  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.
