Atom-Volkov strong-field approximation for above-threshold ionization

We introduce an approximation for strong-laser-field-induced ionization of atoms, which we call atom-Volkov strong-field approximation (aV SFA). For the final state, instead of a plane wave (used in the standard well-known SFA) or a Coulomb wave (used in the Coulomb-Volkov SFA), in the aV SFA we use the exact atom-specific scattering states. We first introduce the aV SFA as an ansatz and show that it yields results that are closer to the exact results than those obtained using the SFA. After that, we systematically derive an iterative theory whose zeroth order is equal to the introduced aV SFA. We analyze its first-order correction, which corresponds to electron rescattering off the parent ion and show that, in the case of forward scattering, this correction leads to the low-energy structures in the photoelectron spectra which are observed in the experiments.

Figure 1

The differential ionization rates of Xe as functions of the electron kinetic energy for the laser wavelength 800 nm and the laser intensity $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The results obtained using the SFA are shown by the black solid line with squares, while the results obtained using the method of the present paper with the atom-Volkov ansatz are shown by the red dashed line with circles. For comparison, the green solid line represents the spectra obtained solving the TDSE with a cos-squared pulse envelope and a total pulse duration of ten optical cycles, while the results obtained using the Coulomb-Volkov SFA from Ref. [14] are denoted by the cyan dot-dashed line with diamonds.

Figure 2

The differential ionization rate of argon atoms as a function of the electron energy in units of the ponderomotive energy $U_p$. Intensity and wavelength of the laser field are $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and 2000 nm, respectively. The laser field is linearly polarized and electrons emitted in the laser-polarization direction are considered. The results obtained by numerical integration are presented by symbols: black stars connected by a dotted line (SFA) and blue circles connected by a solid line (aV). The results obtained using forward-scattered saddle-point solutions are presented by the green dot-dashed line [ISFA, defined below Eq. (31)], by the red solid line (IaV), and by the cyan dashed line (LFA, defined in the last paragraph of Sec. 5).