The Scattering of Waves by Dislocations

An exact solution is given for scattering by the potential ρ -1 in two dimensions. This is compared with the results of the first and second Born approximations for the same potential in an analysis similar to that of Dalitz for the Coulomb potential r -1 in three dimensions. Seeger and Bross have shown that, in the scattering of conduction electrons by an edge dislocation, the second-order terms diverge logarithmically with increase of the radius of the cylinder in which the potential of the dislocation is assumed to act. Similar logarithmic terms appear in the second Born approximations for the potentials r -1 and ρ -1 , and, following Dalitz, reasons are given for believing that they represent a phase shift produced by the refraction of the incident and scattered waves, and that they do not contribute to the scattered amplitude. The cross sections for scattering by a dislocation are probably never much greater than those given by the first Born approximation, and may even be smaller. It is not possible to deduce the large values suggested by some experimental observations.