Book Description

Motivated by the observation that the photon asymmetry in radiative muon capture is determined by terms of 0 (1/m 2 ) in an expansion in powers of the nucleon mass m, a new calculation of radiative muon capture in 40 Ca was made which is consistent, within the standard theory, to 0(1/m 2 ) - The Hamiltonian was expanded via a Foldy-Wouthuysen reduction through 0(1/m 2 ) instead of the usual 0(1/m) to allow for the first time a calculation of the 0(1)xO (1/m 2 ) contributions to the rate. The results show that the Q(1/m 2 ) terms are definitely necessary but that the most significant ones arise from the 0 (1/m)xO (1/m) contributions which can be obtained from the usual 0 (1/m) Hamiltonian. A number of nuclear effects were also considered including an improved giant dipole resonance model and a model using Hartree-Fock wave functions including spin-orbit coupling. As in most previous calculations the ratio of radiative to ordinary rates and the photon asymmetry are relatively insensitive to the details of the model, though the absolute rates can be quite sensitive. Fits to the available data to extract the induced pseudoscalar coupling g p were also done. In an improvement to the closure approximation, the photon spectrum was expanded about the average maximum photon energy k m and the correction terms evaluated using for one a modified Thomas-Reiche-Kuhn sum rule. The resulting rate is much less dependent: on k m than the usual closure result- The ratio k m /V appropriate for closure calculations, with V the average neutrino energy, was determined and found to be approximately constant and, with correction terms included, somewhat higher than values previously used- By similar technigues a consistency relation was derived which can be solved to explicitly estimate "physical" values of km and V.