On the basis of taking into account the interaction between a photon and a complex electromagnetic field consisting of a combination of the field of a wave and a homogeneous magnetic field, the process of e$^{-}$ e$^{+}$ pair formation is investigated. The case of the two-photon formation of an electron-positron pair with the propagation of photons in opposite directions in an external magnetic field H is analyzed In detail. A correction is obtained to the Breit-Uiler cross section in the limit H ≪H$_10$ ~ 10 $^{13}$ G. It is shown that the magnitude of this correction depends significantly on the energy of the interacting photons and changes sign at an energy h$_ω$ ~ 1,33 mc$^{2}$.
Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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