The differential cross section for electron-hydrogen atom collisions in the presence of a CO2 laser field is analysed as a function of the incident electron energy. We show that the criticism of the second Born treatment of elastic scattering and excitation by fast electrons is unjustified for various geometrical configurations. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion.

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.

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