The scattering of electromagnetic radiation such as X-rays by free charged particles, especially electrons, when the photon energy is small compared with the energy equivalent to the rest mass of the charged particle. The energy lost by the radiation is accounted for by classical theory as a result of the radiation emitted by the charged particles when they are accelerated in the transverse electric field of the radiation. It is named after Sir Joseph John Thomson, who calculated an expression for this process in 1906.