Stopped Muon Decay Lifetime Shifts due to Condensed Matter

Up to second order in alpha, vacuum electro-magnetic corrections to weak interaction induced charged particle lifetimes have been previously studied. In the laboratory, stopped muon lifetimes are measured in a condensed matter medium whose radiation impedance differs from that of the vacuum. The resulting condensed matter corrections to first order in $\alpha $ dominate those vacuum radiative corrections (two photon loops) which are second order in alpha.