Radiative muon capture for N = Z nuclei

The commonly used elementary hamiltonian of radiative muon capture has been confirmed, while the alternative Hwang-Primakoff approach is shown not to be gauge invariant.In the inclusive process on N = Z nuclei, the closure approximation is avoided by using a realistic nuclear excitation spectrum.The study is exemplified by a detailed application to ⁴⁰Ca. Predictions are given for the high-energy photon spectrum, circular polarization and asymmetry with respect to the muon polarization for various values of the pseudoscalar coupling constant g_p. A semi-quantitative agreement is found with the data on the spectrum; more precise experiments are necessary to determine g_p.