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Low-energy (20 eV) free electrons produced in above-threshold ionization have been scattered by an intense optical standing wave (the Kapitza-Dirac effect). At intensities of 10^13 to 10^14 W/cm^2 there is very high momentum transfer between the standing-wave "lattice" and the electrons (1000). In this regime, the scattering rate approaches the optical frequency, and the electron motion is most easily analyzed by classical mechanics.
Bucksbaum et al. (Mon,) studied this question.