A Classical and Semi-analytical Analysis of Isotropic Scattering of Neutrons through a Protective Wall of Iron-via Two Energy Groups-for Two Examples of Thicknesses

We introduce and present a deterministic and semi-analytical method for doing transport analysis on neutrons and isotropically scattering ‘hard' photons which are placed in 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. An inspection of 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. Although it is more lengthy, our algorithm and formulation is much more complete than the popular formula used among radiologists of Intensity x B E x Intensity exp x ( ) = ,0 ( ) • ( ) (−µ ).