Neural-network–based algorithm for the inverse problem of measuring K-shell ionization cross-sections of Si induced by 3–25 keV electrons and 4.5–9 keV positrons using the thick-target method

Abstract In this study, a neural network method is proposed for solving the inverse problem in the measurement of inner-shell ionization cross-sections using the thick-target method. It was applied to calculate the K -shell ionization cross-section of silicon (Si) from positron impacts in the energy range from 4.5 to 9 keV, using a Monte Carlo simulation program called PENELOPE to construct a comprehensive characteristic X-ray yield and cross-section database, serving as a foundation for training the neural network. The experimental values are compared with those obtained using regularization, yield differential, and distorted-wave Born approximation (DWBA) theoretical models. Our findings reveal that the cross-section results obtained from all three algorithms are in good agreement with the theoretical DWBA values within the error range. Moreover, our study highlights the superiority of the neural network algorithm in solving ill-posed problems, compared with traditional regularization algorithms and the yield differential method. Furthermore, we re-analyse the experimental data of electron-induced ionization cross-sections on a pure thick Si target in the energy range from 3 to 25 keV, which were originally obtained by Zhu et al . who used a regularization method. The reprocessed cross-sections obtained in this study exhibit good agreement with the reported results within the error range. To the best of our knowledge, this is the first experimental report of the K -shell ionization cross-sections of Si from positron impact.