Why is the diffraction peak a peak?

It is proved that the high-energy differential cross section for an elastic process has a maximum exactly in the forward direction and that the slope of the diffraction peak is at most (log s)/sup 2/. The widths of the diffraction peaks defined by the absorptive part and the differential cross section are compared. The assumptions are that the amplitude is dominated by the even signature amplitude and that the total cross section, if it decreases, decreases less fast than s/sup -1/2/. Strictly speaking, the results hold only for a sequence of energies approaching infinity. The proofs are given for the spin-O- spin-O case, but it is not unreasonable to hope that they can be generalized to arbitrary spins. (13 refs).