We discuss different approaches to the problem of reproducing the observed
features of nuclear single-particle (s.p.) spectra. In particular, we analyze
the dominant energy peaks, and the single-particle strength fragmentation,
using the example of neutron states in 208Pb. Our main emphasis is the
interpretation of that fragmentation as due to particle-vibration coupling
(PVC). We compare with recent Energy Density Functional (EDF) approaches, and
try to present a critical perspective.Comment: 7 pages. Contribution to the "Focus issue on Open Problems in Nuclear
Structure", Journal of Physics