Phenomenological charge-dependent forces in atomic nuclei

The Nolen-Shiffer anomaly is studied along with double Coulomb differences (mass differences of mirror nuclei which differ by two nucleons). It is shown that calculating these differences one must take into account renormalization of the Coulomb amplitude due to polarization of the closed shells and the ''effect of tails'', i.e. the difference between proton and neutron single-particle functions. Both effects were ignored by authors of earlier papers on the subject. It has turned out that the latter effect is especially important, its sign being dependent upon the character of the density dependence of the amplitude respondible for pairing. Phenomenological non-Coulomb charge-dependent forces, which make it possible to eliminate the Nolen-Shiffer anomaly, enable one to reproduce simultaneously double-Coulomb differences only making an assumption that the amplitude corresponds to the surface pairing