Delbrück scattering above the pair production threshold: Going beyond the Born approximation

Abstract

We present a theoretical method to calculate Delbrück scattering amplitudes for photon energies above the electron-positron pair production threshold. The method is based on the application of the relativistic Dirac-Coulomb Green function and describes the interaction of the virtual $e^{+}{e}^{-}$ pair with the Coulomb field of a target to all orders in the coupling strength parameter $\hat{I}\pm Z$. To illustrate the application of the developed approach, detailed calculations have been performed for the scattering of 2.754~MeV photons off bare ions with a wide range of nuclear charge numbers. Results of these calculations clearly indicate that the higher-order terms beyond the Born approximation lead to a strong enhancement of the imaginary part of the Delbrück amplitude and have to be taken into account for the analysis and guidance of gamma-ray scattering experiments.