Shell-model study of the 4th- and 6th-forbidden $\beta$-decay branches of ${}^{48}\mathrm{Ca}$

The highly forbidden ${\beta }^{-}$ decay of ${}^{48}\mathrm{Ca}$ is reexamined by performing shell-model calculations with the GXPF1A effective interaction. We examine the three available decay branches to the lowest $6^{+}$, $5^{+}$, and $4^{+}$ states of ${}^{48}$Sc, and extract a theoretical half-life of $T_{1/2}^{\beta }=5.2_{-1.3}^{+1.7}\times {10}^{20}{g}_A^{-2}$ yr for the ${\beta }^{-}$ decay, where $g_A$ is the value of the axial-vector coupling constant. The current half-life estimate suggests stronger competition between the single-$\beta$-decay and double-$\beta$-decay branches of ${}^{48}\mathrm{Ca}$ than previously expected on theoretical grounds.

Figure 1

$\beta$-decay scheme of ${}^{48}\mathrm{Ca}$. In addition to the three ordinary $\beta$-decay branches of ${}^{48}\mathrm{Ca}$, the ground-state-to-ground-state double-$\beta$-decay branch $0^{+}\to 0^{+}$ is also shown. The values for the partial half-lives of the ordinary $\beta$-decay branches are taken from Table 1 with $g_A=1.25$. For ${}^{48}$Sc, only the dominant decay branches are indicated.