Approximations in the quasiparticle random phase evaluation of double beta decay rates

Abstract

Within the quasiparticle random phase approximation, we compare two-neutrino double beta decay amplitudes calculated with zero-range and finite-range nucleon-nucleon interactions. We find that if, as is customary, interaction constants are fit to energies of giant Gamow-Teller states and to β+ strengths, the two interactions lead to very similar two-neutrino double beta amplitudes. We discuss additional approximations related to the inclusion (or neglect) of the Hartree-Fock part of the pairing interaction, and to the treatment of differences between the initial and final nuclear ground states. The numerical values of the amplitudes depend more on the way these approximations are made than on the form of the nucleon-nucleon force.