Reciprocity Relations in Response Matrix Theory

Using the multigroup diffusion equation, a reciprocity relation is established for an arbitrarily shaped body. This relation expresses the flux caused by a source inside the body in terms of the flux resulting from an incident current on that body. In the multigroup case for one-dimensional bodies with flat sources and in the one-group case for rectangular two-dimensional bodies with an arbitrary source, practical formulas are derived from this relation. These give the leakage from a body in terms of its reflection and transmission properties. An advantage of the use of this reciprocity relation is the improved computational efficiency in response matrix calculations.