Energy-Dependent Neutron Transport Theory in Adjacent Half-Spaces

The solutions to the one-dimensional energy-dependent Boltzmann equations for two different media are shown to possess such a full-range completeness property that an arbitrary function satisfying a Hölder condition can be expanded in terms containing solutions to both equations. These solutions are given by Leonard and Ferziger. This property makes it possible to solve energy-dependent neutron transport problems for two adjacent media. In comparison with half-space problems, one must solve two more inhomogeneous Fredholm integral equations. The scheme of the extension to multilayer system is also represented. In using the multigroup method, the series solutions of the Fredholm equations are rapidly convergent, if the energy dependences of the total cross sections in both adjacent media are roughly of the same form.