Nuclear matrix elements for rare decays

Neutrinoless double electron capture ( 0 ν ECEC) is being vigorously investigated because of the possibility of it telling us something about the absolute mass scale of the neutrino. The resonant 0 ν ECEC is particularly interesting due to the potentially huge enhancement of its decay rate by a resonance condition. Recently the mass differences of two atom pairs were measured in order to study the enhancement of the 0 ν ECEC rates of 74Se and 112Sn. The associated nuclear matrix elements were also evaluated. The neutrino mass can also be detected by using beta decays with low Q values. Related to this we have investigated the second-forbidden decay branch of 115In with its ultra-low Q value. Open questions about nuclear and atomic contributions to the associated decay rate emerge.