Renormalized Proton-Neutron Quasiparticle Random-Phase Approximation and Its Application to Double Beta Decay

A self-consistent method of treating excitations of the proton-neutron quasiparticle random-phase approximation is presented. The non-self-consistent methods violate the Pauli exclusion principle and lead to an eventual collapse of the ground state. This behavior renders a reliable calculation of the nuclear matrix elements, relevant for the prediction of double-beta-decay half-lives, difficult. The present formalism promotes the Pauli exclusion principle and avoids the collapse of the double-beta-decay matrix elements. We have applied this formalism to the double beta decay of ${}^{100}$Mo.