Electron self-energy, Fermi surface changes and generalized golden rule in dilute alloys

Abstract

The decay of a travelling wave in a dilute alloy has been studied by evaluating the matrix element of the system's Green function diagonal in the state which is prepared to be the travelling wave at an initial time. This quantity has a pole at a complex energy equal to the sum of the unperturbed energy of the travelling wave and the electron self-energy. Various model systems are considered including the case that lattice distortion and charge transfer effects have to be accounted for. The imaginary part of the self-energy measures the decay, which cannot simply be described in terms of a generalized golden rule containing the system's total t-matrix. The real part is interpreted as a measure of the change of the Fermi surface on alloying while it is not equal to the level shift. The formalism allows for the conclusion that the Anderson and McMillan condition [2] for an effective medium of a scatterer in condensed matter contains an unphysical feature. An alternative prescription is proposed.