We discuss and enlarge upon a very neat and succinct relation proposed
recently by Giffon, Predazzi and Samokhin, linked to the behaviour of
elastic scattering at asymptotically high energies. We demonstrate th
at their result, which was established within a limited class of possi
ble asymptotic behaviours, is actually extremely general and can be pr
oved in an essentially axiomatic framework. We discuss how this relati
on can be used as a basis for detecting new phenomena at RHIC and LHC
energies. (C) 1997 Elsevier Science B.V.