Shell-model calculations of two-neutrino double-β decay rates ofCa48with the GXPF1A interaction

Abstract

The two-neutrino double-\ensuremath{\beta} decay matrix elements and half-lives of $^{48}\mathrm{Ca}$ were calculated within a shell-model approach for transitions to the ground state and to the ${2}^{+}$ first excited state of $^{48}\mathrm{Ti}$. We use the full $\mathit{pf}$ model space and the GXPF1A interaction, which was recently proposed to describe the spectroscopic properties of the nuclei in the nuclear mass region $A=47$--66. Our results are ${T}_{1/2}({0}^{+}\ensuremath{\rightarrow}{0}^{+})=3.3\ifmmode\times\else\texttimes\fi{}{10}^{19}$ yr and ${T}_{1/2}({0}^{+}\ensuremath{\rightarrow}{2}^{+})=8.5\ifmmode\times\else\texttimes\fi{}{10}^{23}$ yr. The result for the decay to the $^{48}\mathrm{Ti}$ ${0}^{+}$ ground state is in good agreement with experiment. The half-life for the decay to the ${2}^{+}$ state is two orders of magnitude larger than that obtained previously.