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

TL;DR

This paper compares Monte Carlo and deterministic methods for modeling the multiple scattering of neutrons and photons in rectangular targets, demonstrating rapid convergence in simple geometries relevant to radiative dosimetry and shielding.

Contribution

It introduces a Monte Carlo evaluation of a Fredholm integral equation for scattering flux and compares it with a deterministic iteration method.

Findings

Monte Carlo method shows rapid convergence for flux and current.

The approach is effective for simple geometries in radiative dosimetry.

Kernel-based estimation captures angular dependence accurately.

Abstract

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.