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We consider the process of electron-ion recombination in a powerful laser field and investigate the spectrum of emitted x-ray radiation. This process is of interest in the interaction of laser radiation with gaseous or solid targets in connection with harmonic and coherent x-ray production. The process is treated in the framework of the inverse Keldysh-Faisal-Reiss model describing the ingoing electron either by a Gordon-Volkov wave or by a Coulomb-Volkov solution. Even for higher energies of the impinging electrons, considerable Coulomb effects are recognized. We evaluate the rates of the generated x-ray field and determine the energy range of its spectrum. The maximum photon energy achieved by this process is estimated by ប X ϭE p ϩU p ϩ͉E B ͉ ϩ2ͱ2U p E p , with E p being the kinetic energy of the ingoing electron, U p the ponderomotive energy, and E B the binding energy. The equivalence of the two models for the zero-range interaction is also shown.

An explanation of discrepancies between predictions of the Kroll-Watson theory and cross sections measured in the Wallbank-Holmes experiments on electron-atom scattering in the presence of a powerful lowfrequency laser field is presented. Our model calculations for helium and argon as target atoms come out to be in good agreement with experimental results; i.e., obtained cross sections are by many orders of magnitude larger than those predicted by the Kroll-Watson theory. A mechanism responsible for such a substantial increase of the calculated cross sections is found to be due to the diffraction scattering of electrons by atomic obstacles. ͓S1050-2947͑97͒50912-7͔ PACS number͑s͒: 34.50.Rk, 32.80.Ϫt, 03.65.Nk RAPID COMMUNICATIONS R4396 56 A. JAROŃ AND J. Z. KAMIŃ SKI

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