Two-Neutrino Double Beta Decay: Critical Analysis

We have performed a critical analysis of different approximation schemes for the calculation of two-neutrino double beta decay (2β2ν-decay) matrix elements. For that purpose the time integral representation of the 2β2νdecay matrix element has been used. We have shown that within the singleparticle approximation of the nuclear Hamiltonian the 2β2ν-decay matrix element is equal to zero because of the mutual cancelation of the direct and cross terms. The quasiboson approximation (QBA) and renormalized QBA (RQBA) schemes imply for the 2β2ν-decay transition operator to be a constant, if one requires the equivalence of initial and final Quasiparticle Random Phase Approximation (QRPA) and renormalized QRPA (RQRPA) Hamiltonians. It means that 2β2ν-decay is a higher order process in the boson expansion of the nuclear Hamiltonian and its higher order boson approximations are important. The equivalence of the initial and final QRPA and RQRPA