Potential scattering in a low-frequency laser field

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Abstract
Using a classical description for the laser field, previous formulations of the low-frequency laser-assisted potential scattering theory are generalised to account for arbitrary polarisation and for spatial variations of the field amplitude. Attention is paid to providing a relatively simple derivation of the basic results, and to establishing contact with similar or more restricted results obtained within other treatments. Restricted to the first Born approximation and pure Coulomb potential, it is found that the field momentum introduces new divergences, whenever Kf-Ki+NK=0, Kf, Ki and K being, respectively, the final and initial particle wavevectors and the field wavevector. The role of the laser momentum is found to be critically important also in forward and small-angle scattering, when the transferred momentum is typically very small. Finally, the present derivation adds a new limitation to the validity of a well known formal low-frequency result.