Floquet calculations of ionization of the molecular hydrogen ion by intense laser fields in the low-frequency limit

The coupled-channel Floquet equations in both length and velocity gauges are solved in a pseudospectral representation to analyse ionization of the lowest two electronic states of the H2+ ion by strong continuous laser fields. A complex absorbing potential is used to obtain Siegert-type solutions resulting in accurate resonance positions and widths. The roles of two possible ionization mechanisms, tunnel ionization and resonance excitation multi-photon ionization are explored. The ionization rates of the lower and upper states, which correspond to gerade and ungerade states in the field-free case are investigated as a function of internuclear separation R. The previously investigated double-peak structure at ω = 0.0428 au is studied systematically as ω is decreased towards zero to understand how it relates to a similar structure in the dc limit. It is shown that the connection is not straightforward, since the ionization rates for the two states do mix strongly as ω is reduced for both peak regions. The mixing becomes pronounced even for the first peak around R = 5 au when ω < 0.02 au. For the outer peak around R = 9.5 au, we find that the rates for the upper and lower states become the same at ω = 0.01 au and correspond to 10–15% of the upper-state rate in the dc limit. An increase in laser intensity from 1.0 × 1014 to 2.0 × 1014  W cm−2 results in a similar outer peak with an about seven-fold increase in the ionization rate. (paper)