  Charge radii are one of the most fundamental properties of atomic nuclei
characterizing their charge distributions. Though the general trend as a
function of the mass number is well described by the $A^{1/3}$ rule, some fine
structures, such as the evolution along the calcium isotopic chain and the
corresponding odd-even staggerings, are notoriously difficult to describe both
in density functional theories and ab initio methods. In this letter, we
propose a novel ansatz to describe the charge radii of calcium isotopes, by
adding a correction term, proportional to the number of Cooper pairs, and
determined by the BCS amplitudes and a single parameter, to the charge radii
calculated in the relativistic mean field model with the pairing interaction
treated with the BCS method. The new ansatz yields results consistent with data
not only for calcium isotopes, but also for ten other isotopic chains,
including oxygen, neon, magnesium, chromium, nickel, germanium, zirconium,
cadmium, tin, and lead. It is remarkable that this ansatz with a single
parameter can describe nuclear charge radii throughout the periodic table,
particularly the odd-even staggerings and parabolic behavior. We hope that the
present study can stimulate more discussions about its nature and relation with
other effects proposed to explain the odd-even staggerings of charge radii.
