Direct calculation of the two-neutrino double-beta decay rate including the full lepton-energy dependence

The calculation of the two-neutrino double-beta decay (DBD) rates has so far relied on approximations that decouple the nuclear structure from the emitted lepton kinematics. To ensure a more rigorous treatment, we propose an approach which incorporates the full interdependence between nuclear structure and lepton kinematics within a unified formula and performs calculations without resorting to these approximations. Deviations of the decay rates and electron spectra from the traditional methods, such as closure, non-closure, and Taylor expansion approximations, are presented and discussed for the isotopes ⁸² 82 Se and ¹³⁶ 136 Xe. Our approach gives a more realistic description of the DBD process and paves the way for further theoretical and experimental investigations into the correlated nuclear structure interplay with emitted lepton kinematics contributing to the dynamics of the process. Extensions of this framework to other isotopes and to neutrinoless double-beta decay are currently underway.