In this thesis, a method to calculate two-neutrino double beta decay matrix elements employing the Shell Model Monte Carlo is presented. This method is validated against direct-diagonalization for the decay of 48Ca. The first realistic calculation of the nuclear matrix element within the shell model for 76Ge is performed; the result is in reasonable agreement with experiment.
The sensitivity of the shell model results to the nuclear Hamiltonian has been studied for the case of 48Ca where the Hamiltonian used is known to be an optimal one. While one cannot make the nuclear matrix element arbitrarily small, the uncertainty in certain pieces of the Hamiltonian such as the monopole isovector pairing, provides room for at least a factor of two in the matrix element (and hence a factor of four in the half-life) from such calculations.
A Maximum Entropy method to obtain realistic strength functions from imaginary time response functions has been applied to Gamow-Teller response functions calculated using the Shell Model Monte Carlo and the results are validated against direct-diagonalization and experiment.
Future prospects for double beta decay calculations and astrophysical applications of the Gamow-Teller strength functions are briefly discussed.
