Thomson scattering
/ TOM-son /
Shine a gentle electromagnetic wave on a free electron and the electron jiggles in the wave's oscillating electric field; a jiggling charge radiates, so it re-broadcasts the wave in new directions. Thomson scattering is this elastic scattering of low-energy light off a free charged particle — the classical picture of light bouncing off an electron.
The incoming wave drives the charge into oscillation at the wave's own frequency; by Larmor's formula the oscillating charge re-radiates at that same frequency (hence elastic — no energy lost to the electron). Working through the driven-dipole radiation gives a total scattering cross-section independent of frequency: the Thomson cross-section sigma_T = (8 pi / 3) r_e^2, where r_e = q^2 / (4 pi epsilon_0 m c^2) is the classical electron radius. Numerically sigma_T = 6.65 x 10^-29 m^2. The scattered light is partially polarized and follows a (1 + cos^2(theta)) angular pattern.
Thomson scattering is the classical, low-energy limit of Compton scattering; it holds only when the photon energy is far below the particle's rest energy, hf << mc^2, so the electron's recoil is negligible and the frequency is unchanged. Once the photon energy becomes comparable to mc^2, recoil shifts the wavelength and you must switch to the quantum Compton (Klein-Nishina) treatment. Because sigma scales as 1/m^2, electrons scatter about 10^6 times more strongly than protons. Thomson scattering sets the opacity of ionized plasmas and shaped the last scattering of the cosmic microwave background.
The Thomson cross-section of an electron is sigma_T = 6.65 x 10^-29 m^2, the same for red light, radio waves or soft X-rays — as long as the photon energy stays far below the electron's 511 keV rest energy. It is because sigma ~ 1/m^2 that free electrons, not the far heavier protons, dominate the scattering of light in a plasma.
A free charge re-radiates the wave elastically; the cross-section sigma_T = (8 pi/3) r_e^2 is frequency-independent.
Thomson scattering is frequency-independent and elastic only in the low-energy limit hf << mc^2; once the photon energy approaches mc^2, electron recoil (Compton scattering) shifts the wavelength and this classical picture fails. Do not confuse it with Rayleigh scattering, whose omega^4 dependence comes from BOUND, not free, charges.