A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle st
ates (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.
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 n
eutron 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.
