Variance Budgeting for Probability Tables in the Unresolved Resonance Region

Resonance self-shielding in the unresolved resonance region (URR) is driven by the variance of the cross-section distribution, which probability tables are designed to represent. This paper identifies two mechanisms by which standard nuclear data processing distorts this variance. First, the multiplicative normalization used to enforce mean consistency between the probability table and the evaluated cross section inadvertently rescales the variance. Second, when the evaluated cross section carries resonant structure within a probability table energy bin, the transport code sees both this within-bin structure and the full probability table fluctuation content, double counting the variance. A variance-preserving affine transformation is derived that enforces the evaluated mean while preserving the variance and is extended to a per-reaction variance-budgeting methodology applicable when the evaluated cross section carries within-bin structure. The method is implemented in NJOY/PURR and validated through a controlled 235U transmission study. Integral benchmarks using the HEU-MET-INTER-011 suite show that standard processing overpredicts the URR self-shielding reactivity worth by approximately 150% relative to the variance-preserved result, demonstrating that the effect is quantitatively significant for the ENDF/B-VIII.1 235U evaluation.