Bayesian Learning of (n,p) Reaction Cross Sections with Quantified Uncertainties

Abstract

Accurate neutron-induced $(n,p)$ reaction cross sections are essential for applications in nuclear energy, radionuclide production, materials studies, and nuclear astrophysics. However, experimental data remain sparse for many isotopes, and evaluated nuclear data libraries can show systematic deviations from available measurements. We develop a Bayesian neural network (BNN) residual learning model, denoted \texttt{BNN-R5}, to improve $(n,p)$ reaction cross-section predictions. The model uses five physically motivated nuclear descriptors and does not employ experimental or evaluated cross-section values as input features. Rather than predicting the cross sections directly, \texttt{BNN-R5} learns the log-space residual between the evaluated TENDL-2023 data and experimental measurements, thereby providing a data-driven correction to the evaluated library. The model is trained using stochastic variational inference, which provides predictive mean values together with Bayesian uncertainty estimates. Across a broad range of target nuclei, the corrected cross sections generally show improved agreement with experimental data and outperform the original TENDL-2023 evaluations. Feature-importance analysis using SHapley Additive exPlanations (SHAP) identifies the pairing term $\delta$ as the most influential descriptor, followed by the excitation-energy variable $\ln(\Delta E)$ and the neutron number $N$, while the proton number $Z$ has the smallest overall influence. These results demonstrate that Bayesian residual learning provides a robust and interpretable framework for improving evaluated nuclear data and predicting reaction cross sections in data-sparse regions of the nuclear chart.