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Multiple Scattering and Radiation Damping. II
Phys. Rev. 89, 490 – Published 15 January, 1953
DOI: https://doi.org/10.1103/PhysRev.89.490
Abstract
The analysis of multiple elastic scattering by a system of fixed scatterers in terms of two-body collision matrices is extended to large bodies. The dynamical theory of particle wave propagation in crystals is formulated and discussed from this viewpoint, as an extension of Ewald's theory to scatterers of finite size. A theory of wave propagation in a random medium, including disordered crystals, is obtained as the limiting case for a crystal with infinite unit cell. Contrary to the usual approach, this analysis considers a definite "frozen" configuration of the medium; statistical averaging over configurations may be used on the intensities obtained.
In crystals and dense liquids, radiation damping is compensated by the reaction of surrounding scatterers. Therefore, it is found convenient to restate the basic equations of multiple scattering in terms of a matrix which is essentially the Green's function for the single scattering event, with "standing wave" rather than "outgoing wave" boundary conditions. This has the advantage of eliminating the spurious radiation damping terms at the outset; one obtains nonattenuated waves in nondissipative crystals or dense liquids by a simple expansion method.
Application is made to the following problems: the equivalent of the Lorentz-Lorenz formula for matter waves; index of refraction for an interaction of the form of a one-level Breit-Wigner formula; attenuation of long waves in a disordered crystal containing protons with random spins; double refraction effect in a liquid or crystal containing protons with partially oriented spin.
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