Abstract
In this paper, the use of piecewise constant functions (PCFs) in two-angle linear transport theory to represent the scattering cross sections ([sigma]([nu]), [nu][element of][-1,1], and the angular scattering source density S[Omega], [Omega][equivalent to]([mu]pw)[element of]U, on a partition (S[sub N] or finite element discretization, for example) of the unit sphere U of directions is considered. Average oriented transition cross sections [sigma][sub tn]([plus minus], B[prime],B) describe scattering from [Omega][prime][equivalent to][mu][prime],pw [prime](equivalent of)B[prime][contained in]U to [Omega][equivalent to][mu], (pw)(equivalent of)B[contained in]U with the constraint 0<[plus minus](pw-pw[prime]) < [pi]. Unit steps [sigma][nu] = H[nu]-[gamma]) and [sigma][nu] = [delta][nu]-[gamma] are pretreated on an intrinsic [gamma] grid for the chosen partition. All [sigma][sub tn]([plus minus],B[prime]), B are derived by interpolation.
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