Iteration models and elastic reactions beyond the diffraction peaks

We investigate the consequences of the assumption that elastic reactions are described in a large domain of energy and transfer momentum by an iteration model. We use a method which leads to a simple and general approximation of the iteration-model amplitudes at intermediate momentum transfer ($0.5\lesssim \mathrm{}\left|t\right|\mathrm{}\lesssim 10$ ${\mathrm{GeV}}^2$). Using this approximation, we obtain a good description of the available data on hadron-hadron elastic scattering at different energies. A study of the generating "Born term" of the iteration series can be performed directly from the intermediate-momentum-transfer analysis. At low energy, it is compatible with Regge-pole models with exchange-degenerate Regge trajectories. At very high energy, however, one has to add to the Pomeron singularity a new real contribution. We study the implications of this real contribution which will serve as a test for the iteration approach.