Compton shift
The wavelength shift Δλ = (h/m_e c)(1 − cos θ) of light scattered off electrons, where θ is the scattering angle. Angle-dependent, independent of the incident wavelength; first measured by Arthur Compton in 1923 with X-rays on graphite — the experiment that established photons as mechanically legitimate particles.
Definition
The Compton shift is the wavelength change Δλ = λ' − λ = (h/m_e c)(1 − cos θ) experienced by light scattered off a free or weakly-bound electron, where θ is the scattering angle and h/(m_e c) ≈ 2.426 × 10⁻¹² m is the Compton wavelength of the electron. The shift increases monotonically with angle from zero at θ = 0° (forward scattering) to its maximum 2h/(m_e c) at θ = 180° (backward scattering), and is independent of the incident wavelength — a striking departure from the classical Thomson-scattering prediction of zero shift. The formula falls out of treating the photon as a relativistic particle with four-momentum (E/c, p) where E = pc = hc/λ, applying conservation of energy and three-momentum to a billiard-ball collision with an electron initially at rest, and solving for the outgoing photon wavelength.
Arthur Compton measured the shift in 1923 at Washington University in St. Louis, scattering monochromatic Mo Kα X-rays (λ ≈ 0.071 nm) off a graphite target and recording the scattered-photon wavelength as a function of angle with a Bragg spectrometer. The data matched the photon-as-particle prediction quantitatively; classical wave theory had no mechanism to produce any shift. The 1923 paper in The Physical Review established the photon as a mechanically legitimate particle, completing the transition begun by Einstein's 1905 photoelectric paper. Compton shared the 1927 Nobel Prize with C. T. R. Wilson, whose cloud chamber had made the recoil electrons directly visible. The Compton wavelength remains the natural length scale for any scattering process where photon momentum couples to an electron's rest mass.