Coulomb and rescattering effects in above threshold ionization

We present a generalization of the strong-field approximation S-matrix theo ry, which includes both, the Coulomb and rescattering effects. The Coulomb effects are responsible for a considerable increase (about two orders of ma gnitude) of the ionization rates, while the rescattering effects give rise to the appearance of the second plateau of the above threshold ionization s pectrum. Coulomb effects change the behavior of the rates at the first plat eau, but they do not influence the qualitative behavior of the spectrum of the high-energy electrons in the second plateau. Our results are in excelle nt agreement with recent experiments [Walker, B., Sheehy, B., Kulander, K.C ., and DiMauro, L.F., 1996, Phys. Rev. Lett., 77, 5031]. Our theory predict s the correct position of the cutoff in the energy spectra for different an gles between the ionized electron momentum and the polarization vector of t he laser field. The sidelobes are also at the right positions and we show t hat these positions correspond to the last rounded top before the cutoff of above threshold ionization spectra for the corresponding angle. We have al so confirmed the experimentally observed sharp minima in the ATI spectra at some fixed energies, and explain this by quantum interference effects. Our model is simple and can be easily generalized to different inert gases.