A Theory of Multiple Scattering of Waves in a Random Medium

概要

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A theory of the multiple scattering of waves or particles interacting with a system of many scatterers in a medium is developed. A relationship between the total field and the effective field or the field seen by a given scatterer is obtained in a self-consistent manner using the Feenberg-Feshbach perturbation method. A configurational averaging procedure is applied to a wave equation to derive an equation obeyed by the coherent total field, which is in turn expressed by partial or conditional averages of the total field with one or more scatterer positions held fixed. A formal solution for such a set of hierarchy equations is ob-tained by introducing the mass operator, which is expressed in the form of continued frac-tions involving an effective transition operator and many-scatterer correlation functions. An equation for the effective transition operator is obtained in a self-consistent manner. It is shown that results thus obtained can be applied to the case of strong or dense scatterers as well as that of weak or dilute scatterers. Various approximate expressions are obtained for the mass operator and the effective transition operator, which, when using approximation procedures of lower orders, reduce to the results obtained previously. As an application, a brief discussion of the index of refraction of the medium is given.
理論物理学刊行会の論文
1969-12-25