Reflection and Transmission Functions in Reactor Physics

The utility of reflection and transmission function (or collectively, response function) concepts in reactor physics is investigated. A review of previous work is given, indicating the relation between the differential (invariant imbedding) and functional (adding) equations for the response functions. In addition, a numerical halving technique is developed from the adding relations. By combining the invariant imbedding and functional equations, an efficient calculational technique for albedo, shielding, and criticality problems in slab geometry is obtained. The feasibility of performing response function experiments to obtain cross section and criticality information is also examined. The envisioned experimental setup is described and calculations are carried out to verify the numerical procedures.