Abstract
Under weak smoothness assumptions on the modulus of elastic scattering amplitudes in the physical region, we prove, using positivity properties of the absorptive parts, that the ratio of the widths of the diffraction peaks for reactions A+ B→ A+ B and A + B→ A + B approaches unity at infinite energy. It follows that if persistent shrinking is observed for one of the two reactions, the same must be true for the other one at sufficiently high energies.
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