Electron Scattering from a Standing Light Wave

The transition probability for electron scattering in the Kapitza-Dirac experiment is calculated using nonrelativistic theory as a function of the time of flight t of the electron through the light beam, and as a function of the intensity. It is found that for intensities up to approximately 10⁷ W/cm² the probability equals sin²a₀t, where a₀ is proportional to the intensity. At intensities of the order of 10⁹ W/cm², the dependence of the probability on the time is more complicated but it also oscillates between zero and nearly unity as the time increases. Both first- and second-order Bragg reflections are considered as well as conditions off the Bragg maximum.