Muon capture on nuclei with N>Z, random phase approximation, and in-medium value of the axial-vector coupling constant

We use the random phase approximation to describe the muon capture rate on ⁴⁴Ca, ⁴⁸Ca, ⁵⁶Fe, ⁹⁰Zr, and ²⁰⁸Pb. With ⁴⁰Ca as a test case, we show that the continuum random phase approximation (CRPA) and the standard RPA give essentially equivalent descriptions of the muon capture process. Using the standard RPA with the free nucleon weak form factors we reproduce the experimental total capture rates on these nuclei quite well. Thus, unlike the allowed β decays, with very small momentum transfer and exclusively the 1⁺ multipole, the muon capture rate, with momentum transfer of approximately muon mass magnitude, and a mixture of multipoles (dominated by 1^-), does not require any quenching of the axial-vector coupling constant.