A Two-Region Problem in Time-Dependent Monoenergetic Neutron Transport Theory. II. Applications

Using an exact transport solution, numerical calculations of interface flux and current are made for a plane burst of neutrons introduced at the boundary separating two semi-infinite media. Asymptotic flux expressions for large time at the interface are also presented, and these have the exponential dependence given by diffusion theory. Following the neutron burst, the interface current is found to change directions once, at most. The magnitude of the interface current is shown to depend initially on the difference in scattering cross sections of the half-spaces and asymptotically on the difference in absorption cross sections. In the special case of identical half-spaces, diffusion theory yields a more accurate representation of the flux than does P₁ theory, although for long times both approximate solutions rapidly approach the exact result.