Microscopic optical model potentials for elastic hadron-nucleus scattering usually take the form of a convolution of a two-body effective interaction with the target ground-state mixed density. Within the Brueckner-Bethe-Goldstone g-matrix approach for the effective interaction, nuclear medium effects are made explicit by means spatial integrals throughout the bulk of the nucleus. In this contribution we discuss a novel and exact approach to track down the manifestation of intrinsic nuclear medium effects. After examining the momentum-and coordinate-space structure of a two-body effective interaction-spherically symmetric in its mean coordinate-it is demonstrated that the intrinsic medium effects in the optical potential depend solely on the gradient of a reduced interaction. This feature implies the confinement of intrinsic medium effects to regions where the density varies most, i.e. the nuclear surface. This finding may be of special significance in the study of nuclear collisions sensitive to the peripheric structure of nuclei. We illustrate some of its implications in the context of 10Be + p elastic scattering at 39.1A MeV.