  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.
