High-order above-threshold ionization: improved strong-field approximation vs. numerical solution of the time-dependent Schrödinger equation

For decades the strong-field approximation has been a theoretical backbone for describing the strong-field related phenomena such as above-threshold ionization and high-order harmonic generation, even though it is well-known that it cannot accurately account for the long-range Coulomb interaction between the liberated electron and residual atomic ion. In this paper, we theoretically investigate high-order above-threshold ionization. We use numerical solutions of the time-dependent Schrödinger equation and an improved strong-field approximation that includes electron rescattering. The analysis is performed for atomic anions and neutral atoms exposed to elliptically polarized laser fields. To validate the strong-field approximation and test its applicability, we compare both theoretical approaches for various targets and laser field parameters. We also show that the improved strong-field approximation in which the final electron plane wave is replaced by the Coulomb distorted plane wave leads to a better agreement with the results obtained using the solutions of the time-dependent Schrödinger equation.