Verification of an Approximate Formula for Multiple Scattering of Slow Electrons.

by H. H. Natsuyama, Robert E. Kalaba

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Verification of an approximate formula recently proposed by two Russian authors for the multiple scattering of slow electrons in a gas. This study shows how the true solution can be computed accurately and makes comparisons to determine the range of validity of the approximate formula. For the precise calculation of the reflected flux, the reflection function r(z, u, x) is introduced in analogy with radiative transfer theory, and r is computed very accurately as the solution of an initial value problem for ordinary differential equations. Then the reflected flux is computed via quadrature and compared with the Russian formula. It is found that the approximate formula for the reflected flux is remarkably accurate and may be useful for predicting average reflected densities. The distribution function at the top, however, is poorly represented in the Russian formulation. Regarding internal distribution, it is concluded that the cosine pattern is found for medium to great thickness, while the cosine pattern is a poor approximation for thinner media. 16 pp. Refs.

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