  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 states (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.
