Decay rate of bound muons

Abstract

The total rate and the electron energy spectrum are calculated for the decay of a negative muon bound in an atomic 1s state, using relativistic electron and muon wave functions appropriate to an extended nuclear charge distribution, and using a general local, nonderivative, decay interaction. The rate and the spectrum are computed numerically for iron, antimony, lead, and uranium, and the rate is found to be in qualitative agreement with earlier calculations. The results are compared with experiment after approximate corrections are made for energy loss by the decay electrons in the target, and for the detection threshold for these electrons. These corrections are found to explain the great reduction in the experimental ratio of bound to free muon decay rates for heavy elements, thus removing the previous theoretical-experimental discrepancy for these elements. The observed peak in the bound muon decay rate near iron is not predicted, but a consideration of possible additional contributions to the experimental decay rate suggests that the large background of low-energy gamma rays associated with the accompanying muon capture might be connected with this peak.