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We analyze the usefulness of the optical potential as suggested by the doublespectral Mandelstam representation at very high energies, such as in theproton-proton scattering at ISR and the LHC. Its particular meaning regardingthe interpretation of the scattering data up to the maximum available measuredenergies is discussed. Our analysis reconstructs 3D dynamics from the effectivetransverse 2D impact parameter representation and suggests that besides theonset of gray nucleons at the LHC there appears an inelasticity depletion(hollowness) which precludes convolution models at the attometer scale.

Proton-Proton On Shell Optical Potential at High Energies and the Hollownes Effect