New charge radius relations for atomic nuclei

We show that the charge radii of neighboring atomic nuclei, independent of atomic number and charge, follow remarkably very simple relations, despite the fact that atomic nuclei are complex finite many-body systems governed by the laws of quantum mechanics. These relations can be understood within the picture of independent-particle motion and by assuming that neighboring nuclei have similar patterns in the charge density distribution. A root-mean-square (rms) deviation of 0.0078 fm is obtained between the predictions in these relations and the experimental values, i.e., a precision comparable modern experimental techniques. Such high accuracy relations are very useful to check the consistence of the nuclear charge radius surface and moreover to predict unknown nuclear charge radii, while large deviations from experimental data are seen to reveal the appearance of nuclear shape transition or coexsitence.