Observables in muon capture on ²³Na and the effective weak couplings g̃_a and g̃_p

We report measurements of capture rates and hyperfine dependences in muon capture on ²³Na to various states in Ne and F isotopes. We also report comparisons of the capture rates and hyperfine dependences for six ²³Na → ²³Ne 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 g̃_a = -1.01 ± 0.07 and an effective coupling ratio g̃_p/g̃_a = 6.5 ± 2.4. The value of g̃_a is consistent with values of g̃_a extracted from β⁺/β^- decay and (p,n)/(n,p) charge exchange data, and the value of g̃_p/g̃_a is consistent with the predictions of PCAC and pion-pole dominance. We evaluate the nuclear model dependence of these values of g̃_a and g̃_p/g̃_a and examine the role of the Gamow-Teller and other matrix elements in the ²³Na → ²³Ne transitions.