Compton scattering (or the Compton effect) is the quantum theory of scattering of a high-frequency photon through an interaction with a charged particle, usually an electron. Specifically, when the photon interacts with a loosely bound electron, it releases the electron from an outer valence shell of an atom or molecule.

The effect was discovered in 1923 by Arthur Holly Compton while researching the scattering of X-rays by light elements, which earned him the Nobel Prize in Physics in 1927. The Compton effect significantly deviated from dominating classical theories, using both special relativity and quantum mechanics to explain the interaction between high frequency photons and charged particles.

Photons can interact with matter at the atomic level (e.g. photoelectric effect and Rayleigh scattering), at the nucleus, or with only an electron. Pair production and the Compton effect occur at the level of the electron. When a high-frequency photon scatters due to an interaction with a charged particle, the photon's energy is reduced, and thus its wavelength is increased. This trade-off between wavelength and energy in response to the collision is the Compton effect. Because of conservation of energy, the energy that is lost by the photon is transferred to the recoiling particle (such an electron would be called a "Compton recoil electron").

This implies that if the recoiling particle initially carried more energy than the photon has, the reverse would occur. This is known as inverse Compton scattering, in which the scattered photon increases in energy.

In Compton's original experiment (see Fig. 1), the energy of the X-ray photon (≈ 17 keV) was significantly larger than the binding energy of the atomic electron, so the electrons could be treated as being free after scattering. The amount by which the light's wavelength changes is called the Compton shift. Although Compton scattering from a nucleus exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis and further verified by his graduate student Y. H. Woo in the years following. Compton was awarded the 1927 Nobel Prize in Physics for the discovery.

The effect is significant because it demonstrates that light cannot be explained purely as a wave phenomenon. Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain shifts in wavelength at low intensity: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength. Thus, if we are to explain low-intensity Compton scattering, light must behave as if it consists of particles. Or the assumption that the electron can be treated as free is invalid resulting in the effectively infinite electron mass equal to the nuclear mass (see e.g. the comment below on elastic scattering of X-rays being from that effect). Compton's experiment convinced physicists that light can be treated as a stream of particle-like objects (quanta called photons), whose energy is proportional to the light wave's frequency.

As shown in Fig. 2, the interaction between an electron and a photon results in the electron being given part of the energy (making it recoil), and a photon of the remaining energy being emitted in a different direction from the original, so that the overall momentum of the system is also conserved. If the scattered photon still has enough energy, the process may be repeated. In this scenario, the electron is treated as free or loosely bound. Experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the BKS theory.

Compton scattering is commonly described as inelastic scattering. This is because, unlike the more common Thomson scattering that happens at the low-energy limit, the energy in the scattered photon in Compton scattering is less than the energy of the incident photon. As the electron is typically weakly bound to the atom, the scattering can be viewed from either the perspective of an electron in a potential well, or as an atom with a small ionization energy. In the former perspective, energy of the incident photon is transferred to the recoil particle, but only as kinetic energy. The electron gains no internal energy, respective masses remain the same, the mark of an elastic collision. From this perspective, Compton scattering could be considered elastic because the internal state of the electron does not change during the scattering process. In the latter perspective, the atom's state is changed, constituting an inelastic collision. Whether Compton scattering is considered elastic or inelastic depends on which perspective is being used, as well as the context.