The utility of reflection and transmission function (or collectively,response function) concepts in reactor physics is extensivelyinvestigated. Previously obtained differential (invariant imbedding)and functional (adding) equations for the response functions are re-derivedin a unified manner. In addition a numerical halving techniqueis developed from the adding relations.
Existing response function calculations are summarized andextended by combining the invariant imbedding and functional equations.For deep-penetration shielding problems in slab geometry,this combined response function approach is shown to be more efficientthan conventional Monte Carlo or discrete ordinates techniques.The response function approach is also shown to be efficient for acriticality search in slab geometry. As a step toward a more generaltreatment, invariant imbedding equations are derived, but not solved,in finite cylindrical geometry.
Finally the feasibility of performing response function experimentsto obtain cross-section and criticality information is examined.The envisioned experimental set-up is described and calculations arecarried out to verify the analytical procedures, with particular emphasison the propagation of errors. Cross-sections can be determinedusing the halving scheme, which provides a theoretically soundtechnique for multiple scattering correction. Thus experiments maybe done on moderately thick slabs. Criticality parameters can beobtained from measured response functions using the criticalitysearch procedure. Because response function experiments areexpected to be relatively quick and cheap compared to present cross-sectionand critical experiments, it is concluded that responsefunction experiments should be carried out as soon as possible todetermine whether they are as useful as our analysis indicates.
