RENORMALIZED QUASI-PARTICLE RANDOM-PHASE-APPROXIMATION AND DOUBLE-BETA DECAY - A CRITICAL ANALYSIS OF DOUBLE FERMI TRANSITIONS

The proton-neutron monopole Lipkin model, which exhibits some properti es that are relevant for those double beta decay (beta beta) transitio ns mediated by the Fermi matrix elements, is solved exactly in the pro ton-neutron two-quasiparticle space. The exact results are compared wi th the ones obtained by using the quasiparticle random phase approxima tion (QRPA) and renormalized QRPA (RQRPA) approaches. It is shown that the RQRPA violates the Ikeda sum rule and that this violation may be common to any extension of the QRPA where scattering terms are neglect ed in the participant one-body operators as well as in the Hamiltonian . This finding underlines the need of additional developments before t he RQRPA could be adopted as a reliable tool to compute beta beta proc esses.