Modified saddle-point method applied to direct ionization of noble gas atoms

When exposed to strong laser fields, atoms or molecules can absorb more photons from the laser field than is necessary for ionization. This process is called above-threshold ionization (ATI). In analyzing this process, the strong-field approximation (SFA) turns out to be a very useful theoretical tool. In the SFA the differential ionization rate, which is an observable quantity, can be expressed as an integral over the ionization time and can be calculated by numerical integration (NI) or using the saddle-point method (SPM). When we use the Slater orbitals to describe the ground-state wave function of the valence electron, the results obtained using the SPM and NI do not agree. We find the reasons for this disagreement and introduce a modified SPM that leads to excellent agreement between the SPM and NI results for various strong laser fields.