  We address the question of how to improve the agreement between theoretical
nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly
magic nuclei, the SPEs can be deduced from spectroscopic properties of odd
nuclei that have one more, or one less neutron or proton. Theoretically, bare
SPEs, before being confronted with experiment, must be corrected for the
effects of the particle-vibration-coupling (PVC). In the present work, we
determine the PVC corrections in a fully self-consistent way. Then, we adjust
the SPEs, with PVC corrections included, to empirical data. In this way, the
agreement with experiment, on average, improves; nevertheless, large
discrepancies still remain. We conclude that the main source of disagreement is
still in the underlying mean fields, and not in including or neglecting the PVC
corrections.
