Discrete ordinates cross-sections generation in parallel plane geometry -- 1: Concept

Cross-section formulations derived from the linear Boltzman transport equation have been the subjects of several studies. In these studies, theoretical foundations and concepts are provided, and the solution techniques are derived. The author presents new methods for generating cross-section sets for transport problems, with an arbitrary scattering anisotropy of order L (L ≤ N - 1), approximated by the SN (and PN-1) methods. The formulations require knowledge of the eigensolutions, which may be determined by a recent eigenvalue equation found in Yavuz. The motivation for this study is to generate few-group cross sections for pin cells (and/or assemblies) using a Monte Carlo code, for example, MCNP, with a continuous-energy cross-section library. However, this work is a first step, and it describes a new concept to perform inverse transport calculations, provided that the surface Green's functions over desired angular and energy intervals are known