Double β-decay nuclear matrix elements for the A = 48 and A = 58 systems

The nuclear matrix elements entering the double β decays of the 48Ca-48Ti and 58Ni-58Fe systems have been calculated using a realistic two nucleon interaction and realistic shell model spaces. Effective transition operators corresponding to a variety of gauge theory models have been considered. The stability of such matrix elements against variations of the nuclear parameters is examined. Appropriate lepton violating parameters are extracted from the A = 48 data and predictions are made for the lifetimes of the positron decays of the A = 58 system