Electron – atomic-hydrogen elastic collisions in the presence of a laser field

We study the ``elastic'' scattering of fast electrons by atomic hydrogen in the presence of a laser field. Our method takes into account the ``dressing'' of the target states by including the laser-atom interaction to first order, while the laser-projectile interaction is treated to all orders. This allows us to treat laser fields which, although weak compared to the atomic unit of field strength, can nevertheless be strong by laboratory standards. In the limit of weak fields our results reduce to those obtained recently by a perturbative approach (in the laser-projectile interaction) for all laser frequencies.