Two-neutrino double beta decay ofCa48

We have performed quasiparticle random phase approximation (QRPA) calculations for the 2νββ decay matrix element ${\mathit{M}}_{\mathrm{GT}}^{2\nu }$ of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ using realistic effective interactions derived from the Paris, Bonn, and Reid potentials. Unlike earlier QRPA calculations where the BCS self-energies were suppressed, we have retained these self-energies together with the use of the single-particle levels provided by a ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ core. Different choices for the single-particle levels are employed, and their effects on ${\mathit{M}}_{\mathrm{GT}}^{2\nu }$ are compared. A majority of our calculated ${\mathit{M}}_{\mathrm{GT}}^{2\nu }$ matrix elements are in good agreement with the experimental bounds of ‖${\mathit{M}}_{\mathrm{GT}}$ ${\mathrm{\Vert }}^{2\nu }$<0.05 ${\mathrm{MeV}}^{\mathrm{-}1}$, and exhibit good stability with respect to the variation of the particle-particle interaction strength ${\mathit{g}}_{\mathit{p}\mathit{p}}$.