Effect of particle-vibration coupling on single-particle states: A consistent study within the Skyrme framework

We discuss calculations of the single-particle states in magic nuclei, performed within the particle-vibration coupling (PVC) approach by using consistently the Skyrme effective interaction. The vibrations are calculated within fully self-consistent random-phase approximation and the whole interaction is also used in the PVC vertex. Our main emphasis is therefore the discussion of our results in comparison with those in which some approximation is made. The perspectives for improving current density functional theory (DFT) calculations are also addressed.