Extended theory of Kapitza-Dirac scattering

The standard theoretical treatment of the Kapitza-Dirac effect—that is, the scattering of an electron passing through a standing-wave laser field—is extended here through the use of the Pauli equation to account for the interaction of the electron spin with the magnetic field of the standing wave. Prescriptions for determining unitarity-preserving approximations for the transition probabilities for scattering both with and without rotation of the electron spin direction are provided. This formalism is used to develop a perturbation theory for the spin-flip probability which, in the strong-field limit of interest here, reduces to a fairly simple relation between S-matrix elements for scattering with and without change in spin orientation, each expressed in terms of a Bessel function. A similar perturbative procedure is applied to estimate corrections to the standard theory for scattering in the absence of spin-flip processes, in which interactions that change the net number of photons in the field are ignored.