机器学习方法研究原子核的电荷半径  

Machine Learning Method in Study of Nuclear Charge Radius

作　　者：董潇旭 耿立升[1,2,3] DONG Xiaoxu;GENG Lisheng(School of Physics,Beihang University,Beijing 102206,China;Peng Huanwu Collaborative Center for Research and Education,Beihang University,Beijing 100191,China;Beijing Key Laboratory of Advanced Nuclear Materials and Physics,Beihang University,Beijing 102206,China)

机构地区：[1]北京航空航天大学物理学院,北京102206 [2]北京航空航天大学彭桓武科教合作中心,北京100191 [3]北京航空航天大学、北京先进核材料与物理重点实验室,北京102206

出　　处：《原子能科学技术》2023年第4期679-695,共17页Atomic Energy Science and Technology

基　　金：国家自然科学基金(11735003,11975041)。

摘　　要：原子核的电荷半径是表征其电荷分布范围的物理量,对理解原子核这个复杂的量子多体系统内部核子间的相互作用发挥着重要的作用。但传统的物理模型对原子核电荷半径的描述还难以令人满意,特别是对于像钙同位素链所表现出的强烈的奇偶效应类现象。近些年来,随着机器学习方法在物理学领域的广泛应用,已有多种机器学习模型用于研究原子核电荷半径,这使得原子核电荷半径的计算精度得到大幅提升。本文综述了近年来包括贝叶斯概率分类器、核岭回归模型、人工神经网络以及贝叶斯神经网络在内的机器学习方法在原子核电荷半径研究中应用的最新进展,对比了不同机器学习方法、不同训练集与不同输入对机器学习预测原子核电荷半径结果的影响,并对机器学习在原子核物理中的进一步应用进行了展望。The charge radius of an atomic nucleus describes its charge distribution,which is important for the understanding of the nucleon-nucleon interaction in medium.However,conventional physical models can not yet provide a satisfactory description of nuclear charge radii through-out the nuclear chart,especially for exotic phenomena such as the strong odd-even staggerings of the calcium isotopes.Recently,machine learning methods are widely applied to study various physical observables,such as nuclear charge radii.The applications of machine learning methods in studies of nuclear charge radii were briefly reviewed in this paper,including the naive Bayesian probability(NBP)classifier,kernel ridge regression(KRR)model,artificial neural network(ANN)and Bayesian neural network(BNN).In particular,the Bayesian neural network with six input features containing the relevant physical information,and a three-parameter phenomenological formula(NP formula)were combined to yield the so-called D6 model.It achieves a root-mean-square deviation(RMSD)between its predictions and the experimental data of 0.014 fm.It also yields the most accurate predictions for the charge radii of calcium isotopes,particularly the odd-even staggerings,which are in good agreement with the experimental data.The influence of different machine learning methods,training sets and input features on the predictions for nuclear charge radii,were compared in this work.Further applications of machine learning methods in nuclear physics are also commented.

关 键 词：原子核电荷半径 机器学习 贝叶斯神经网络 

分 类 号：O57[理学—粒子物理与原子核物理]