Predictions of nuclear charge radii and physical interpretations based on the naive Bayesian probability classifier

Abstract

Background: The nuclear charge radii provide direct information for the nuclear structures. In recent years, many pioneering researches have been devoted to the nuclear charge radii based on the Bayesian neural networks (BNN) method. Purpose: The neural networks always have complex structure. To analyze the data relationships clearly, a statistical method is introduced to study the nuclear properties by combining the sophisticated nuclear models with the naive Bayesian probability (NBP) classifier. Method: In the framework of the NBP method, the predicted charge radii are interpreted as the most reasonable expectations. The prior probabilities and the condition probabilities are computed by the experimental data and the raw results of nuclear models. The posterior probabilities of expectations are updated by the Bayesian formula. The predicted charge radii are regarded as the expectations with maximum probability. Moreover, the abilities of global optimizations and extrapolations of the NBP method are analyzed to demonstrate the availability of the NBP method. Results: For the HFB model and the semiempirical formula, the accuracy of charge radii predictions improves 41% and 32% after NBP refinements, respectively. Calculations also illustrate that the NBP method has robust extrapolating abilities, and the charge radii of unknown regions in the nuclear chart can be predicted by the NBP method. Conclusions: The NBP method contains the advantages of local relations and global descriptions, which can provide fine-tuning for the theoretical results of sophisticated nuclear models. The method proposed in this paper can also be used for other research of nuclear properties.