Ionization of atoms in weak fields and the asymptotic behavior of higher-order perturbation theory

Using the imaginary time method, we study the structure of the perturbation series for the hydrogen atom in electric ℰ and magnetic ℋ fields. It is shown that there is a “critical” value of the ratio γ=ℋ|ℰ at which the perturbation series for the ground state changes from having a fixed sign (for γ<γ _c ) to having a variable sign (for γ>γ _c ). This conclusion is confirmed by direct higher-order perturbation calculations. The change in the asymptotic regime is explained by competition among the contributions of the various complex trajectories that describe the subbarrier motion of the electrons. Here the parameter γ _c depends on the angle θ between the electric and magnetic fields. Zh. éksp. Teor. Fiz. 113, 2047–2055 (June 1998)