Reflection and Transmission by a Strongly Absorbing Slab

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Abstract
Reflection and transmission of monoenergetical particles with a known ingoing distribution by a strongly absorbing slab is studied from the numerical standpoint. Various approximation methods based on known theoretical solutions are presented: in section III we propose an approximation based on Chandrasekhar X and Y functions; in section IV we obtain the reflection and transmission by using a variational technique, and we show that a successive-collision technique gives identical results; and in section V we propose a diffusion-like approximation, with adjusted coefficients, of the form The first approximation gives good results for low c values; the second one, for high c values. The diffusion-like approximation, however, is accurate to more than 2% for all values of c between 0.1 and 0.9. Moreover it is far easier to compute than any of the former ones.

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