High-order above-threshold ionization beyond the first-order Born approximation

In the improved strong-field approximation, which describes high-order above-threshold ionization (HATI), the rescattering of the ionized electron on the parent ion is described within the first-order Born approximation. The low-frequency approximation for laser-assisted scattering goes beyond the first Born approximation. In the present paper, we derive the low-frequency approximation for HATI. The rescattering amplitude in the first Born approximation is replaced by the exact scattering amplitude calculated on the energy shell. Our numerical results for the angle-resolved HATI energy spectra show that the difference between the improved strong-field approximation and the low-frequency approximation 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 back-rescattering ridge, the rescattering T-matrix element can be factorized into the product of the incoming flux and the elastic-scattering cross section so that the latter can be extracted from the angle- and energy-resolved HATI spectra.