Abstract
A semi-analytical method for solving the monoenergetic transport equation with isotropic scattering in plane geometry is developed, in which the slab system is subdivided into a number of discrete space points in x, while the angular variable is treated analytically. This is equivalent to taking N to ∞ in SN theory and avoids the numerical instabilities inherent in the limiting process. General boundary conditions are introduced allowing finite multilayer slabs, cells, and shielding problems with specified incident angular distribution of neutrons to be handled by the same formalism. Analytical expressions are derived for the angular distributions, and fluxes are obtained by solving a matrix problem, where the matrix elements are integrals over rational functions of the angular variable. Computing times are comparable to low-order SN calculations.
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