Recent results from neutrino oscillation experiments have convincingly demonstrated that neutrinos have mass and they can mix. The neutrinoless double beta decay is the most sensitive process to determine the absolute scale of the neutrino masses, and the only one that can distinguish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from neutrinoless double beta decay experiments is a precise knowledge of the nuclear matrix elements (NME) for this process. Newly developed shell model approaches for computing the NME and half-lifes for the two-neutrino and neutrinoless double beta decay modes using modern effective interactions are presented. The implications of the new results on the experimental limits of the effective neutrino mass are discussed by comparing the decays of "Ca and ~(76)Ge.
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