Spectrum and Asymmetry of Direct Neutrons from Muon Capture in Calcium

The energy spectrum and asymmetry of neutrons emitted directly on the capture of polarized muons by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been calculated in a simple nuclear shell model, taking account of terms proportional to the nucleon momentum. The energy spectrum is within the error brackets of recent experiments with the nucleon-momentum terms making a small contribution. The asymmetry coefficient is strongly affected by the inclusion of the momentum-dependent terms and is found to change sign and increase in magnitude with increasing energy, in qualitative agreement with recent experiments.