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 neighboring nuclei having similar pattern 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 comparable precision as modern experimental techniques. Such high accuracy relations are very useful to check the consistence of nuclear charge radius surface and moreover to predict unknown nuclear charge radii, while large deviations from experimental data is seen to reveal the appearance of nuclear shape transition or coexsitence.
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