Critical assessment of mean field models based on effective interactions

Mean field schemes, from simple Hartree–Fock plus random phase approximation calculations of the ground and excited states to more sophisticated approaches which include pairing as well, have been popular for quite a long time. In these models, the input is an effective interaction. We still lack a precise link between this interaction and a more fundamental theory; however, there have been various new recent attempts to correlate empirical pieces of evidence about nuclear (and neutron) matter, or experimental results, with the properties of the effective interactions. In this contribution, we claim that, while we have indeed made some progress in our understanding of certain features of the interactions, we are still missing a clue about its proper density dependence and about its isovector properties.