Breakdown of the single-active-electron approximation for one-photon ionization of the $B^1{\Sigma }_u$${}^{+}$ state of ${\mathrm{H}}_2$ exposed to intense laser fields

Ionization, excitation, and de-excitation to the ground state are studied theoretically for the first excited singlet state $B^1{\Sigma }_u{}^{+}$ of ${\mathrm{H}}_2$ exposed to intense laser fields with photon energies between about 3 and $13$ eV. A parallel orientation of a linear polarized laser and the molecular axis is considered. Within the dipole and the fixed-nuclei approximations the time-dependent Schrödinger equation describing the electronic motion is solved in full dimensionality and compared to simpler models. A dramatic breakdown of the single-active-electron approximation is found and explained to be due to the inadequate description of the final continuum states.

Figure 1

Ionization yield as a function of the peak laser intensity. The TDSE calculation is performed using length-form transition dipole moments with a $\cos {}^2$ envelope for the electric field [(black) circles] and velocity-form transition dipole moments with a Gaussian envelope for the vector potential [(red) squares]. The FWHM for both pulses is $2.5$ cycles of 8-eV photon energy. The ionization yields obtained with the LOPT [(blue) solid line], DFT-SAE [(violet) diamonds], DFT-SAE scaled by shifting the photon energy by $-2.44$ eV (using the value at 10.44 eV) [(orange) asterisks], and p-SAE [(maroon) crosses] are also shown and compared to the results of Barth et al. [25] [(green) triangles].

Figure 2

Ionization [(black) circles], population of the other bound states [OBS; (red) squares], and population of the $X^1{\Sigma }_g{}^{+}$ ground state [(blue) asterisks] obtained with the CI-TDSE as a function of the incident photon energy for a 10-fs laser pulse with a peak intensity of $1.0\times {10}^9$ W/cm${}^2$.

Figure 3

Photon-energy dependent ionization yield for various theoretical models with laser parameters as in Fig.  2. The ionization yields obtained with the CI-TDSE [(black) circles], LOPT [(red) dashed line], p-SAE [(blue) squares], and DFT-SAE [(violet) diamonds] are compared. The ionization yields obtained by a shift of the photon energy to compensate the corresponding error in the ionization potential with respect to the CI of the p-SAE [(maroon) triangles] and DFT-SAE [(green) crosses] are also shown.

Figure 4

The one-photon ionization cross section (within LOPT) of the ${\mathrm{H}}_2$ $B^1{\Sigma }_u{}^{+}$ state for the CI [(black) solid line], the CI${}^{\mathrm{a}}$ [(red) dashed line], and the p-SAE [(blue) dot-dashed line] basis sets.