Born-Floquet theory of laser-assisted electron-atom collisions

We present a non-Hermitian Born-Floquet theory of scattering of fast electrons by atoms in the presence of a strong monochromatic laser field. The interaction of the laser field with both the incident electron and the target atom is treated nonperturbatively, while the interaction of the incident electron with the target atom is treated in first Born approximation. Fluorescence is neglected. Detailed calculations are performed for the ‘‘elastic’’ scattering of 500 eV electrons by atomic hydrogen accompanied by the transfer of photons. The contribution of the entire spectrum of unperturbed atomic states to the dressing of the target is exactly taken into account by performing the calculations on a complex Sturmian basis set. In the nonresonant case, and for electric field strengths that are small with respect to the atomic unit, our Born-Floquet results are in agreement with those obtained using the semi-perturbative approach of Byron and Joachain (in which target dressing is treated in first-order perturbation theory) even at intensities where multiphoton ionization is nonperturbative. The Born-Floquet approach is particularly useful to study resonant cases, where the laser frequency matches a transition frequency in the atom. Two such situations are analyzed.