Novel ansatz for charge radii in density functional theories

Abstract: 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.