Measurement of partial muon capture rates in 1 s − 0 d shell nuclei

We report yields for 38 \ensuremath{\gamma}-ray lines and 29 $({\ensuremath{\mu}}^{\ensuremath{-}},\ensuremath{\nu})$ transitions following negative muon capture on ${}^{24}\mathrm{Mg},$ ${}^{28}\mathrm{Si},$ ${}^{31}\mathrm{P},$ and ${}^{32}\mathrm{S}.$ Our results substantially increase the world data set for partial $({\ensuremath{\mu}}^{\ensuremath{-}},\ensuremath{\nu})$ transitions on $1s\ensuremath{-}0d$ shell nuclei. They also resolve a number of inconsistencies between previously published \ensuremath{\gamma}-ray yields and accepted \ensuremath{\gamma}-decay branching ratios. We compare the measured capture rates for the allowed Gamow-Teller (GT) transitions (supplemented with earlier ${}^{23}\mathrm{Na}$ data) with a shell model calculation using the full $1s\ensuremath{-}0d$ space and universal SD interaction. We find a ``best fit'' value of the effective weak axial coupling of ${g}_{a}=\ensuremath{-}{0.91}_{\ensuremath{-}0.17}^{+0.15},$ fair agreement for the per-target summed GT capture rates, but poor agreement for the individual GT capture rates. By replacing the shell model $\ensuremath{\sigma}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}$ matrix element values with experimentally determined $\ensuremath{\sigma}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}$ matrix element values, improved predictions for the individual GT capture rates are obtained. Last, we comment on recent determinations of the weak coupling ${g}_{p}$ via muon capture on $1s\ensuremath{-}0d$ shell nuclei.