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In 1970, on purely theoretical grounds, all total hadronic total crosssections were predicted to increase without limit for higher and higherenergies. This was contrary to the conventional belief at that time. In 1978,an accurate phenomenological model was formulated for the case of proton-protonand antiproton-proton interactions. The parameters for this model were slightlyimproved in 1984 using the additional available experimental data. Since then,for thirty years these parameters have not changed. This development, includingespecially the difficult task of formulating this phenomenological model andthe comparison of the predictions of this model with later experimentalresults, is summarized.

Do we understand near-forward elastic scattering up to TeV energies?