BORN-FLOQUET THEORY OF LASER-ASSISTED ELECTRON-ATOM COLLISIONS

We present a non-Hermitian Born-Floquet theory of scattering of fast e lectrons by atoms in the presence of a strong monochromatic laser fiel d. The interaction of the laser field with both the incident electron and the target atom is treated nonperturbatively, while the interactio n of the incident electron with the target atom is treated in first Bo rn approximation. Fluorescence is neglected. Detailed calculations are performed for the ''elastic'' scattering of 500 eV electrons by atomi c hydrogen accompanied by the transfer of photons. The contribution of the entire spectrum of unperturbed atomic states to the dressing of t he target is exactly taken into account by performing the calculations on a complex Sturmian basis set. In the nonresonant case, and for ele ctric field strengths that are small with respect to the atomic unit, our Born-Floquet results are in agreement with those obtained using th e semiperturbative approach of Byron and Joachain (in which target dre ssing is treated in first-order perturbation theory) even at intensiti es where multiphoton ionization is nonperturbative. The Born-Floquet a pproach is particularly useful to study resonant cases, where the lase r frequency matches a transition frequency in the atom. Two such situa tions are analyzed.