Testing the photon--photon sector of quantum electrodynamics with free-electron lasers

Bright short-wavelength free-electron lasers with a high repetition rate may allow for experimental tests of the photon--photon sector of quantum electrodynamics. Since the relevant cross sections are optimal for photons with an energy of the order of the electron rest mass, Compton backscattering of the free-electron-laser electron beam is suggested to generate intense photon beams in this energy range that are then brought to head-on collision. The rates for photon--photon scattering, electron--positron pair creation by two and three photons, and harmonic production in Compton backscattering are estimated. Chances of experimental verification may be highest for pair creation by two photons (the Breit--Wheeler process)