Here α = 1 / 137 is the fine structure constant, m$_{e}$ and e are the electron mass and charge, and f = √$_{2}$ F . Note that this expression vanishes, indeed, either if − kF $^{2}$k 2 F ⇔ k 2 ⊥ = 0 , or if − k ˜ F $^{2}$k 2 F ⇔ k 2 0 − k 2 3 = 0 , as it should in accordance with what the symmetry of the external field prescribes, as it was established in the body of this article, eqs. (47), (50). The integral (57) has an infinite number of branching points, the same as Λ$_{1}$$_{,}$$_{2}$$_{,}$$_{4}$, with singular inverse square-root behavior - the cyclotronic resonances at thresholds of electron-positron pair creation by a photon [5, 14]. However, the lowest-lying resonance is not in the point (in the variables, referring to the special frame) k 2 0 − k 2 3 = 4 m 2 $_{e}$, like in κ 2 = − Λ$_{4}$, but in the point k 2 0 − k 2 3 = [( m 2 e + 2 ef ) 1 / 2 + m$_{e}$ ] $^{2}$, like in κ 3 = − Λ$_{2}$, because this value borders the convergence domain of the τ -integration in (57). This means that the (small as compared with the magnetic) electric field cannot affect the phenomenon of the mode-2 photon capture with its adiabatic conversion into a free [20] or bound [17] electron-positron pair in the lowest Landau level. 

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