The Thermal-Neutron Milne Problem and the Albedo of a Semi-Infinite Absorbing Medium-I: Theory

The Milne problem for thermal neutrons is studied with an arbitrary scattering kernel, using concepts derived from the invariant imbedding method. An eigen-value equation for the Milne leakage current is given and an expression for the flux inside the medium expressed in terms of the Milne leakage current and the reflection operator is found. Though no unique definition of the extrapolation length exists in the general case, a very simple expression for the extrapolation length of the scattering rate is given.