Relativistic and Neutrino Mass Effects in Partial Muon Capture

The characteristics of the partial nuclear muon capture with massive left-handed Dirac neutrino and relativistic component of the muon wave function have been derived. The multipole amplitudes are given as a function of neutrino mass parameter and reduced nuclear matrix elements which are modified by the small component of the muon wave function. As an example, the capture rate, asymmetry and polarization of recoil nuclei are investigated in terms of these multipole amplitudes.