Solution of the Initial-Value Transport Problem for Monoenergetic Neutrons in Slab Geometry

Abstract

The initial-value transport problem of monoenergetic neutrons migrating in a thin slab is solved by applying the normal-mode expansion method of Case to the results of Lehner and Wing. Fredholm integral equations are derived for the expansion coefficients. In addition, exact expressions for the eigenvalues of the problem are derived and the results of calculations are presented. The solution is shown to have properties expected from elementary diffusion theory.