The Equivalence of the Isotropic and Monodirectional Source Problems.

by H. H. Natsuyama, Robert E. Kalaba

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A demonstration that the solution of the problem of multiple scattering in a slab that is illuminated by parallel rays of radiation can be expressed in terms of the solution of the problem in which there are isotropic sources of radiation. The quantities of interest for the monodirectional case (the X, Y, I, S, J, and T functions) are given algebraically in terms of the b and h functions that express the internal intensities for the isotropic source problem. For I, this avoids a matrix inversion, thus overcoming a difficulty associated with the direct application of Chandrasekhar's invariance principles. This study is an extension of RM-4906-PR; the formulas given can be used with the tables of RM-4958-PR and a desk calculator to compute the standard functions for the monodirectional case. 13 pp. Refs.

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