Multi-photon interactions in lepton photo-production on nuclei at high energies

We study multi-photon effects in quantum electrodynamics in lepton photo-production on heavy nuclei and nuclear medium at high energies. We are interested in energy, charge density and nuclear geometry dependence of the cross sections. We use the impact parameter representation that allows us to reduce the problem of photo-production to the problem of propagation of electric dipoles in the nuclear Coulomb field. In the framework of the Glauber model we resum an infinite series of multiphoton amplitudes corresponding to multiple rescattering of the electric dipole on the nucleus. We find that unitarity effects arising due to multi-photon interactions are small and energy-independent for scattering on a single nucleus, whereas in the case of macroscopic nuclear medium they saturate the geometric limit of the total cross section. We discuss an analogy between nuclear medium and intense laser beams.