Decay of Bound Muons

The decay rate of bound muons from the $K$ shell is calculated for elements up to lead. The muon is represented by a relativistic wave function for a point nucleus with parameters adjusted for finite-nuclear-size effects. The outcoming electron is represented by a Sommerfeld-Maue wave function. The decay rate is found to be a monotonically decreasing function of the atomic number. An estimate of the error is obtained by comparing with an exact calculation for the lowest electron angular state. The spectrum and angular distribution of the electrons are also presented.