Local charge radius relations based on neutron shell effects

In this paper, we obtained the mean mass density parameter (MMDP) [Formula: see text] based on the nuclear mass AME2020 and nuclear charge radius CR2013 databases. On this basis, we study the dependence relationship between neutron number N and the two neighboring isotopes MMDP difference [Formula: see text], and then obtained the empirical formula for [Formula: see text]. By combining this empirical formula with the AME2020 and CR2013 databases, the root-mean-square deviation (RMSD) for 606 nuclear charge radii with [Formula: see text] 21 between the calculated and experimental values is 0.0046[Formula: see text]fm. Considering the odd–even staggering and isospin term correction, the study found that the RMSD is reduced to 0.0040[Formula: see text]fm. This work also uses Levenberg–Marquart (L-M) neural network approach to study the nuclear charge radius. The RMSD of nuclear charge radius is only 0.0030 fm, where the accuracy is increased by about 25%. Furthermore, the predicted values of nuclear charge radius obtained using this modified empirical formula and Neural Network model are competitive with the results of other models. These results indicate that nuclear charge radius relation and Neural Network model based on [Formula: see text] proposed in this work have a certain accuracy, simplicity and reliability.