  Parameterizations of the pp scattering data at the LHC collision energies
indicate a hollow in the inelasticity profile of the pp interaction, with less
absorption for head-on collisions than at a non-zero impact parameter. We show
that some qualitatively unnoticed features may be unveiled by a judicious
application of the inverse scattering problem in the eikonal approximation and
interpre- tation within an optical potential model. The hollowness effect is
magnifed in a 3D picture of the optical potential, and will presumably be
enhanced at yet higher energies. Moreover, in 3D it sets in at much smaller
energies than at the LHC. We argue that hollowness in the impact parameter is a
quantum effect, relying on the build-up of the real part of the eikonal
scattering phase and its possible passage through $\pi/2$. We also show that it
precludes models of inelastic collisions where inelasticity is obtained by
naive folding of partonic densities.
