AbstractA theoretical method to calculate Delbrück scattering amplitudes for photon energies above the electron‐positron () pair production threshold is presented. The method is based on the application of the relativistic Dirac–Coulomb Green function and describes the interaction of the virtual pair with the Coulomb field of a target to all orders in the coupling strength parameter . 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.