核散裂和弹核碎裂反应中余核产生的贝叶斯神经网络预测模型

Predicting Model for Fragment Production in Nuclear Spallation and Projectile Fragmentation Reactions by Bayesian Neural Network

核散裂反应和炮弹碎裂反应中的余核产生截面是核反应理论和实验中的重要问题。为了提高核散裂和弹核碎裂反应中余核(尤其是靠近滴线的稀有同位素)产生截面的预测,本文介绍了基于贝叶斯神经网络方法的两类预测模型。一类是无物理模型引导的BNN模型,另一类是有物理模型引导的BNN+模型。结果发现BNN模型需要学习充足的信息量,才能拥有较好的预测能力。而BNN+模型既能继承物理模型的优点,又能弥补该模型的缺陷。在同样少的样本数据下,BNN+模型仍具有很好的预测能力。

Fragment productions in spallation reactions and projectile fragmentation reactions are important topics in nuclear reaction both theoretically and experimentally,which find important applications in fundamental nuclear physics,radioactive ion beam facilities,nuclear waste disposal,medical isotopes production,etc.Besides the many models to predict the fragment productions,such as the transport model,empirical parametrizations or formula,machine learning models have been constructed to predict fragment cross-sections in proton induced spallation reactions and projectile fragmentation reactions.In this paper,the recently proposed models using Bayesian neural network(BNN)models were introduced for precise prediction of fragments,especially for extreme rare isotopes with large isospins in nuclear spallation and projectile fragmentation reactions.Two types of models were introduced,i.e.[KG-*3],the BNN models which were constructed based on massive learning to experimental data,and the physical model guided BNN+models which were constructed based on massive learning to the differences between measured data and physical model predictions.The simplified EPAX(sEPAX)formula and the FRACS formulas were adopted as the physical model to guide the BNN+model for spallation reaction(BNN+sEPAX)and projectile fragmentation reaction(BNN+FRACS),respectively.The BNN and BNN+models have the structure of one input layer with key parameters related to the reaction,one hidden layer with optimized numbers of neural nodes and one output layer.For the numbers of learning data set,it was 15370 measured fragments in the proton induced nuclear spallation reactions and 6393 measured fragments in the projectile fragmentation reactions.It is found that the machine learning models provide new type of predictive models for nuclear reactions besides the physical models.The BNN model needs sufficient information to achieve good prediction ability,while the BNN+model can inherit the advantage of the physical model and make up for the defects of the physical model,which makes it achieve good predictive ability when known data are insufficient.The predicted results show that the BNN and BNN+models have high predictions to fragments cross-sections in spallation reactions smaller than 136 Xe within an incident energy range from tens of MeV/u to a few GeV/u,and projectile fragmentation reactions for projectile from 40 Ar to 208 Pb within the range of incident energy from tens of MeV/u to 1 GeV/u.Particularly,the BNN model for projectile fragmentation reaction predicts a 0.46 fb compared to the experimental estimation 0.5 fb for 39 Na isotope in the 345 MeV/u 48 Ca+9Be reaction,indicating it is capable for high quality prediction to near drip-line isotopes.