Multicenter continuum-distorted-wave eikonal-initial-state description of the electron-impact ionization of aligned ${\mathrm{H}}_2$ molecules

In this work, the multicenter continuum-distorted-wave (CDW) eikonal-initial-state (EIS) model is introduced. In contrast to previously reported CDW EIS analyses for electron-molecule collisions, in which the ionized electron interacted with the molecular ion via a one-center effective potential, the multicenter nature of the molecular ion is explicitly taken into account. Results obtained for electron-impact ionization of oriented ${\mathrm{H}}_2$ molecules at the fully differential level are presented and contrasted with recent experimental data and reported theoretical calculations obtained with the time-dependent close-coupling method. The present results suggest that this simple molecule still represents a challenging target from a theoretical point of view and that many aspects of the ionization process at the fully differential level remain to be understood.

Figure 1

Approximations to the ${\text{H}}_2{}^{+}$ ion residual potential for a continuum state electron.

Figure 2

Partial waves $u_{jl}(k,r)$ (solid lines) and $u_{jl}^{\mathrm{Coul}}(k,r)$ (dashed lines) for (a), (c), and (e) $l=0$ and (b), (d), and (f) $l=1$ for continuum electron energies of (a) and (b) 18 eV, (c) and (d) 10 eV, and (e) and (f) 4 eV.

Figure 3

Fully differential cross sections for the 54-eV electron-impact ionization of aligned ${\mathrm{H}}_2$ molecules and equal energy sharing ($E_1=E_2=18\mathrm{eV}$) with one electron emission angle fixed at ${\theta }_1=-{50}^{\circ }$ [${\mathbf{k}}_1$ indicated in (a)] as a function of the emission angle of the second electron into the perpendicular $xy$ plane: (a) $(\alpha =0^{\circ },\beta =0^{\circ })$, (b) $(\alpha =0^{\circ },\beta ={90}^{\circ })$, (c) $(\alpha ={45}^{\circ },\beta ={90}^{\circ })$, (d) $(\alpha ={45}^{\circ },\beta ={45}^{\circ })$, (e) $(\alpha ={90}^{\circ },\beta ={45}^{\circ })$, and (f) $(\alpha ={135}^{\circ },\beta ={45}^{\circ })$. The light gray dashed vertical lines indicate the direction of the atoms' positions or their projections to the $xy$ plane. The experimental and theoretical data from Ref. [42] are scaled to the present theoretical results.

Figure 4

Same as Fig. 3 for the MC CDW EIS model for two different molecular orientations (a), (c), and (e) $(\alpha ={45}^{\circ },\beta ={90}^{\circ })$ and (b), (d), and (f) $(\alpha ={45}^{\circ },\beta ={45}^{\circ })$ as a function of (c) and (d) the angle ${\theta }_{12}$ between the continuum electron momenta ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ and (e) and (f) the emission angle ${\varphi }_2$. Graphical representations of these two emission geometries for the particular case ${\varphi }_2=0^{\circ }$ (with ${\theta }_{12}={140}^{\circ }$) are shown in (a) and (b).

Figure 5

Same as Fig. 4 for two other molecular orientations (a), (c), and (e) $(\alpha ={90}^{\circ },\beta ={45}^{\circ })$ and (b), (d), and (f) $(\alpha ={135}^{\circ },\beta ={45}^{\circ })$, with (a) and (b) ${\varphi }_2=0^{\circ }$ and ${\theta }_{12}={140}^{\circ }$.

Figure 6

Same as Fig. 3 with the ${\mathrm{H}}_2$ molecule aligned along the $y$ axis and for variable-energy sharing, with emission energies (a) $E_1=18$ eV, $E_2=18$ eV, and $\mathrm{\Delta }E=0$ eV; (b) $E_1=26$ eV, $E_2=10$ eV, and $\mathrm{\Delta }E=16$ eV; and (c) $E_1=32$ eV, $E_2=4$ eV, and $\mathrm{\Delta }E=28$ eV.