Static-electric-field behavior in negative ion detachment by an intense, high-frequency laser field

Based upon the exact numerical solution of the complex quasienergy problem for a 3-dimensional short-range potential as well as upon analytical evaluations, we demonstrate for any finite frequency ω that the action of an ultra-intense laser field (with electric vector F(ωt)) on a weakly bound atomic system may be described by the cycle-averaging of results for an instantaneous static electric field of strength |F(ωt)|. The accurate description of the intensity dependence of the decay rate of a bound level over a broad interval of laser frequencies is one of the challenging problems of strong field laser-atom physics. Existing qualitative results obtained from nonperturbative (in the intensity) analyses of atomic decay rates in a laser field depend significantly on the relation between the laser frequency ω and ω0 =|E0|/ħ (where E0 is the binding energy), as well as that between the laser amplitude F (see (2) below) and the characteristic internal atomic field strength, F0 = (2m|E0|/|e|ħ )1⁄2. (Below we use the following scaled units: energies, ω and F are measured in units |E0|, ω0, and F0, respectively.) For small frequencies, ω  1, and for field strengths F ≥ ω (or equivalently for γK < 1, where γK = ω/F is the wellknown Keldysh parameter), the tunneling mechanism for the decay is realized, which is valid only for weak (although nonperturbative) fields, F  1 (see [1] and the improved analyses in [2]). The tunneling mechanism for the decay has been confirmed by many experiments for frequencies up to ω ~ (0.1–0.2), particularly for the rare gases [3]. For the case of ground state atomic hydrogen, H(1s), Pont et al. [4, 5] performed a low-frequency analysis of the decay rate Γ beyond the Keldysh approach (up to F ≤ 0.2) using the ω2 expansion of the complex quasienergy using the basis of quasistationary states of the hydrogen atom in a static electric field (whose magnitude equals that of the instantaneous laser field, see below). For ω = 0.134 (λ = 616 nm), a comparison of the F dependence of these “static-field-based” results with the exact ones shows a reasonable agreement (which becomes better for stronger F ) except for the structure seen in the exact Γ(F) which is due to Rydberg levels shifting in and out of resonance as the intensity varies. With increasing F (e.g. for F ≥ 0.2 in the case of H(1s)), over-barrier ionization becomes important. Recently, the over-barrier decay rate Γ in the low-frequency limit, ω  1,