Perturbation theory for the effects of impurities on simple metals

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Abstract
If the impurity pseudopotential is small, standard perturbation theory can be used to describe the effects of a dilute concentration of impurities on the conduction electrons of a simple metal. Thus, a unified approach to the calculation of scattering and of changes in energy and wavefunctions is achieved. A discussion of the relative size of the perturbation terms for all sizes of impurity potential shows that the results of the free-electron gas model need be modified only when an electron is near a Brillouin zone boundary. The results for the change in energy depend on the configuration of the impurities. We correct the results of earlier theories, and contrast them with our approach. When the impurity potential is large, scattering theory has to be used, but the results have the same form, the t-matrix replacing the impurity pseudopotential. The change in the Fermi surface is shown to be that predicted by the rigid-band model; calculations are in reasonable agreement with experiment. The spin-flip scattering of conduction electrons by impurities in copper is enhanced because the neck wavefunctions are p-like. The results of the theory agree with experiment within experimental error. The origin of anisotropy in electric-field gradients is also discussed.