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Properties of single-particle states in a fully self-consistent particle-vibration coupling approach

The properties of single-particle states in the magic nuclei $^{40}$Ca and $^{208}$Pb, in particular the energies, spectroscopic factors and the effective mass, have been studied in a fully self-consistent particle-vibration coupling (PVC) approach within the framework of Skyrme energy density functional theory. All selected phonons are obtained by the Random Phase Approximation and the same Skyrme interaction is also used in the PVC vertex. We focus on the effect of the non-central two-body spin-orbit and tensor interactions on the single-particle properties. It has been found that the contributions of those terms are important to improve the results of $^{208}$Pb. The calculated single-particle energies and spectroscopic factors are compared to available experimental data. The single-particle level density around the Fermi surface is significantly increased due to the effect of PVC.