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

TL;DR

This paper introduces a comprehensive theoretical approach for calculating Delbrück scattering amplitudes to all orders in lpha Z, incorporating Coulomb corrections via the Dirac-Coulomb Green's function, and compares results with the Born approximation.

Contribution

The paper develops a novel analytical method for precise Delbrück scattering calculations including Coulomb corrections to all orders.

Findings

Coulomb corrections increase the Delbrück amplitude by a few percent.

The method achieves accurate results with reasonable computational effort.

Comparison with the Born approximation shows significant deviations at studied energies.

Abstract

We present a theoretical method to calculate Delbr\"uck scattering amplitudes. Our formalism is based on the exact analytical Dirac-Coulomb Green's function and, therefore, accounts for the interaction of the virtual electron-positron pair with the nucleus to all orders, including the Coulomb corrections. The numerical convergence of our calculations is accelerated by solving the radial integrals that are involved analytically in the asymptotic region. Numerical results for the collision of photons with energies 102.2 keV and 255.5 keV with bare neon and lead nuclei are compared with the predictions of the lowest-order Born approximation. We find that our method can produce accurate results within a reasonable computation time and that the Coulomb corrections enhance the absolute value of the Delbr\"uck amplitude by a few percent for the studied photon energies.