Angle-resolved high-order above-threshold ionization spectra of inert gases in the low-frequency approximation

In the improved strong-field approximation (ISFA), which describes high-order abovethreshold ionization (HATI), rescattering of the ionized electron off its parent ion is usually described within the first-order Born approximation (1BA). Coulomb effects in the rescattering process can be taken into account by replacing the final Volkov wave by the CoulombVolkov wave [1]. One can go beyond the 1BA by replacing in the rescattering amplitude the atomic scattering potential according to V → T (E) = V + V GV (E)V , where GV (E) is the stationary Green’s operator at the energy E(τ) of the recolliding electron at the recollision time τ . This is similar to the low-frequency approximation for laser-assisted scattering ([2] and references therein). We have recently derived the low-frequency approximation (LFA) for HATI [3]. In the present contribution we will show our numerical results for the angle-resolved HATI energy spectra of inert gases; see Fig. 1. We show that the difference between the ISFA and the LFA is significant for scattering away from the laser polarization axis. In the context of quantum-orbit theory and the uniform approximation, we also show that on the backrescattering ridge, the rescattering T -matrix element can be factorized into the product of the incoming flux and the elastic scattering cross section. Hence, the differential cross section of laser-free elastic electron-ion scattering can be extracted from the angle and energy resolved HATI spectra as proposed recently [4]. Fig. 1. 2D momentum distributions for Xe at 1.5× 10 W/cm and 760 nm. The upper (lower) panel: the results obtained using the ISFA (LFA).