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

Abstract

It has been long recognized that radiation transport theory is the foundation for the planning and analysis of X-ray (gamma-ray) radiation therapy and for imaging. In less common but appropriate occasions as an alternative to X-rays or gammas, neutron radiation is used in oncological treatments or in imaging of patients. The following work is also potentially of interest to Radiation Safety Planners. Especially in regard to uses for neutron beams, we introduce and present a deterministic and semi-analytical method for doing transport analysis on neutrons and which are judiciously set to be distributed into two energy groups. There are advantages for doing such 2-group and higher multi-group analysis of radiative particles (i.e. neutrons and photons). These advantages are that we can more directly keep track of what percentages of radiative particles are close to the original high energy and how many are at significantly lower energy. For photons, the profile of any build-up function shows that the function is slightly larger than 1.0 at entry, then it rises to perhaps 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 gets progressively larger. Neutrons deserve a separate treatment. Although it is lengthier, our algorithm and formulation is much more complete than the popular formula used among radiologists where exponential decay is modified with a buildup coefficient. Moreover, a buildup function for neutron fluxes do not appear to be widely offered in radiological and radiation safety publications. This paper demonstrates a method to predict the ratio of high energy (circa 1 MeV) neutrons over low energy neutrons (in a group below 0.201 MeV) which are scattered backwards and forwards out of walls of Fe-56 at various thicknesses.