Deep Penetration of Radiation by the Method of Invariant Imbedding

The method of invariant imbedding has been applied to neutron shielding problems in plane geometry with realistic energy and angle-dependent cross sections. The method seems to offer advantages over competing methods when the shield is heterogeneous and very thick or when the shield is composed of a very large number of different regions. Reflection and transmission equations are derived by the method of invariant imbedding and their numerical solution discussed. A simple exponential approximation is shown to work well for the solution of these equations. Results for several problems including a thick homogenous water shield and a thinner heterogeneous iron/polyethylene/iron shield are compared with results obtained by other methods.