The theory of muon capture by complex nuclei: (III). Radiative muon capture

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Various quantities, in particular the photon spectrum and total rate, for radiative muon capture by complex nuclei are studied with the purpose of obtaining information on the coupling constants. Diagrams with muon and nucleon radiating as well as some diagrams for the induced couplings are taken into account. It is shown that the photon spectrum and the total radiative capture rate are only slightly dependent on the nuclear model, if one considers the ratio to the normal capture rate. Comparisons were made for several approximations and models, including a statistical model and harmonic oscillator wave functions. It is shown that radiative muon capture by nuclei depends strongly on the induced pseudoscalar interaction, just as for the free proton case, but the numerical results for nuclei and the free proton differ considerably. However, the fact that the results for radiative capture depend only slightly on the nuclear model implies that experiments on radiative muon capture seem to be a good method to determine the pseudoscalar interaction. Theoretical results are also derived for the circular polarization of photons emitted in radiative muon capture and for the directional distribution of the photons after capture of polarized muons. The results are presented in the form of general formulae and are evaluated numerically for a series of typical cases. The nuclei 40Ca and 16O are considered in particular.