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It has been long recognized that radiation transport theory is the foundationfor the planning and analysis of X-ray (gamma-ray) radiation therapy and forimaging. In less common but appropriate occasions as an alternative to X-raysor gammas, neutron radiation is used in oncological treatments or in imaging ofpatients. The following work is also potentially of interest to RadiationSafety Planners. Especially in regard to uses for neutron beams, we introduceand present a deterministic and semi-analytical method for doing transportanalysis on neutrons and which are judiciously set to be distributed into twoenergy groups. There are advantages for doing such 2-group and highermulti-group analysis of radiative particles (i.e. neutrons and photons). Theseadvantages are that we can more directly keep track of what percentages ofradiative particles are close to the original high energy and how many are atsignificantly lower energy. For photons, the profile of any build-up functionshows that the function is slightly larger than 1.0 at entry, then it rises toperhaps 2 or 3 within roughly one mean free path of the fast primary particles,and finally approaches the asymptote of 1.0 as the penetration depth getsprogressively larger. Neutrons deserve a separate treatment. Although it islengthier, our algorithm and formulation is much more complete than the popularformula used among radiologists where exponential decay is modified with abuildup coefficient. Moreover, a buildup function for neutron fluxes do notappear to be widely offered in radiological and radiation safety publications.This paper demonstrates a method to predict the ratio of high energy (circa 1MeV) neutrons over low energy neutrons (in a group below 0.201 MeV) which arescattered backwards and forwards out of walls of Fe-56 at various thicknesses.

Two-Group Flux Analysis of Neutrons which enter, internally scatter, and  often escape a Shielding Layer of Iron -- with respective Group Settings  circa one MeV and kilo-eV