# Relativistic Dynamics of the Compton Diffusion on a Bound Electron

## TL;DR

This paper develops a covariant relativistic formalism for Compton scattering on bound electrons, providing more accurate predictions aligned with experimental results and enabling precise QED tests.

## Contribution

It introduces an exact Dirac equation solution for electrons in nuclear Coulomb fields to improve relativistic Compton scattering calculations.

## Key findings

- Enhanced accuracy in Compton scattering predictions.
- Agreement with experimental data for electrons in bound states.
- Foundation for precise QED cross-section calculations.

## Abstract

A covariant relativistic formalism for the electron-photon and nuclear dynamics is summarised making more accurate predictions in agreement with experiments for Compton scattering in shells with large electron binding energy. An exact solution for the Dirac equation for an electron in the nuclear Coulomb field is obtained, in order to write the relativistic dynamics for this QED process. This is a preparation for the calculation of the relativistic cross-section for Compton scattering on bound electrons; as a precision test for QED.