity.

Contribution

It introduces a novel relativistic configuration-interaction density functional approach that includes triaxial deformation, improving predictions of decay matrix elements for $^{76}$Ge.

Findings

Inclusion of triaxiality doubles the predicted nuclear matrix element.

The model accurately reproduces spectroscopic properties of decay partners.

Results suggest reduced experimental material needs for future searches.

Abstract

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.