Neutron Double-Differential Cross Sections for Spallation Reactions from an ANN Model

Abstract

In this paper, we present a data-driven artificial neural network (ANN) model for describing the double differential cross sections (DDCS) of neutron emission in nuclear spallation reactions. The ANN model is found to be precise, flexible, and efficient in predicting differential cross sections of nuclear reactions and in learning the complex dependence of neutron DDCS on the projectile energy ($T_p$), target nucleus ($A$ and $Z$), neutron energy ($T_n$), and neutron emission angle ($θ_n$). The model is trained on replicas of experimental data that incorporate uncertainties. Several regularization schemes are examined during ANN training. The input variables of the constructed ANN framework are also investigated, and the following six key variables are selected for the input layer of the ANN model: $θ_{n}$, ${\rm log}(T_n/T_p)$, $T_n/T_p$, ${\rm log}(T_p)$, $A^{2/3}$, and $N/Z$. The ANN predictions are compared with training data provided by various experimental collaborations, showing excellent agreement. The resulting model is further tested on test data with projectile energies, target nuclei, and neutron emission angles different from those in the training data, indicating strong predictive power and generalization capability of the ANN framework. As an illustration, the neutron DDCS as functions of $T_n$, $θ_n$, and projectile energy $T_p$ are predicted and presented for copper target. The proposed high-precision ANN model is expected to be beneficial for accelerator-driven system (ADS) design and many other applications in nuclear physics, astrophysics, and nuclear technology development.