Laser-assisted inelastic scattering of electrons by helium atoms

The differential cross section for electron-impact excitation of helium atoms in the presence of a linearly polarized laser field is calculated. The interaction of the laser field with both the projectile electron and the target atom is treated in a fully nonperturbative way, while the electron-atom interaction is treated within the first Born approximation. We are interested in studying two cases where the photon energy of the laser field is chosen to be far from resonance and when it matches with 2(1)S -> 2(1)P and 3(1)S -> 3(1)P transition frequencies. The agreement between perturbative and nonperturbative results is good, except close to the resonance where the perturbative cross sections diverge while the nonperturbative ones predict no maximum of the cross sections. Another interesting effect is the presence of an avoided crossing of the Floquet pseudoenergies at resonance.