Cluster model anisotropic electron lifetimes in different approximations. Consequences of the neglect of backscattering and the use of the Born approximation

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Abstract
The consequences of the neglect of backscattering and the Born approximation for the inverse lifetimes associated with impurity scattering in dilute alloys are investigated. The electronic wavefunctions and scattering rates are calculated for clusters in free space with a maximum size of three shells of atoms surrounding the central scatterer. Host cluster electron states are scattered by an impurity cluster, in which the central scatterer is an impurity. The free-space environment is a constant potential equal to the muffin-tin zero of the host potentials. This cluster-in-free-space model has been used before, but now the individual scatterers are described by spherical wells in view of the comparative design of this study. Numerical results obtained for clusters with the BCC structure and with scattering potentials of various depths show that the anisotropy of the lifetimes is adequately represented in the different approximations. However the magnitude of the lifetimes may have been changed drastically from its exact value. The use of the optical theorem for an approximate t matrix is sometimes worse than the Born approximation.

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