Further development of an analytical model for the tunneling ionization of atoms using a low-frequency laser field of arbitrary strength, including the strong-field region, is presented. The model uses a very accurate approximation of the true ionization barrier–potential in the Schrödinger equation by the effective parabolic barrier–potential based on the algorithm suggested by Miller and Good and later employed by Kulyagin and Taranukhin (KT) for calculating the ionization rate, W(F), of hydrogen atoms from the ground state by a linearly polarized laser field. We point out and eliminate a number of principal errors made by KT and calculate W(F) much more accurately. We demonstrate that the dependence of the ionization rate on the strength of the linearly polarized laser field is monotonic and does not show any effect of the stabilization (“local ionization suppression”) claimed by KT. Our results for W(F) are in good agreement with the results of quantum fully numerical simulations. The analytical method, further developed in the present paper, can be extended without difficulty to calculations of the tunneling ionization for a number of other quantum systems. The most immediate extensions are to hydrogen atoms in an elliptically polarized laser field and atoms described by the Thomas–Fermi model.
Spontaneous decay processes in a classical strong low-frequency laser field
