Green-function approach to the theory of tunneling ionization

We solve the problem of tunneling ionization of a multielectron atom in a static electric field by using the Green's function for the Stark-Coulomb problem. This allows us to incorporate the outgoing-wave boundary conditions at infinity. The interaction of the active electron with the atomic residue is described either by a model potential or by the $l$-dependent pseudopotential which prevents virtual transitions to orbitals occupied by inner electrons. The method works well in the broad range of electric fields including the region above the classical ionization threshold (the barrier-suppression region). Calculations of ionization of Ar demonstrate a noticeable difference between the model potential approach and the pseudopotential approach, but both sets of results agree with experimental data.

Figure 1

Ar $3p$ and $4s$ orbitals. Black solid curves: pseudoorbitals. Red (gray) dashed curves: orbitals calculated with the model potential of Tong and Lin [8].

Figure 2

The function $C_l\left(r\right)$, Eq. (28), for the Ar $3p$ orbital. Black solid curves: pseudopotential calculation. Red (gray) dashed curves: model potential calculation.

Figure 3

Ionization rates for the $3p_0$ orbital of Ar. Lower black curve: calculation with the model potential of Tong and Lin [8]. Blue (gray) dotted curve: calculation with the pseudopotential. Red (gray) dashed curve: semiempirical formula of Tong and Lin. Upper black curve labeled ADK (mod): ADK theory with the Stark-shifted energy.

Figure 4

Ar ionization rate in ${\mathrm{fs}}^{-1}$ as a function of the laser intensity. Blue (gray) solid curve: calculation with the pseudopotential. Red (gray) dashed curve: calculation with the model potential of Tong and Lin [8]. Black solid curve: ADK theory. Squares: experimental ionization probability of Guo et al. [36] normalized to the rate calculated with the model potential at $I=2\times {10}^{14} {\mathrm{W}/\mathrm{cm}}^2$.