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An analytic description of laser-assisted electron-atom scattering (LAES) inan elliptically polarized field is presented using time-dependent effectiverange (TDER) theory to treat both electron-laser and electron-atom interactionsnon-perturbatively. Closed-form formulas describing plateau features in LAESspectra are derived quantum mechanically in the low-frequency limit. Theseformulas provide an analytic explanation for key features of the LAESdifferential cross section. For the low-energy region of the LAES spectrum, ourresult generalizes the Kroll-Watson formula to the case of ellipticpolarization. For the high-energy (rescattering) plateau in the LAES spectrum,our result generalizes prior results for a linearly polarized field valid forthe high-energy end of the rescattering plateau [A.\,V. Flegel \textit{et al.},J. Phys. B \textbf{42}, 241002 (2009)] and confirms the factorization of theLAES cross section into three factors: two field-free elastic electron-atomscattering cross sections (with laser-modified momenta) and a laserfield-dependent factor (insensitive to the scattering potential) describing thelaser-driven motion of the electron in the elliptically polarized field. Wepresent also approximate analytic expressions for the exact TDER LAES amplitudethat are valid over the entire rescattering plateau and reduce to thethree-factor form in the plateau cutoff region. The theory is illustrated forthe cases of $e$-H scattering in a CO$_2$-laser field and $e$-F scattering in amid-infrared laser field of wavelength $\lambda=3.5\,\mu$m, for which theanalytic results are shown to be in good agreement with exact numerical TDERresults.

Analytic description of elastic electron-atom scattering in an elliptically polarized laser field