Exotic weak decays of atomic nuclei

The two-neutrino (2 nu 2 beta) and neutrinoless (0 nu 2 beta) double beta decays are studied with respect to the associated nuclear matrix elements (NMEs). It is assumed that the 0 nu 2 beta decay proceeds through the exchange of a Majorana neutrino with non-zero effective mass. In this so called mass mode both the ground-state and excited-state decays are discussed. For the 0 nu 2 beta(-) mode the NMEs computed by the Yale group (using IBA-2) and the Jyvaskyla group (using the QRPA) are compared. The positron emitting/electron capture modes, beta(+) beta(+), beta+EC, and ECEC, are discussed also. Particular attention is devoted to the study of the detectability of the resonant neutrinoless double electron capture (R0 nu ECEC) processes in potential candidate nuclei. As an example, the decays of Ru-96 are reviewed.