Gamma-ray production using multi-photon Compton scattering

The nonlinear Compton scattering cross-section for laser light is formulated by treating the electron in the laser field as a dressed electron, in which the laser field is expressed as classical field. In comparison, multi-photon Compton scattering can be represented by the Feynman diagram where the electron is treated as an undressed one; hence, this formula can be applied only to a low intensity laser. To study the effect of the coherency of the photon on Compton scattering, these two formulas were compared for the case of two-photon scattering. The difference might be due to the fact that the Feynman formula cannot take into account the coherency of the photon. To account for the coherency of a laser field in quantum mechanics, therefore, the formula based on coherent-state formalism is required.