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The paper presents a model of high-energy hadron-hadron scattering where each hadron is a fully absorbing scatterer with a radius that increases with energy. The energy dependence of the radius is chosen such that the total cross section has the energy behavior of the Froissart bound (which means that the cross sections are rising to infinity). The model is used to obtain amplitudes for pion-nucleon scattering.
Hadron-hadron and hadron-nucleus interactions are investigated in the framework of the Reggeon field theory with critical and supercritical pomerons and multiple scattering theory. A good agreement is obtained with experimental data on cross sections of proton-proton and proton-nucleus interactions at high energies.