Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination

Laser-assisted electron-ion recombination is investigated with an emphasis on the spectrum of the emitted high-energy photons and its modification due to the recollision of the incident electron and the ion. Numerical results for the soft-x-ray power spectra, added up over all intermediate laser photon channels, are presented as a function of the incident electron energy for different laser field intensities. For strong laser fields, maxima, and additional structures are found in these spectra for incident electron energies of the order of magnitude of the ponderomotive energy. We show that the laser-assisted electron-ion recombination, that includes the rescattering of the electron at the ion before the recombination, is a process complementary to the well-known processes of high-order harmonic generation and high-order above-threshold ionization. All these processes can be explained, using the three-step scenario. A semiclassical analysis is presented which shows that for the laser-assisted electron-ion recombination real solutions of the saddle-point equations exist, contrary to what is found with high-order harmonic generation and high-order above-threshold ionization when only complex solutions are permitted. For low incoming electron energies, the cutoff of the emitted soft-x-ray photon energies, including the process of rescattering, is higher than in the case of the direct recombination process. The height of the rescattering plateau is 6\char21{}7 orders of magnitude lower than that of the direct process. However, for higher incident electron energies we obtain the unexpected result that the difference between the height of the rescattering plateau and the height of the direct plateau can be less than one order of magnitude.