Shell Model Study of the Double Beta Decays of ${}^{76}$Ge, ${}^{82}$Se and ${}^{136}$Xe

Abstract

The lifetimes for the double beta decays of ${}^{76}$Ge, ${}^{82}$Se and ${}^{136}$Xe are calculated using very large shell model spaces. The two neutrino matrix elements obtained are in good agreement with the present experimental data. For $<m_{\nu }><1$ eV we predict the following upper bounds to the half-lives for the neutrinoless mode: $T_{1/2}^{(0\nu )}(Ge)>1.8510^{25}yr.$, $T_{1/2}^{(0\nu )}(Se)>2.3610^{24}yr.$ and $T_{1/2}^{(0\nu )}(Xe)>1.2110^{25}yr$. These results are the first from a new generation of Shell Model calculations reaching O(10${}^8$) dimensions.