Delbrück scattering calculations

The cross section for elastic scattering of photons on a static Coulomb potential, Delbrück scattering, is calculated in the lowest-order Born approximation. Using conventional Feynman techniques and gauge invariance we obtain expressions for the real and imaginary parts of the scattering amplitude for polarized photons. These rather complicated expressions contain multidimensional integrals which have been evaluated partly by analytical and partly by numerical methods, and Delbrück amplitudes have been obtained for various scattering angles and for photon energies $\omega$ varying from zero to several GeV. The results confirm earlier calculations at very low energies ($\omega \ll 1$ MeV), confirm the imaginary parts but disagree with the real parts previously obtained by Ehlotzky and Sheppey for $\omega <20\mathrm{}$ MeV, and confirm the high-energy results of Cheng and Wu to lowest order. A comparison with some recent experiments is shown.