Transfer Problems and the Reciprocity Principle

Abstract

It is shown that the radiative transfer theorems are the consequences of a simple identity. A uniqueness theorem essential to later arguments is derived. Various results which have been called ''Reciprocity Principles'' are obtained as special cases. In plane problems, Chandrasekhar's equations for the reflection function for a haif-space are derived. These equations are used to obtain the Green's function for one velocity neutron diffusion in the same geometry. A specific reciprocity result is used to obtain the Green's function for two adjacent half-spaces. Chamdrasekhar's equations for a slab are obtained as another specialization of the general reciprocity identity together with certain invariance considerations. (M.H. R.)