Adiabatic Approximation of the Correlation Function in the Density-Functional Treatment of Ionization Processes

The ionization of a one-dimensional model helium atom in short laser pulses using time-dependent density-functional theory is investigated. We calculate ionization probabilities as a function of laser intensity by approximating the correlation function of the system adiabatically with an explicit dependence on the fractional number of bound electrons. For the correlation potential we take the derivative discontinuity at integer numbers of bound electrons explicitly into account. This approach reproduces ionization probabilities from the solution of the time-dependent Schrödinger equation, in particular, the so-called knee due to nonsequential ionization.

Figure 1

Single and double ionization probabilities for exact and LK densities using $I_{\mathrm{c}}=0$ compared to the TDSE solution for a $\lambda =780\mathrm{nm}$ laser pulse.

Figure 2

Comparison of the integrand of the exact $I_{\mathrm{c}}(T)$ (left) and the adiabatic approximation $I_{\mathrm{c}}^A(T)$ (right) for different effective peak intensities of a $\lambda =780\mathrm{nm}$ laser pulse.

Figure 3

Value of the exact $I_{\mathrm{c}}(T)$ as a function of the number of bound electrons (left). Value of $I_{\mathrm{c}}^A(T)$ using exact densities compared to the exact $I_{\mathrm{c}}(T)$ (right). Results for both laser pulses are shown together with differently shaped symbols.

Figure 4

Single and double ionization probabilities for exact and LK densities using the adiabatic approximation of the correlation integral $I_{\mathrm{c}}^A$ compared to the TDSE solution for a $\lambda =780\mathrm{nm}$ laser pulse.