Dynamic Exchange in the Strong Field Ionization of Molecules

We show that dynamic exchange is a dominant effect in strong field ionization of molecules. In ${\mathrm{CO}}_2$ it fixes the peak ionization yield at the experimentally observed angle of 45° between polarization direction and the molecular axis. For ${\mathrm{O}}_2$ it changes the angle of peak emission and for ${\mathrm{N}}_2$ the alignment dependence of yields is modified by up to a factor of 2. The effect appears on the Hartree-Fock level as well as in full ab initio solutions of the Schrödinger equation.

Figure 1

Alignment angle dependent ${\mathrm{CO}}_2$ ionization rates at selected intensities $I$ (in ${\mathrm{W}/\mathrm{cm}}^2$). The convergence with the number of ionic channels indicates the role of multielectron effects. Blue: including only the neutral ground state and ionic $X^2{\mathrm{\Pi }}_g$ ground states, green: as blue with the ionic $A^2{\mathrm{\Pi }}_u$ channel added. Red: as green with $B^2{\mathrm{\Sigma }}_u^{+}$ channel. Black: as red with $C^2{\mathrm{\Sigma }}_g^{+}$ channel. Computations were performed for static fields of strengths $F=0.05$, 0.07, and 0.09 a.u. corresponding to intensities $I=F^2/2$ that label the plots. ${\mathrm{\Gamma }}_{\max }$ indicates maximal decay width in atomic units at the inclosing circle. A total of 6 ionic channels are used in the calculations.

Figure 2

Peak ionization angles as a function of intensity. Solid lines: results with the antisymmetrized ansatz $A$, Eq. (1). Dashed lines: results without antisymmetrization, ansatz $B$, Eq. (2). Colors correspond to different numbers of neutral states and ionic channels, see Fig. 1 (solid lines) and Fig. 4 (dashed lines).

Figure 3

Normalized angle dependent yields from TDSE (lines), QSA (dash-dotted lines) in the single channel picture, and experiments [6, 7] (dashed lines). The laser parameters are 800 nm central wavelength, 40 fs duration with peak intensities of $3\times 10^{13}{\mathrm{W}/\mathrm{cm}}^2$ (Upper panel) and $1.1\times 10^{14}{\mathrm{W}/\mathrm{cm}}^2$ (lower panel).

Figure 4

The role of exchange in ${\mathrm{CO}}_2$ ionization: alignment angle dependence of normalized static SFI rates in different single-channel models. Blue: antisymmetrized ansatz $A$ with the neutral ground state and ionic $X^2{\mathrm{\Pi }}_g$ ground state channels. Green: ansatz $B$ with the same states as blue, red: as green, with the addition of the ionic $A^2{\mathrm{\Pi }}_u$ state. Cyan: as green with the addition of the first excited neutral state. The green and cyan lines coincide at the two higher intensities.

Figure 5

Rate as a function of alignment, computed with the Hartree-Fock neutral ground state, ionic ground state in Koopman’s approximation, and Coulomb potential truncated at 10 a.u. Solid line, with exchange, ansatz $A$, and dashed line, without dynamical exchange, ansatz $B$. Field $\text{strength}=0.06\mathrm{a}\mathrm{.}\mathrm{u}$.

Figure 6

Normalized ionization rates of ${\mathrm{O}}_2$ (left panel) and ${\mathrm{N}}_2$ (center and right) as a function of alignment angle, using only neutral and ionic ground states. Solid: with dynamic exchange, ansatz $A$, and dashed, without exchange, ansatz $B$.