Delbr\"uck scattering above the pair production threshold: Going beyond the Born approximation

TL;DR

This paper introduces a new theoretical method using the Dirac-Coulomb Green function to accurately calculate Delbruck scattering amplitudes for photon energies above the pair production threshold, accounting for all orders of Coulomb interaction.

Contribution

It develops a comprehensive approach to compute Delbruck scattering amplitudes beyond the Born approximation, including higher-order Coulomb effects for high-energy photons.

Findings

Higher-order terms significantly enhance the imaginary part of the amplitude.

The method accurately predicts scattering for a range of nuclear charge numbers.

Results are relevant for gamma-ray scattering experiments.

Abstract

We present a theoretical method to calculate Delbr\"uck scattering amplitudes for photon energies above the electron-positron pair production threshold. The method is based on the application of the relativistic Dirac-Coulomb Green function and describes the interaction of the virtual $e^+e^-$ pair with the Coulomb field of a target to all orders in the coupling strength parameter $\alpha Z$. 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 Delbr\"uck amplitude and have to be taken into account for the analysis and guidance of gamma-ray scattering experiments.