Calibration of nuclear charge density distribution by back-propagation neural networks

Based on the back-propagation neural networks and density functional theory, a supervised learning is performed firstly to generate the nuclear charge density distributions. The charge density is further calibrated to the experimental charge radii by a composite loss function. It is found that, when the parity, pairing, and shell effects are taken into account, about 96% of the nuclei in the validation set fall within 2 standard deviations of the predicted charge radii. Moreover, the kink in charge radii on Hg isotopes has been successfully reproduced. The calibrated charge density is then mapped to the matter density and further mapped to the binding energies according to the Hohenberg-Kohn theorem. It provides an improved description of some nuclei in both binding energies and charge radii. Moreover, the anomalous overbinding in 48Ca implies that the segmental calibrations by neural networks for beyond-mean-field effects deserve further discussion.