The systematics of muon capture in an independent-particle shell model

Abstract

The total muon capture rate has been calculated in a closure approximation for a large number of heavy nuclei. The nuclear model chosen is that of A independent particles ( Z protons and N neutrons) in the ground state of an infinite spherical well potential. This model correctly reproduces the low neutrino momentum behavior deduced by Foldy and Walecka but leads to values of the total capture rate in disagreement with experiment. The values predicted for the weak interaction coupling constants assuming reasonable values for the average momentum of the emitted neutrinos are about two-thirds of the conventional values or, if one accepts the conventional coupling constants, the necessary neutrino momentum is found to be about 10% less than one would expect. The possible causes of this and previous discrepancies are discussed, and it is concluded that difficulties associated with nuclear physics (the closure approximation and the choice of a proper shell-model potential and an appropriate average neutrino momentum) are the most likely sources of error. The effect of the radial variation of the muon wave function on the capture rate is examined closely and found to be less than 10% for all nuclei.