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.

Figure 1

(a) $\delta R_{1p-1n}(Z,N)$ for most stable nuclides. The blue solid line represents the $\delta R_{1p-1n}(Z,N)$ deduced with the empirical $A^{1/3}$ formula. (b) Dependence of the mean value of $\delta R_{ip-jn}(Z,N)$, ${\overline{\delta R}}_{ip-jn}(Z,N)$, together with its uncertainty, on the isobaric distance from stability $\varepsilon$.

Figure 2

Comparisons of predictions in nuclear charge radius and available experimental data for $Z=40$ (a) and 41 (b) isotopic chains.

Figure 3

Chart of the nuclides showing the differences (color coded, in fm) between the predictions and experimental values. The black squares indicate stable isotopes. The magic numbers are displayed by pairs of parallel lines. 325 nuclides whose rms charge radius can be predicted within an accuracy around 0.01 fm are marked by the green triangles.

Figure 4

(a) Differences between our predictions and experimental data for isotopic chains of Pb, Hg, and Pt. (b) $\delta R_{2p-1n}$ in the RMF and HFB-21 mass models with experimental data for Pb isotopes.