Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

We present a modified saddle-point method and apply it to the high-order above-threshold ionization (HATI) and high-order harmonic generation (HHG) processes. When we use the Slater-type orbitals to describe the ground-state wave function of the valence electron in a noble gas atom, we cannot apply the ordinary saddle-point method (SPM) because the singular points of the ionization matrix element, as well as the recombination matrix element for HHG, are in the vicinity of the corresponding saddle points. Therefore, we present a modification of the SPM and show that the obtained results are in excellent agreement with the spectra calculated by numerical integration. Furthermore, we compare the results obtained by the modified SPM with those obtained by the ordinary SPM with the asymptotic ground-state wave function. We conclude that both methods work for HATI, but for HHG we show that it is necessary to use the modified SPM because the recombination happens close to the atomic core, where the electron ground state is well described only by the Slater-type orbitals.