Constraints, limits and extensions for nuclear energy density functionals

In the present contribution, we discuss the behavior of Skyrme forces when they are employed to study both neutron stars and giant resonance states in 208Pb within the fully self-consistent Random Phase Approximation (RPA). We point out that clear correlations exist between the results for the isoscalar monopole and isovector dipole resonances (ISGMR and IVGDR), and definite quantities which characterize the equation of state (EOS) of uniform matter. We propose that the RPA results or, to some extent, the mentioned EOS parameters, are used as constraints when a force is fitted. This suggestion can be valid also when the fit of a more general energy density functional is envisaged. We use our considerations to select a limited number of Skyrme forces (10) out of a large sample of 78 interactions