The diffusion of charged heavy particles in metals is discussed by the method of the density matrix, extending the Kagan-Klinger theory to include electron-particle interaction. This method can be applied to both cases of band-like and hopping-like diffusions. The diffusion of the particles at low temperatures is determined by electron-particle scattering and the overlap integral between two electron clouds situated at different sites. The overlap integral between two electron clouds is extended to the system with two partial wave components of T-matrix at each site.
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Yamada et al. (1986) studied this question.
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