Shell Model Monte Carlo (SMMC) techniques are used to calculate two-neutrino double beta decay matrix elements. We validate the approach against direct diagonalization for $^{ 48}$Ca in the complete $pf$-shell using the KB3 interaction. The method is then applied to the decay of $^{ 76}$Ge in the $(0f_{ 5/2},1p,0g_{ 9/2})$ model space using a newly calculated realistic interaction. Our result for the matrix element is $0.13\pm0.05$ MeV$^{ -1}$, in agreement with the experimental value.
Categories: nucl-th