Nonperturbative gluon radiation and energy dependence of elastic scattering

The energy dependence of the total hadronic cross sections is caused by gluon bremsstrahlung which we treat nonperturbatively. It is located at small transverse distances about 0.3 fm from the valence quarks. The cross section of gluon radiation is predicted to exponentiate and rise with energy as s(delta) with delta = 0.17+/-0. 01. The total cross section also includes a large energy independent Born term which corresponds to no gluon radiation. The calculated total cross section and the slope of elastic scattering are in good agreement with the data.