Exact Calculation of Two-neutrino Double Beta Decay Rate

The calculation of the two-neutrino double-beta decay (DBD) rates has relied so far on approximations that decouple the nuclear and atomic parts. To provide a more rigorous treatment, we propose an approach which incorporates the full interdependence between nuclear structure and lepton kinematics. Deviations of the decay rates and electron spectra from the traditional methods, such as closure, non-closure and Taylor expansion approximation, are presented and discussed for the isotopes $^{82}$Se and $^{136}$Xe. Our approach gives a more realistic description of the DBD process, and opens the avenue of additional, new theoretical and experimental investigations into nuclear and atomic effects in the process. Extensions of this framework to other isotopes and to neutrinoless double-beta decay are currently underway.