Study of single-photon Compton scattering process of bound electrons in intense laser fields by using frequency-domain theory

Compton scattering is defined as an inelastic scattering process in which the interaction between strong laser fields and electrons in matter leads to photon emission. In recent years, with the rapid development of X-ray free-electron lasers, the intensity of X-ray lasers has steadily increased, and the photon energy in Compton scattering process has risen correspondingly. Previous studies focus on single-photon Compton scattering of free electrons. However, the mechanism of non-relativistic X-ray photon scattering by bound electrons remains to be elucidated. Therefore, we develop a frequency-domain theory based on non-perturbative quantum electrodynamics to investigate single-photon Compton scattering of bound electrons in strong X-ray laser fields. Our results show that the double-differential probability of Compton backscattering decreases with the increase of incident photon energy. This work establishes a relationship between Compton scattering and atomic ionization in high-frequency intense laser fields, thereby providing a platform for studying atomic structure dynamics under high-intensity laser conditions.