**Thomson Scattering** (also known as **electron scattering** or **coherent scattering**) is the elastic scattering of electromagnetic radiation by a free charged particle (not necessarily an electron). A single, isolated electron cannot absorb a passing photon (see [[No Isolated Emission]]), but it can scatter it into some other direction. This classical treatment of the electron-photon scattering makes the following assumptions: - Elastic scattering (i.e. no energy loss in photon) - The photon energy is much smaller than the mass-energy of the particle (Equivalently, the wavelength of the light is much greater than the Compton wavelength of the particle, so quantum effects can be ignored). - The electron is non-relativistic. In the low energy limit, it is the same as [[Compton Scattering]]. > [!note] Thompson Cross Section > The interaction cross section is independent of frequency, and is given by... > > $\sigma_{T} = \frac{8 \pi}{3} \left( \frac{e^{2}}{4 \pi \epsilon_{0} m c^{2}} \right)^{2} = \frac{8 \pi}{3} \left( \frac{\alpha \lambda_{c}}{2 \pi} \right)^{2}$ > > ...where $\alpha \simeq 1/137$ is the fine-structure constant and $\lambda_c$ is the Compton wavelength of the particle. > > $\alpha \equiv \frac{1}{4 \pi \epsilon_{0}} \frac{e^{2}}{\hbar c} \simeq \frac{1}{137} \hspace{2cm} \lambda_{c} \equiv \frac{2 \pi \hbar}{m c} = \frac{h}{m c}$ > > Because the Thomson scattering cross-section is so small, electron scattering is usually not an important contributor to the total [[Optical Depth#Opacity|opacity]]. It dominates only at very high temperatures, where the other sources tend to decrease. ^cross-section