Shell-model calculation for two-neutrino double beta decay ofCa48

The 2νββ decay matrix element of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ has been studied in a large basis shell-model space. The theoretical and experimental ${\mathrm{\beta }}^{\mathrm{-}}$ and ${\mathrm{\beta }}^{+}$ spectra and their relation to 2νββ are discussed. A new empirical effective interaction is found to give the best agreement to ${\mathrm{\beta }}^{\mathrm{-}}$ and ${\mathrm{\beta }}^{+}$ spectra with the effective Gamow-Teller operator σ̃t=0.77σt. The predicted ${\mathit{T}}_{1/2}$=1.9×${10}^{19}$ yr differs by a factor of 2 from the present experimental limit of ${\mathit{T}}_{1/2}$>3.6×${10}^{19}$ yr. We also compare the matrix elements obtained at various levels of the truncation in the shell-model space.