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The possibility of performing the experimental research in the field offundamental physics based on the unique instrument -- European X-ray FreeElectron Laser (E-XFEL) is considered in this paper. The calculations of thereaction $\gamma + \gamma \to e^{+} + e^{-}$ cross section for gamma quantawith $E \sim~(1-100)\,\mbox{GeV}$ energy with X-ray photons are performed. Thepossibility of experimental registration of reaction $\gamma + \gamma \to e^{+}+ e^{-}$ product are reviewed. Also, the optical depth of the interactionbetween gamma-rays with the E-XFEL's photon pulses is estimated. Astrophysicalapplications are discussed.

On the possibility of research the photon-photon interaction at the European X-ray Free Electron Laser -- European XFEL