Lepton pair production by a high energy photon in a strong electromagnetic field

Using the impact-factor representation, we consider lepton pair production by an incident high energy photon in the strong electromagnetic field of a nucleus. By summing leading terms of the perturbation series, we obtain a simple formula for the amplitude, valid to all orders in $\mathcal{O}\left(\alpha Z\right)$ and an arbitrary field of the nucleus. Using these results, we derive, in a simple manner, the results for lepton pair production by a virtual incident photon in a Coulomb field. For a real incident photon our results coincide with the known ones. Also, a particular example of a non-Coulomb potential is discussed in some detail.