We report measurements of capture rates and hyperfine dependences in muon capture on ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ to various states in Ne and F isotopes. We also report comparisons of the capture rates and hyperfine dependences for six ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ → ${}_{}{}^{23}{}_{}{}^{}\mathrm{Ne}$ transitions with the 1s-0d shell model with the empirical effective interaction of Brown and Wildenthal and the realistic effective interaction of Kuo and Brown. Fits to the data with the Brown and Wildenthal interaction yield an effective coupling ${\mathit{g}\mathit{̃}}_{\mathit{a}}$ = -1.01 ± 0.07 and an effective coupling ratio ${\mathit{g}\mathit{̃}}_{\mathit{p}}$/${\mathit{g}\mathit{̃}}_{\mathit{a}}$ = 6.5 ± 2.4. The value of ${\mathit{g}\mathit{̃}}_{\mathit{a}}$ is consistent with values of ${\mathit{g}\mathit{̃}}_{\mathit{a}}$ extracted from ${\mathrm{\beta }}^{+}$/${\mathrm{\beta }}^{\mathrm{-}}$ decay and (p,n)/(n,p) charge exchange data, and the value of ${\mathit{g}\mathit{̃}}_{\mathit{p}}$/${\mathit{g}\mathit{̃}}_{\mathit{a}}$ is consistent with the predictions of PCAC and pion-pole dominance. We evaluate the nuclear model dependence of these values of ${\mathit{g}\mathit{̃}}_{\mathit{a}}$ and ${\mathit{g}\mathit{̃}}_{\mathit{p}}$/${\mathit{g}\mathit{̃}}_{\mathit{a}}$ and examine the role of the Gamow-Teller and other matrix elements in the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ → ${}_{}{}^{23}{}_{}{}^{}\mathrm{Ne}$ transitions. © 1996 The American Physical Society.

• Received 4 June 1996

DOI:https://doi.org/10.1103/PhysRevC.54.2714