Fully Differential Cross Sections for Photo-Double-Ionization of ${\mathrm{D}}_2$_

We report the first kinematically complete study of the four-body fragmentation of the ${\mathrm{D}}_2$ molecule following absorption of a single photon. For equal energy sharing of the two electrons and a photon energy of 75.5 eV, we observed the relaxation of one of the selection rules valid for He photo-double-ionization and a strong dependence of the electron angular distribution on the orientation of the molecular axis. This effect is reproduced by a model in which a pair of photoionization amplitudes is introduced for the light polarization parallel and perpendicular to the molecular axis.

Figure 1

Illustration of the selection rules: The dots show the FDCS for the PDI of helium at 24 eV above threshold for equal energy sharing [$E_1/(E_1+E_2)=0.5\pm 0.1$]. The polarization axis is horizontal. The first electron is fixed at ${\theta }_1=55°\pm 12°$ (arrow). For equal energies, the two-electron states with ${}^{1}P^0$ symmetry (final state in the PDI of He) have a node for ${\theta }_2=180°-{\theta }_1$ indicated by the cone (selection rule F), where ${\theta }_{1,2}$ are the polar angles of electrons 1 and 2 with respect to the polarization axis (see 12). The dashed straight line indicates the forbidden back-to-back emission (selection rule C). The dashed curve is a fit to the data using the Gaussian parameter ${\theta }_{12}=99.5°\pm 1.5°$ (see, e.g., 9 and references therein).

Figure 2

A density plot of the angular distribution of the second electron when the first electron is detected at ${\theta }_1=55°\pm 12°$ (circled cross). The patterns show the PDI of ${\mathrm{D}}_2$ (a)–(c) at 75.5 eV and He (d) at 103 eV photon energy (sum electron energy 24 eV), equal energies [$E_1/(E_1+E_2)=0.5\pm 0.1$], and linearly polarized light. Horizontal axis: polar angle ${\theta }_2$ of electron 2 with respect to the polarization axis, vertical axis: difference between the azimuthal angles of the two electrons $\Delta {\varphi }_{ee}$. The back-to-back emission is at the full dot on the $\Delta {\varphi }_{ee}=180°$ line. The dashed vertical line is the nodal cone ${\theta }_2=180°-{\theta }_1=125°$. The color scale is linear in the count rate. (a) ${\mathrm{D}}_2$ molecule ${\theta }_R=45°\pm 11°$, i.e., a mixture of $\Sigma$ and $\Pi$ transition (integrated over $\Delta {\varphi }_{eR}$); (b) ${\mathrm{D}}_2$ integrated over all molecular orientations; (c) ${\theta }_R=90°\pm 11°$, i.e. $\Pi$ transition (integrated over $\Delta {\varphi }_{eR}$); (d) results from helium.

Figure 3

FDCS for PDI of ${\mathrm{D}}_2$, for equal energies $E_1/(E_1+E_2)=0.5\pm 0.1$, ${\theta }_1=20°\pm 10°$ (arrows), polarization horizontal, and electron 2 coplanar. (a) Integrated over all molecular orientations. (b)–(f) molecule coplanar ($\Delta {\varphi }_{eR}=0°,180°\pm 45°$) and (b) ${\theta }_R=20°$, (c) ${\theta }_R=45°$, (d) ${\theta }_R=90°$, (e) ${\theta }_R=110°$, (f) ${\theta }_R=160°$ (all $\pm 12°$). The data are internormalized for all angles ${\theta }_R$; the multiplier used is indicated in each panel. The calculation (solid lines) corresponds to Eqs. (5) and (6) of Feagin [9] on (a) and (b)–(f), respectively. The open triangles in (a) show the same calculation with $f_{\Sigma }=f_{\Pi }$. The dashed lines show the Gaussian fit to the helium calibration data of this measurement (similar to Fig. 1). The dashed line indicates selection rule C. The solid line in (a) represents selection rule F valid on a cone in the PDI of helium.