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

TL;DR

This paper develops an analytic quantum mechanical framework using TDER theory to describe laser-assisted electron-atom scattering in elliptically polarized fields, generalizing previous models and confirming key factorization properties.

Contribution

It introduces closed-form formulas for LAES spectra in elliptically polarized fields, extending the Kroll-Watson formula and prior rescattering results, with analytic expressions valid across the entire plateau.

Findings

Derived formulas explain plateau features in LAES spectra.

Generalized Kroll-Watson formula for elliptic polarization.

Confirmed factorization of LAES cross section into three factors.

Abstract

An analytic description of laser-assisted electron-atom scattering (LAES) in an elliptically polarized field is presented using time-dependent effective range (TDER) theory to treat both electron-laser and electron-atom interactions non-perturbatively. Closed-form formulas describing plateau features in LAES spectra are derived quantum mechanically in the low-frequency limit. These formulas provide an analytic explanation for key features of the LAES differential cross section. For the low-energy region of the LAES spectrum, our result generalizes the Kroll-Watson formula to the case of elliptic polarization. For the high-energy (rescattering) plateau in the LAES spectrum, our result generalizes prior results for a linearly polarized field valid for the 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 the LAES cross section into three factors: two field-free elastic electron-atom scattering cross sections (with laser-modified momenta) and a laser field-dependent factor (insensitive to the scattering potential) describing the laser-driven motion of the electron in the elliptically polarized field. We present also approximate analytic expressions for the exact TDER LAES amplitude that are valid over the entire rescattering plateau and reduce to the three-factor form in the plateau cutoff region. The theory is illustrated for the cases of $e$-H scattering in a CO$_2$-laser field and $e$-F scattering in a mid-infrared laser field of wavelength $\lambda=3.5\,\mu$m, for which the analytic results are shown to be in good agreement with exact numerical TDER results.