Consistent model for the screening of slow muons in metals

By using a sum rule for scattering phase shifts at the Fermi level, a consistent screened potential of a slow positive muon in an electron gas is constructed. This consistent model potential is applied in the theoretical characterizations of the overlap parameter in muon quantum diffusion, the retarding force of the electron gas, and the Knight shift. Comparisons with available experimental results are made, and a good agreement is found.