On the Energy-Dependent Neutron Transport Problem with Arbitrary Geometry

Abstract

This paper is concerned with the stationary neutron transport problem which describes the transport of energy-dependent anisotropic scattered neutrons in a one, two, or three-dimensional inhomogeneous medium of arbitrary convex shape containing distributed source and incident neutrons. The approach to the problem is by successive approximation which leads to the existence of a unique solution as well as a recursion formula for the determination of the solution and error estimates for the approximations. In addition to the energy-dependent problem, a discussion is given to the constant-energy neutron transport and radiative transfer problems, including a slab problem. Some recursion formulas for calculating the solutions are obtained. All the formulas obtained in this paper involve only straightforward integration which offers a promising possibility for the calculation of numerical results by using a computer. A brief discussion on the calculation of approximate solutions and their errors is included.