  We use the random phase approximation to systematically describe the total
muon capture rates on all nuclei where they have been measured. We reproduce
the experimental values on these nuclei to better than 15% accuracy using the
free nucleon weak form factors and residual interactions with a mild $A$
dependency. The isospin dependence and the effects associated with shell
closures are fairly well reproduced as well. However, the calculated rates for
the same residual interactions would be significantly lower than the data if
the in-medium quenching of the axial-vector coupling constant is employed to
other than the true Gamow-Teller amplitudes. Our calculation thus suggests that
no quenching is needed in the description of semileptonic weak processes
involving higher multipole transitions and momentum transfer $\sim m_{\mu}$,
with obvious importance to analogous weak processes.
