Muon capture, continuum random phase approximation, and in-medium renormalization of the axial-vector coupling constant.

We use the continuum random phase approximation to describe the muon capture on 12C,16O, and 40Ca. We reproduce the experimental total capture rates on these nuclei to better than 10% using the free nucleon weak form factors and two different residual interactions. However, the calculated rates for the same residual interactions are significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed.