Admissible Reconstruction of Reaction-Channel Levels on Fixed Subgroup Support and Probabilities in Algebraic Probability Table Construction

This work considers admissibility-enforcing reconstruction of reaction-channel subgroup levels on prescribed total-subgroup support and probabilities, a setting in which conventional exact reconstruction may produce negative reaction-channel levels. The proposed reconstruction relaxes conventional full matching by retaining selected low-order channel quantities associated with limiting dilution responses exactly, while fitting the remaining matching conditions in a constrained least-squares sense under nonnegativity. The exact-retention constraints are embedded through a null-space parametrization, which reduces the reconstruction to a convex optimization problem over the remaining degrees of freedom. Two variants are examined: a single-retention formulation, which is automatically feasible for nonnegative retained data, and a two-retention formulation, which is more restrictive and depends on compatibility with the fixed total-subgroup rule. Numerical tests for 238U capture data show that the proposed reconstruction removes the negative reaction-channel levels observed in the violating groups. Restoring admissibility entails deterioration in response accuracy relative to the unconstrained full-matching baseline, reflecting the trade-off between exact matching and nonnegativity on the fixed rule. Of the two variants considered, the single-retention formulation shows more stable overall behavior in the present comparison. In particular, for all violating cases at orders N≥10, it restores nonnegativity, with the reported 95th-percentile relative errors in the folded effective cross section not exceeding 8.90×10−7.