Eikonal theory of charged particle potential scattering in the presence of a low frequency laser field

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Abstract
An eikonal treatment for elastic scattering by a static potential V(r) in the presence of a low-frequency laser radiation field taken in the dipole approximation with linear polarisation is presented. The differential cross section of the scattering processes accompanied by the emission or absorption of N photons is found as a product of a Bessel function, containing the effect of the radiation field, times the field-free eikonal differential cross section with, however, initial and final wave vectors of the free particle motion duly renormalised to include the effect of the radiation field. The comparison with other treatments of the same physical process shows agreement with more sophisticated approaches and confirms once more the superiority of the eikonal approximation over the first Born approximation.