Two-photon double ionization of the H${}_2$ molecule: Cross sections and amplitude analysis

We perform time-dependent calculations of triply differential cross sections (TDCS) of two-photon double-electron ionization of the aligned H${}_2$ molecule. Our TDCS results for equal energy sharing between photoelectrons agree quite well with a recent time-dependent calculation by Guan et al. [X. Guan, K. Bartschat, and B. I. Schneider, Phys. Rev. A 77, 043421 (2008)] who employed a slightly different numerical technique. We supplement these studies by calculating TDCS at an unequal energy sharing and by generating symmetrized ionization amplitudes.

Figure 1

Coplanar TDCS of double ionization of H${}_2$ at a photon energy of 30 eV and equal energy sharing for the perpendicular field-molecule orientation for ${\theta }_1=0^{\circ }$ (upper left), ${\theta }_1={30}^{\circ }$ (upper right), ${\theta }_1={60}^{\circ }$ (bottom left), and ${\theta }_1={90}^{\circ }$ (bottom right). Shown are the present TDSE results [(red) solid line, length gauge; (cyan) dot-dashed line, velocity gauge]; the TDSE-PS results [7], (green) long dash; the ECS data [6], (blue) short dash; and the TDCC data [4, 5], (magenta) dots.

Figure 2

Same as in Fig. 1 for the parallel field orientation.

Figure 3

Coplanar TDCS of double ionization of H${}_2$ at a photon energy of 30 eV and unequal energy sharing for the perpendicular field-molecule orientation for ${\theta }_1=0^{\circ }$ (upper left), ${\theta }_1={30}^{\circ }$ (upper right), ${\theta }_1={60}^{\circ }$ (bottom left), and ${\theta }_1={90}^{\circ }$ (bottom right) and for the energy of the fixed electron, $E_1=5.4$ eV.

Figure 4

The same as in Fig. 3 for the parallel field-molecule orientation.

Figure 5

Double ionization probability of H${}_2$ at photon energy of 30 eV and equal energy sharing for the parallel field-molecule orientation for ${\theta }_1=0^{\circ }$ (upper left), ${\theta }_1={30}^{\circ }$ (upper right), ${\theta }_1={60}^{\circ }$ (bottom left), and ${\theta }_1={90}^{\circ }$ (bottom right). Shown are: probability computed using ”true” (as explained in the text) amplitude (red) solid line, ”reduced” amplitude (green) dashed line, results of the fitting procedure (blue) dots.

Figure 6

Real [(red) solid line)] and imaginary [(green) dashed line] parts of the coefficients $A$, $B$, and $C$ as functions of angle ${\theta }_{12}$ between the electron momenta near ${\theta }_{12}={180}^{\circ }$.