We report yields for 38 γ-ray lines and 29 $({\mu }^{-},\nu )$ 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 $({\mu }^{-},\nu )$ transitions on $1s-0d$ shell nuclei. They also resolve a number of inconsistencies between previously published γ-ray yields and accepted γ-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 $1s-0d$ space and universal SD interaction. We find a “best fit” value of the effective weak axial coupling of $g_a=-{0.91}_{-0.17}^{+0.15\mathrm{}},$ fair agreement for the per-target summed GT capture rates, but poor agreement for the individual GT capture rates. By replacing the shell model $\sigma {\tau }^{\pm }$ matrix element values with experimentally determined $\sigma {\tau }^{\pm }$ 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 $1s-0d$ shell nuclei.

• Received 15 March 1999

DOI:https://doi.org/10.1103/PhysRevC.60.055501