“…As was pointed out in Refs. [50,51], there are correlations between the nuclear charge radii and the excitation energies of the first excited 2 + states, E 2 + 1 , we choose the energies E 2 + 1 as a raw input. To modulate the irregularity due to the large difference in the energies E 2 + 1 between the magic nuclei and its neighboring ones, we smooth the mass number dependence of energies E 2 + 1 by the Lorentzian function,…”