Mathematical Behavior and Computation of Transmission Probabilities for Annular Regions

One convenient way of treating neutron transport problems is to use the transmission probability method. For cylindrical geometry consisting of many annular subregions, this method can be formulated in terms of T/sub i//sup OO/, the transmission probability from the outer-to-outer surface of the i-th annulus, and T/sub i//sup OI/, the transmission probability from the inner-to-outer surface of the i-th annulus. The quantities T/sub i//sup OO/ and T/sub i//sup OI/ are extremely complex functions of r/sub i-1//r/sub i/, the ratio of the inner-to-outer radius, and the optical path length r/sub i/..sigma../sub ti/ for region i. The latter quantity can have a wide range of values in the problems of practical interest. This paper describes new improved methods for treating these transmission probabilities of the basis of their indiviual mathematical properties. These improved methods have three objectives: to provide a rigorous treatment of the asymptotic behavior of these functions which is currently lacking in the MC/sup 2/-2 code; to provide a separate treatment of T/sub i//sup OO/ and T/sub i//sup OI/ according to their distinct functional dependences; to eliminate the two-dimensional tables currently in use to obtain these functions in the MC/sup 2/-2 code. 2 figures.