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 C-12, O-16 and Ca-40. 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.