  By examining the structure in momentum and coordinate space of a two-body
interaction spherically symmetric in its local coordinate, we demonstrate that
it can be disentangled into two distinctive contributions. One of them is a
medium-independent and momentum-conserving term, whereas the other is
functionally --and exclusively-- proportional to the radial derivative of the
reduced matrix element. As example, this exact result was applied to the
unabridged optical potential in momentum space, leading to an explicit
separation between the medium-free and medium-dependent contributions. The
latter does not depend on the strength of the reduced effective interaction but
only on its variations with respect to the density. The modulation of radial
derivatives of the density enhances the effect in the surface and suppresses it
in the saturated volume. The generality of this result may prove to be useful
for the study of surface-sensitive phenomena.
