Nonsequential multiple ionization, where two or more electrons are ripped off the atom by the laser field in one coherent process, has attracted much interest for over a decade. Representative references include for experimental data and [7-16] for theoretical work; the not-too-recent work is covered in the review articles. Unlike above-threshold ionization (ATI) or higli-harmonic generation (HHG), this process cannot proceed in the absence of electron-electron correlation. Moreover, this correlation affords a sizeable premiu n for collaboration between the two electrons: for optimal laser intensities, the ratio of nonsequential over sequential double ionization, which materializes in the famous "knee", can be as high as six orders of magnitude. Until about a year ago, experimental data were restricted to the total yields. Recently, however, application of the COLTRIMS (cold-target recoil-ion-momentum spectroscopy) technique has allowed for the determination of the (three-dimensional) momenta of the ion and the electrons so that now the completely differential ionization rate has become accessible. Early on, rescattering was identified as a promising candidate for the physical mechanism of nonsequential double ionization (NSDI), the same mechanism that is known to be responsible for ATI and HHG. However, serious quantitative problems with this scenario precluded its acceptance until recently. This problem has now been revisited and appears to have been reso ved. More and more, rescattering is emerging as the dominant mechanism, but depending on the atomic species and the laser intensity, others may be required in addition. Thus far, there are only few theoretical results for the momentum distributions in NSDI and even fewer explicit calculations. The intense-field many-particle 5-matrix theory which has successfully reproduced many data for the total yields has been extended to calculations of the differential rates. A calcu-lationally simpler version of essentially the same model yields similar results in those parameter regimes where it is applicable. There is also a simulation on the basis of the time-dependent Schroedinger equation in one dimension for each electron. Much can be learned already from purely classical kinematical considerations along the lines of the so-called simple-man model of intense -laser atom processes. In this paper, we present a simple fully quantum-mechanical model hat is able to predict the momentum distributions for any given scenario, such as sequential ionization, nonsequential ionization via rescattering, or nonsequential ioniza-tion via rescattering into an excited state followed by tunneling. The absolute yield for a given scenario cannot be predicted, but its intensity dependence can. Most importantly, different scenarios generate very different momentum distributions. Comparison of the calculated with the measured momentum distributions then can support or discredit the respective scenario.
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