Predictions of nuclear charge radii based on the convolutional neural network

In this study, we developed a neural network that incorporates a fully connected layer with a convolutional layer to predict the nuclear charge radii based on the relationships between four local nuclear charge radii. The convolutional neural network(CNN) combines the isospin and pairing effects to describe the charge radii of nuclei with A ≥ 39 and Z ≥ 20. The developed neural network achieved a root mean square(RMS) deviation of 0.0195 fm for a dataset with 928 nuclei. Specifically, the CNN reproduced the trend of the inverted parabolic behavior and odd–even staggering observed in the calcium isotopic chain, demonstrating reliable predictive capability.

Evolution of nuclear charge radii in copper and indium isotopes

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering(OES).The modified root mean square(rms)charge radius formula,which phenomenologically accounts for the formation of neutron-proton(np)correlations,is here applied for the first time to the study of odd-Z copper and indium isotopes.Theoretical results obtained by the relativistic mean field(RMF)model with NL3,PK1 and NL3^(*)parameter sets are compared with experimental data.Our results show that both OES and the abrupt changes across N=50 and 82 shell closures are clearly reproduced in nuclear charge radii.The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers,namely N=28 to 50 for copper isotopes and N=50 to 82 for indium isotopes.This implies that the np-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-Z isotopic chains.Also,our conclusions have almost no dependence on the effective forces.

Predictions of nuclear charge radii

In this study,we improve the relations of the charge-radius difference of two isotopes by considering a term that relates to the proton number and the parity of the neutron number.The correction reduces the root-mean-squared deviation to 0.0041 fm for 651 nuclei with a neutron number larger than 20,in comparison with experiment-al data compiled in the CR2013 database.The improved relations are combined with local relations consisting of the charge radii of four neighboring nuclei.These combinations also prove to be efficient in describing and predicting nuclear charge radii and can reflect the structure evolutions of nuclei.Our predictions of 2467 unknown nuclear charge radii at competitive accuracy,which are calculated using these two types of relations,are tabulated in the Supplemental Material.