Interplay of tensor correlations and vibrational coupling for nuclear single-particle states

In this contribution we introduce, for the first time, a fully microscopic approach to particle-vibration coupling (PVC) based on the use of the Skyrme effective interactions. The capability of these forces to describe single-particle states in atomic nuclei, is a longstanding issue; it is certainly clear that the fragmentation of the single-particle strength lies beyond any mean field framework. After describing the formalism on which our microscopic approach is based, we discuss few preliminary results for 40Ca and 208Pb. Some perspectives are presented.