Knock-on type exchange and the density dependence of an effective interaction

We investigate the origin of the density-dependence of the strength of an effective interaction previously derived from a Brueckner-Hartree-Fock calculation of the optical-model potential in nuclear matter. From the analysis of a model based on the Hartree-Fock approximation and on a Yukawa interaction with a Majorana exchange component, we study to what extent this dependence derives from the momentum-dependence of the exchange contribution of the knock-on type. The model is also used to discuss zero-range pseudopotential methods for including this knock-on contribution.