Uncertainties of responses calculated with a "tuned" library: Geometrical and algebraic insights

The standard American evaluated nuclear data library ENDF/B-VII was "tuned" based on simple measured critical assemblies. This tuning was not done according to a fully defined mathematical algorithm, such as the adjustment algorithm. In this work, we investigate how tuning affects the uncertainties (covariances) of the cross-section libraries. First, we analyze what happens to cross-section uncertainties as a result of adjustment. The effect of adjustment on the uncertainties is geometrically demonstrated for simple cases. For those parts of the sensitivities of the assembly to be calculated that are parallel to the sensitivities of the assemblies on which adjustment was based, there is significant reduction in the uncertainties. For orthogonal parts, there is no change in the uncertainties. These findings are algebraically proven based on the adjustment algorithm. Then we analyze the differences between tuned libraries and adjusted libraries. We conclude that for tuned libraries, the uncertainties in the direction of sensitivities on which adjustment or tuning were based are improved, similar to the improvement for an adjusted library. However, the displacement of the nominal values of the library parameters to their tuned value, instead of their adjusted value, adds an additional uncertainty. This additional uncertainty is typically small in the direction that was improved by adjustment. The magnitude of the additional uncertainty in perpendicular directions depends on the particular details of the tuning performed.