Coulomb corrections to the Delbrueck scattering amplitude at low energies

TL;DR

This paper investigates Coulomb corrections to Delbrueck scattering at low photon energies, using relativistic Green functions, revealing a few percent correction for high-Z nuclei and comparing different calculation methods.

Contribution

It provides a novel calculation of Coulomb corrections to Delbrueck scattering using the exact relativistic Green function approach at low energies.

Findings

Coulomb corrections are a few percent for large nuclear charge.

Results agree with magnetic loop contributions to the g-factor.

Discrepancies found with dispersion relation calculations.

Abstract

In this article, we study the Coulomb corrections to the Delbrueck scattering amplitude. We consider the limit when the energy of the photon is much less than the electron mass. The calculations are carried out in the coordinate representation using the exact relativistic Green function of an electron in a Coulomb field. The resulting relative corrections are of the order of a few percent for scattering on for a large charge of the nucleus. We compare the corrections with the corresponding ones calculated through the dispersion integral of the pair production cross section and also with the magnetic loop contribution to the g-factor of a bound electron. The last one is in a good agreement with our results but the corrections calculated through the dispersion relation are not.