Unitarization of the BFKL Pomeron on a nucleus

We analyze the evolution equation describing all multiple hard Pomeron exchanges in hadronic or nuclear structure functions that was proposed earlier in Phys. Rev. D 60, 034008 (1999). We construct a perturbation series providing us with an exact solution to the equation outside of the saturation region. The series demonstrates how at moderately high energies the corrections to the single BFKL Pomeron exchange contribution, which are due to the multiple Pomeron exchanges, start unitarizing the total deep inelastic scattering cross section. We show that as the energy increases the scattering cross section of the quark-antiquark pair of a fixed transverse separation on a hadron or nucleus given by the solution of our equation inside of the saturation region unitarizes and becomes independent of energy. The corresponding $F_2$ structure function also unitarizes and becomes linearly proportional to $\ln s.\mathrm{}$ We also discuss possible applications of the developed technique to diffraction.