Bayesian evaluation of residual production cross sections in proton-induced nuclear spallation reactions

Abstract

Residual production cross sections in spallation reactions are key data for nuclear physics and related applications. Spallation reactions are very complex due to the wide range of incident energies and abundant fragments involved. Therefore, it is challenging to obtain accurate and complete energy-dependent residual cross sections. With the guidance of a simplified EPAX formula (sEPAX), the Bayesian neural network (BNN) technique is applied to form a new machine learning model (BNN + sEPAX) for predicting fragment cross sections in proton-induced nuclear spallation reactions. Three types of sample dataset for measured residual production cross sections in proton-induced nuclear spallation reactions are made, i.e. D1 consists of isotopic cross sections in reactions below 1 GeV/u, D2 consists of fragments excitation functions of reactions up to 2.6 GeV/u, and D3 is a hybrid of D1 and D2. With the constructed BNN and BNN + sEPAX models, the isotopic and mass cross section distributions are compared for the 356 MeV/u 40Ca + p and 1 GeV/u 136Xe + p reactions, and fragment excitation functions in 40Ca + p, 56Fe + p, 138Ba + p and 197Au + p reactions. It is found that the BNN model needs sufficient information to achieve good extrapolations, while the BNN + sEPAX model performs better extrapolations based on less information due to the physical guidance of the sEPAX formulas. It is suggested that the BNN + sEPAX model provides a new approach to predict the energy-dependent residual production cross sections produced in proton-induced nuclear spallation reactions of incident energies from tens of MeV/u up to several GeV/u.