采用厚靶法测量4~9 keV正电子碰撞Al的K壳层电离截面的神经网络反演方法

Neural Network Inversion Approaches for Measuring the K-Shell Ionization Cross Sections of Al in the Energy Range of 4~9 keV Using the Thick Target Method

摘要: 低能正负电子致原子内壳层电离截面数据对于探究阈能附近正负电子与原子的相互作用机制具有重要意义。由厚靶产额求解原子内壳层电离截面的问题是一类不适定的反问题，常见的正则化方法、微分产额法求解结果精度和稳定性不佳。本文构建了卷积神经网络模型，基于已有文献测量的4~9 keV正电子致厚Al靶K壳层特征X射线实验产额，利用蒙特卡洛程序PENELOPE模拟构建产额–截面数据集并进行训练，反演得到与实验特征X射线产额对应的实验电离截面，以解决该类问题的不适定。将反演得到的截面结果与DWBA理论模型及已发表文献采用产额微分法得到的实验截面进行比较，同时结合神经网络结构对神经网络算法的可靠性进行评估，验证神经网络算法在处理正电子碰撞原子内壳层电离数据的适用性。结果表明，MC-神经网络方法处理得到的实验截面与DWBA理论模型一致性较好。研究结果表明，MC-神经网络法在Al的K壳层电离截面反问题求解中具有良好的准确性和稳定性；该方法提供了与DWBA理论高度自洽的实验截面数据，并验证了该MC-神经网络反演框架的有效性，但其反演性能与DWBA理论模型高度相关，存在一定的局限性。

Abstract: The cross-section data of inner-shell ionization of atoms by low-energy positrons and electrons is of great significance for exploring the interaction mechanism between positrons and electrons and atoms near the threshold energy. The problem of solving the inner-shell ionization cross-section of atoms from the thick-target yield is an ill-posed inverse problem. The common regularization methods and differential yield method have poor accuracy and stability in the solution. In this paper, a convolutional neural network model is constructed. Based on the experimental yields of K-shell characteristic X-rays of thick Al targets induced by positrons of 4~9 keV measured in a published literature, a yield-cross-section dataset is constructed and trained by the Monte Carlo program PENELOPE. The experimental ionization cross-section corresponding to the experimental characteristic X-ray yield is obtained by inversion to solve the ill-posedness of this type of problem. The obtained cross-section results are compared with the DWBA theoretical model and the experimental cross-sections obtained by the yield differential method in the published literature. At the same time, the reliability of the neural network algorithm is evaluated by combining the neural network structure, and the applicability of the neural network algorithm in processing positron collision with atomic inner-shell ionization data is verified. The results show that the experimental cross-sections obtained by the MC-neural network method are in good agreement with the DWBA theoretical model. The research results show that the MC-neural network method has good accuracy and stability in solving the inverse problem of the K-shell ionization cross-section of Al. This method provides experimental cross-section data highly consistent with the DWBA theory and validates the effectiveness of the MC-neural network inversion framework, but its inversion performance is highly dependent on the DWBA theoretical model, which implies certain limitations.