Although self-consistent mean-field methods, or implementations of the density functional theory for atomic nuclei, are becoming increasingly accurate, some observables are not well reproduced by those models. In particular, the fragmentation and the decay properties of both single-particle and vibrational states cannot be accounted for. Models based on the introduction of further correlations or, in other words, that go beyond the mean-field approximation, have often been discussed in the past. We have recently developed a consistent model based on the use of a Skyrme-type force without the intervention of any other ad hoc parameter. A few typical results are discussed, after we have mentioned briefly the essential features of the model. Moreover, we discuss the necessity of fitting a new force within this context, the difficulties arising because of divergences that need to be renormalized, and our roadmap for curing these divergences.