Shell Model Monte Carlo Method for Two-Neutrino Double Beta Decay

Shell model Monte Carlo techniques are used to calculate two-neutrino double beta decay matrix elements. We test 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 $\left({0f}_{5/2}{,1p,0g}_{9/2}\right)$ model space using a newly calculated realistic interaction. Our result for the matrix element is $0.12\pm 0.05{\mathrm{MeV}}^{-1\mathrm{}}$, in reasonable agreement with the experimental value.