Theory of the Kapitza-Dirac Diffraction Effect

We treat the Kapitza-Dirac diffraction effect observed recently by Batelaan et al. using a newly developed nonperturbative quantum-field scattering theory. Our theory shows that an electron beam passing perpendicularly through a focused standing light wave can produce diffraction patterns. Our theory predicts (1)the minimum value of the ponderomotive energy is (ℏω)²/m_ec², (2)the critical laser intensity above which the first pair of electron diffraction peaks will occur, and (3)the existence of sidebands in the electron spectra separated far from the central band by a momentum of several hundred photons. Our theory provides a unified explanation of the experimental results of Bucksbaum et al. and Batelaan et al.