Kinematic Change in Conduction-Electron Density of States Due to Impurity Scattering. I. The Problem of a Single Impurity

For conduction-electron-impurity scattering the conduction-electron density of states is calculated by making use of the thermodynamical Green's-function technique with particular respect to its spatial structure. If the interaction depends on the momenta of the scattered waves in such a way that it is important only in the neighborhood of the Fermi surface (characterized by the corresponding energy width Δ), a coherence length can be introduced: ξ_Δ=vFΔ, where vF is the Fermi velocity. Present experimental data obtained for different Kondo systems can be interpreted as yielding 5-50{} for ξ_Δ. The spatial variation of the change in the electron density of states is found to be as follows: (a) In the short-range region rξ_Δ, the change is negative definite because of the interference between the incoming and outgoing scattered waves, and (b) in the long-range region rξ_Δ, it shows the Friedel oscillation. The results are expressed also by a phase shift δ. Only the amplitude of change in the electron density of states depends on the scattering amplitude; however, the spatial structure is unaffected.