Electron Scattering from a Standing Light Wave

Abstract

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 ${10}^7$ W/${\mathrm{cm}}^2$ the probability equals ${sin}^2{a}_{0}t$, where $a_0$ is proportional to the intensity. At intensities of the order of ${10}^9$ W/${\mathrm{cm}}^2$, 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.