The Half-Life and the Nuclear Matrix Element of the $2\nu \beta \beta$ Decay in ${}^{76}Ge$

Abstract

We apply the shell-model wave-functions of ${}^{76}Ge$ to calculate the nuclear matrix elements and the half-life of the $2\nu \beta \beta$ decay in ${}^{76}Ge$. Our result is comparable to the recent observed $2\nu \beta \beta$-decay half-life of ${}^{76}Ge$. Furthemore it provides the upper limit of the effective neutrino mass is about 0.4 eV from the recent experimental data of the $0\nu \beta \beta$-decay half-life.

6 pages