Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions in real time. The feasability and convenience of this approach to this particular problem has been shown in previous publications. Calculations are here improved by using more realistic interactions derived from phase-shifts by inverse scattering. Of particular interest is the effect of the strong correlations in the nuclear medium on the response. This as well as the related energy weighted sum rule, dependence on mean field and effective mass are some of the main objects of this investigation. Comparisons are made with the collision-less limit, the HF+RPA method. The importance of vertex corrections is demonstrated.