Shell-model calculations of two-neutrino double-beta decay rates of ${}^{48}$Ca with GXPF1A interaction

Abstract

The two-neutrino double beta decay matrix elements and half-lives of ${}^{48}$Ca, are calculated within a shell-model approach for transitions to the ground state and to the $2^{+}$ first excited state of ${}^{48}$Ti. We use the full $pf$ 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 $T_{1/2}(0^{+}\to 0^{+})$ = $3.3\times 10^{19}$ $yr$ and $T_{1/2}(0^{+}\to 2^{+})$ = $8.5\times 10^{23}$ $yr$. The result for the decay to the ${}^{48}$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 obtained previously.

6 pages, 4 figures