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We present a theoretical method to calculate Delbr\"uck scatteringamplitudes. Our formalism is based on the exact analytical Dirac-CoulombGreen's function and, therefore, accounts for the interaction of the virtualelectron-positron pair with the nucleus to all orders, including the Coulombcorrections. The numerical convergence of our calculations is accelerated bysolving the radial integrals that are involved analytically in the asymptoticregion. Numerical results for the collision of photons with energies 102.2 keVand 255.5 keV with bare neon and lead nuclei are compared with the predictionsof the lowest-order Born approximation. We find that our method can produceaccurate results within a reasonable computation time and that the Coulombcorrections enhance the absolute value of the Delbr\"uck amplitude by a fewpercent for the studied photon energies.

Calculations of Delbr\"uck scattering to all orders in $\alpha Z$