The second Born approximation in electron-atom collisions in the presence of a laser field

The second-order Born approximation (SBA) has been used to calculate the differential cross section for electron-hydrogen collisions in the presence of a linearly polarized laser field. We present a more precise treatment of the small-energy region of an incident electron by improving the calculation of the second Born term in this energy region. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Our SBA results agree very well with those obtained in the first-order Born approximation at larger incident electron energies