A Two-Region Problem in Time-Dependent Monoenergetic Neutron Transport Theory. I. Analysis

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence. The general result is expressed mainly as a sum of definite, multiple integrals. Certain simplifications were possible at the interface and these are explicitly noted.