Self-consistent description of single-particle levels of magic nuclei

Single-particle levels of seven magic nuclei are calculated within the energy density functional (EDF) method by Fayans et al. [ Nucl. Phys. A 676, 49 (2000)]. Three versions of the EDF are used, the initial Fayans functional, DF3, and its two variations, DF3-a and DF3-b, with different values of spin-orbit parameters. Comparison is made with predictions of the Skyrme-Hartree-Fock method with the HFB-17 functional. For the DF3-a functional, phonon coupling (PC) corrections to single-particle energies are found self-consistently with an approximate account for the tadpole diagram. Accounting for the PC corrections improves the agreement with the data for heavy nuclei, e. g., for Pb-208. On the other hand, for lighter nuclei, e. g., Ca-40,Ca-48, PC corrections make the agreement a little worse. As estimations show, the main reason is that the approximation we use for the tadpole term is less accurate for light nuclei.