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