Electron scattering and photoionization of one-electron diatomic molecules

We develop an efficient numerical procedure for solving the scattering problem on one-electron diatomic molecules in the fixed-nuclei approximation. For this purpose, we use the $R$-matrix propagation method together with the discrete variable representation method in prolate spheroidal coordinates. The demonstrated elastic scattering differential cross sections and the photoionization differential cross sections for H${}_2^{+}$ and HeH${}^{2+}$ exhibit oscillating structures owing to the two-center nature of the molecules. We analyze them by using the Coulomb corrected independent-atom model to identify the two-center quantum interference, and it is found that multiple-scattering effects become important in the heteronuclear system.

Figure 1

The laboratory frame ES DCSs for fixed-in-space H${}_2^{+}$ ($R=2$) for $\Theta =0^{\circ }$, ${45}^{\circ }$, and ${90}^{\circ }$ and for electron energies 10, 50, and 150 eV. The ESCDSs are shown in the ${\theta }_k^{\prime }{\phi }_k^{\prime }$ plane except for the first column for $\Theta =0^{\circ }$, where the ES DCS is independent of the angle ${\phi }_k^{\prime }$. In the first column, solid (black) curves, accurate ES DCSs; dotted (black) curves, results of one-center Coulomb scattering by total nuclear charge $Z_1+Z_2$, $|f^c(\mathit{k},{\mathit{k}}_{\mathrm{i}}){|}^2$; and dashed (red) curves, results of the CCIAM [Eq. (57)]. Dashed (red) lines in the two-dimensional ES DCSs indicate the positions of the local minima (nodal lines) predicted by the CCIAM [Eq. (58)]. Filled circles in each panel indicate the directions of the protons.

Figure 2

The same as Fig. 1 except ES DCSs for fixed-in-space HeH${}^{2+}$ ($Z_1=2$, $Z_2=1$, and $R=2$) are shown, and the results for $\Theta ={135}^{\circ }$ and ${180}^{\circ }$ are added. The filled square in each panel indicates the direction of the charge $Z_1=2$ (He${}^{2+}$).

Figure 3

Laboratory-frame PI DCSs for fixed-in-space H${}_2^{+}$ ($R=2$) for $\Theta =0^{\circ }$, ${45}^{\circ }$, and ${90}^{\circ }$ and for photoelectron energies 10, 50, and 150 eV. PI DCSs are shown in the ${\theta }_k^{\prime }{\phi }_k^{\prime }$ plane except in the first column for $\Theta =0^{\circ }$, where PI DCSs are independent of the angle ${\phi }_k^{\prime }$. In the first column, solid (black) curves, accurate PI DCSs; and dashed (red) curves, PI DCSs approximated by the CCIAM. In each panel, two curves are normalized at their maximum value by scaling the dashed (red) curve. Filled circles in each panel indicate the directions of the protons.

Figure 4

The same as Fig. 3 except PI DCSs of HeH${}^{2+}$ ($Z_1=2$, $Z_2=1$, and $R=2$) are shown. The filled square in each panel indicates the direction of the charge $Z_1=2$ (He${}^{2+}$).