Photoproduction of $e^{+}{e}^{-}$ pair in a Coulomb field near the threshold

Abstract

We consider the electron-positron pair production by a photon in Coulomb field near threshold. We obtain the analytical results for the particle energy spectrum and angular distribution exactly in the parameter $Z{e}^2/\hslash v$. We show that Furry-Sommerfeld-Maue approximation for the wave functions used by Nishina, Tomonaga and Sakata is not sufficient and leads to wrong results.