Strong Field Ionization Rate for Arbitrary Laser Frequencies

A simple, analytical, nonrelativistic ionization rate formula for atoms and positive ions in intense ultraviolet and x-ray electromagnetic fields is derived. The rate is valid at arbitrary values of the Keldysh parameter and confirmed by results from ab initio numerical solutions of the single active electron, time-dependent Schrödinger equation. The proposed rate is particularly relevant for experiments employing the new free electron laser sources.

Figure 1

Ionization rate (in atomic units) vs laser intensity according (6) (solid), (7) (dashed), and from the respective tunneling formula (dotted line). Rates obtained numerically using the Floquet method and from the solution of the TDSE are shown by dots and triangles, respectively. Upper panel: H(1s) in a field corresponding to the second harmonic of a Ti:sapphire laser ($\lambda =400\mathrm{nm}$). Inset: same but for $\lambda =422\mathrm{nm}$. Lower panel: ${\mathrm{Xe}}^{17+}$ ($4p0$-electron with $I=434\mathrm{eV}$, $n^{*}=3.19$) in a $\lambda =13.3$-nm x-ray field.