Single-center model for double photoionization of the ${\mathrm{H}}_2$ molecule

We present a single-center model of double photoionization (DPI) of the ${\mathrm{H}}_2$ molecule which combines a multiconfiguration expansion of the molecular ground state with the convergent close-coupling description of the two-electron continuum. Because the single-center final-state wave function is only correct in the asymptotic region of large distances, the model cannot predict the magnitude of the DPI cross sections. However, we expect the model to account for the angular correlation in the two-electron continuum and to reproduce correctly the shape of the fully differential DPI cross sections. We test this assumption in kinematics of recent DPI experiments on the randomly oriented and fixed in space hydrogen molecule in the isotopic form of ${\mathrm{D}}_2$.

Figure 1

Total DPI cross section calculated in three gauges of the dipole operator: length (L: dotted line), velocity (V: solid line), and acceleration (A: dashed line). Normalization is made to the calculation of Le Rouzo [11] in the $V$ gauge (thick solid line) by dividing the present results by the factors of 20, 2.1, and 4.5 for the $L$, $V$, and $A$ gauges, respectively. The experimental data by Dujardin et al. [1] are indicated by dots.

Figure 2

Triply differential cross section of DPI on ${\mathrm{H}}_2$ at $E_1=E_2=10\mathrm{eV}$ and a coplanar kinematics. A $V$-gauge calculation with amplitudes $g_{\Sigma }$ and $g_{\Pi }$ [Eq. (15)] is displayed by a solid line. An atomiclike calculation with identical amplitudes $g_{\Sigma }=g_{\Pi }$ is shown by a dashed line. A fixed escape angle of one of the photoelectrons is indicated by an arrow on the inset polar plots. The polarization axis of light is horizontal. Experimental data are from Wightman et al. [5]

Figure 3

The DPI amplitudes $g_{\Sigma }$, $g_{\Pi }$ for ${\mathrm{H}}_2$ are shown by the solid and dashed lines, respectively. Their atomic counterparts $g_{\Sigma }=g_{\Pi }$ for He are displayed by the thick solid line. The moduli are on the left panel and the phases are on the right panel.

Figure 4

Triply differential cross section of DPI on ${\mathrm{H}}_2$ at $E_1=E_2=12.5\mathrm{eV}$ and a coplanar kinematics. The fixed photoelectron escape direction at ${\theta }_1=10°$ is indicated by an arrow. The top-left panel shows the FDCS averaged over all molecular orientations. Other panels correspond to a fixed molecular angle ${\theta }_R$ relative to the polarization of light (horizontal). A $V$-gauge calculation with amplitudes $g_{\Sigma }$ and $g_{\Pi }$ [Eq. (15)] is displayed by a solid line. Experimental data are from Weber [34].

Figure 5

Triply differential cross section of DPI on ${\mathrm{H}}_2$ at $E_1=E_2=12.5\mathrm{eV}$ and noncoplanar geometry. The fixed escape direction of one of the photoelectrons is perpendicular to the plane which contains the polarization of light, the molecule which is at 55° to the polarization axis, and the escape direction of another photoelectron. The experimental data are from Weber et al. [10].