Analysis and Monte Carlo Modelling of Multiple Scattering of a Beam of Neutrons or Photons off of the Two Surfaces of a Broad Material Target as a Function of its Thickness

We consider the scattering of neutrons and photons on solid volume rectangular targets. It is common to treat this problem using the Maxwell Boltzmann Transport Equation and to use underlying symmetries to simplify the calculation. For isotropic scattering centers we can introduce a direct Fredholm integral equation approach to finding the flux. Here we compare a Monte Carlo evaluation of the resulting Fredholm equation to a deterministic iteration method of solution. We include a kernel based method for estimating the overall angular dependence. We find that for simple geometries utilized in studies of radiative dosimetry, of neutron shielding assessments, and indirectly of criticality that we get reasonably rapid convergence of flux and current values.