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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. @S0163-1829~99!50542-0# The motion of light particles in metals is a topic of fundamental interest since it involves the interaction of simple, singly charged units ~positive muons: m 1 ), with electrons and nuclei belonging to the metals. The goal of the theoretical investigation to be described here is to provide a consistent model for the screening of m 1 which is the basic input in the following three ~i‐iii! important areas of the topic. i. At low temperatures, where these light particles ( m m .mp/9 in proton mass! may still be mobile, their diffusion is dominated by quantum tunneling between lattice sites. 1 Specifically, copper and aluminum fcc metals are well suited for detection of muon diffusion because of the large nuclear moments of target atoms, which give rise to strong depolarization effects when the muons move slowly enough. 2 In 1984, Kondo recognized the crucial role of conduction electrons in the diffusion process. 3 It turns out that one should take into account the overlap of two many-body ground states with the same local, screened potential at different sites ~characterized by a distance a )o fm 1 in the electron gas. 4‐6 The overlap parameter @K(a)# is related to the scattering phase shifts ( d l) of electrons, caused by this screened potential, at the Fermi energy p F /2 ~we use atomic units e 2 5me5\51 throughout!. The small-distance ( pFa!1) behavior is expressed as 5,6

Consistent model for the screening of slow muons in metals