Compton scattering in the presence of coherent electromagnetic radiation

The presence of coherent electromagnetic radiation has a profound effect on the Compton scattering of x rays from electronic systems. Here, two electronic systems are considered—bound electrons in atoms and an electron gas. The scattering cross section is expressed in terms of a power series in even derivatives of the double integral of the electronic-momentum distribution function over ${\overrightarrow{\mathrm{p}}}_{\perp }$, the planar momentum vector perpendicular to $\overrightarrow{\mathrm{k}}$, the momentum transfer to the electron. It is shown that the effect offers an important experimental technique for measurements of details of electronic-momentum distribution in the scattering system.