The helicity amplitudes of high-energy photon splitting in an external Coulomb field are obtained exactly in the parameter $Z\alpha$. The consideration is based on the quasiclassical approach, valid for small angles between all photon momenta. A new representation of the quasiclassical electron Green function is exploited. General expressions obtained are analyzed in detail when the transverse momenta of both final photons are much larger than the electron mass. It is shown that, at $Z\alpha \sim 1$, Coulomb corrections essentially change the cross section as compared to the Born approximation. Screened and unscreened potentials are considered.

• Received 27 October 1997

DOI:https://doi.org/10.1103/PhysRevA.57.2325