Thomson scattering

Thomson scattering is the low-energy elastic scattering of electromagnetic radiation by a free charged particle. Before cosmological recombination, repeated photon-electron scattering couples photons to the baryon velocity and damps higher photon multipoles.

For a dilute ionized plasma with nonrelativistic electrons and photon energies well below $m_e{c}^2$, independent Thomson scattering events give photon survival probability $\exp (-n_e{\sigma }_{T}s)$ over proper distance $s$. Its mean gives the displayed mean free path. The scattering rate is ${\Gamma }_{\gamma }=n_e{\sigma }_{T}c$. Photons are tightly coupled when this rate greatly exceeds the Hubble parameter; photon decoupling becomes possible as the free-electron fraction falls. Frequent elastic scattering does not by itself imply chemical equilibration of the photon number.

Coherent Thomson scattering by cold electrons changes a photon's direction without changing its frequency in the electron rest frame. A monochromatic incident radiation field therefore remains monochromatic after arbitrarily many such scatterings. Large scattering optical depth can isotropize radiation but does not imply a Planck photon distribution. True absorption and emission, or suitable additional inelastic processes and photon production, are needed to establish a blackbody spectrum independently of the initial radiation field.

A free nonrelativistic charge driven by a weak plane electromagnetic wave has peak acceleration $|q|E_0/m$. Its time-averaged Larmor formula power is $q^4{E}_0^2/(12\pi {ϵ}_0{m}^2{c}^3)$. Divide by incident light intensity ${ϵ}_{0}c{E}_0^2/2$ to obtain the displayed cross section, independent of frequency. For an electron, it is $8\pi r_e^2/3$. The approximation assumes negligible Compton recoil kinematics and small driven velocity compared with the speed of light.