. Together with the photoelectric effect and pair production,
Compton scattering contributes to the attenuation of 
's in matter.
As the binding energy of electrons in atoms is low compared to that of passing near-relativistic particles, this is the relevant process in particle detectors.
Closely related are Thomson scattering (classical treatment of photon scattering) and Rayleigh scattering (coherent scattering on atoms).
Compton scattering has a cross-section proportional to 1/E. For a discussion, see [Leo94].