On the Electron Coincidence Spectrum in Double Beta Decay

Though simple qualitative arguments imply that the electron coincidence spectra for two-neutrino, and for no-neutrino double β-decay are broadly peaked at ½E0 and infinitely sharply peaked at E0 respectively (E0 is the energy release), a recent calculation has shown that in some circumstances the two-neutrino case spectrum may also be broadly peaked in the region of E0. A simple model, in which only one state of the intermediate nucleus gives a non-zero contribution to the matrix element, is used to recalculate these spectra. Two extreme approximations are considered: the energy of the intermediate state is equal to, or much greater than, that of the initial state. In both cases, the qualitative result is confirmed, and the recent calculation mentioned above is regarded as incorrect. The model is applied to the double β-decays of 96Zr and 48Ca. The relation between the conservation of lepton `charge' and the shape of the spectrum is also considered in some detail.