Abstract
The total rates of ordinary and radiative muon capture in natural zirconium and molybdenum are calculated within the quasiparticle random phase approximation. The total ordinary-muon-capture rates calculated with the unquenched weak axial-vector coupling are consistent with the experimental data and weakly depend on the weak pseudoscalar coupling. The calculated radiative-muon-capture rates have a clear dependence on the pseudoscalar coupling, but highly overestimate the experimental data.
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