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Background. The root-mean-square charge radii are the important characteristics of atomic nuclei which might be measured experimentally. In this research, we study the experimental data on the root-mean-square charge radii of the spherical nuclei available in the literature. The purpose of this analysis is to establish what is the manifestation of the neutron shells in the considered observable and to find regularities in the behavior of the charge radii when a shell is crossed. Materials and methods. The present analysis is performed by means of calculation of the relative charge radius for a given element x = x (N, Nsh , Z ). This value is equal to the charge radius of an isotope with neutron number N over the charge radius of the isotope t with the closed neutron shell N = Nsh . Results. As the result, we have found manifestation of the shells Nsh = 8, 28, 50 and 82. It turns out that the well-known shells with the neutron numbers 20 and 126 do not show up. Conclusions. It is shown that the values of relative charge radius form groups corresponding to different values of Nsh . On the basis of the revealed regularity, the charge radius is predicted for isotope 30 S which is absent among the experimental data.