The nucleus ${}^{54}\mathrm{Mn}$, observed in cosmic rays, decays there dominantly by the ${\beta }^{-}$ branch with an unknown rate. The branching ratio of its ${\beta }^{+}$ decay was determined recently. We use the shell model with only a minimal truncation and calculate both ${\beta }^{+}$ and ${\beta }^{-}$ decay rates. Good agreement for the ${\beta }^{+}$ branch suggests that the calculated partial half-life of the ${\beta }^{-}$ decay, $4.94\times {10}^5\mathrm{yr}$, should be reliable. However, this half-life is noticeably shorter than the range $1–2\times {10}^6\mathrm{yr}$ indicated by the fit based on the ${}^{54}\mathrm{Mn}$ abundance in cosmic rays. We also evaluate other known unique second forbidden $\beta$ decays from the $p$ and $\mathrm{sd}$ shells and show that the shell model can describe them with reasonable accuracy as well.

• Received 12 March 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.281