Ionization of small molecules induced by ${\mathrm{H}}^{+}, \mathrm{H}{\mathrm{e}}^{+}$, and ${\mathrm{N}}^{+}$ projectiles: Comparison of experiment with quantum and classical calculations

We report the energy and angular distribution of ejected electrons from $\mathrm{C}{\mathrm{H}}_4$ and ${\mathrm{H}}_2\mathrm{O}$ molecules impacted by 1 MeV ${\mathrm{H}}^{+}, \mathrm{H}{\mathrm{e}}^{+}$, and 650 keV ${\mathrm{N}}^{+}$ ions. Spectra were measured at different observation angles, from 2 to 2000 eV. The obtained absolute double-differential electron-emission cross sections (DDCSs) were compared with the results of classical trajectory Monte Carlo (CTMC) and continuum distorted wave, eikonal initial state (CDW-EIS) calculations. For the bare ${\mathrm{H}}^{+}$ projectile both theories show remarkable agreement with the experiment at all observed angles and energies. The CTMC results are in similarly good agreement with the DDCS spectra obtained for impact by dressed $\mathrm{H}{\mathrm{e}}^{+}$ and ${\mathrm{N}}^{+}$ ions, where screening effects and electron loss from the projectile gain importance. The CDW-EIS calculations slightly overestimate the electron loss for 1 MeV $\mathrm{H}{\mathrm{e}}^{+}$ impact, and overestimate both the target and projectile ionization at low emitted electron energies for 650 keV ${\mathrm{N}}^{+}$ impact. The contribution of multiple electron scattering by the projectile and target centers (Fermi shuttle) dominates the ${\mathrm{N}}^{+}$-impact spectra at higher electron energies, and it is well reproduced by the nonperturbative CTMC calculations. The contributions of different processes in medium-velocity collisions of dressed ions with molecules are determined.

Figure 1

Schematic figure of the experimental setup.

Figure 2

Contour map of the probability density for the initial electron position for the $2a_1\mathrm{MO}$ of ${\mathrm{H}}_2\mathrm{O}$. Here $x$ and $y$ are coordinates of the projection of the position vectors into the molecule plane. From light to dark each intensity level increases by a factor of 2.

Figure 3

The probability density function of the electron initial radial distance for the $2a_1\mathrm{MO}$ of ${\mathrm{H}}_2\mathrm{O}$. Solid line, present work; dashed line, Illescas et al. [40]; dotted line, the analytical result for a 1/$r$ potential and $E_i=1.18\mathrm{a}.\mathrm{u}.$

Figure 4

The potential energy of the electron in ${\mathrm{H}}_2\mathrm{O}$ in the direction of one of the hydrogen atoms. Solid line, the model potential given by Eqs. (2, 3, 4) [40]; dashed line, present result obtained in the zeroth-order approximation (see text).

Figure 5

Double-differential electron emission cross section (DDCSs) for $\mathrm{C}{\mathrm{H}}_4$ target molecules induced by (a) 1 MeV ${\mathrm{H}}^{+}$; (b) 1 MeV $\mathrm{H}{\mathrm{e}}^{+}$; (c) 650 keV ${\mathrm{N}}^{+}$ projectiles. Spectra are depicted as functions of electron energy for different observation angles.

Figure 6

Double-differential electron emission cross section for $\mathrm{C}{\mathrm{H}}_4$ by 1 MeV ${\mathrm{H}}^{+}$ impact at different observation angles. The multiplying factors, applied for graphical reasons, are shown in parentheses. The measured data are indicated as gray diamonds. The calculated CDW-EIS and CTMC values are depicted by dash-dotted and solid lines, respectively. A few sample error bars are shown at higher electron energies. At lower energies, the size of the diamonds exceeds the uncertainties of the data.

Figure 7

Double-differential electron emission cross section for ${\mathrm{H}}_2\mathrm{O}$ by 1 MeV ${\mathrm{H}}^{+}$ impact compared with CDW-EIS and CTMC calculations. The notations and comments are the same as for Fig. 6.

Figure 8

Double-differential electron emission cross section for $\mathrm{C}{\mathrm{H}}_4$ in collisions with 1 MeV $\mathrm{H}{\mathrm{e}}^{+}$ at different observation angles. The measured data are indicated as gray diamonds. The calculated target and total (target + projectile) ionization values for CTMC are depicted in (a) by dash-dotted and solid lines, respectively. In (b) the CDW-EIS values are presented with the same notation. The multiplying factors are shown in parentheses.

Figure 9

Double-differential electron emission cross section for ${\mathrm{H}}_2\mathrm{O}$ in collisions with 650 keV ${\mathrm{N}}^{+}$ at different observation angles. The multiplying factors are shown in parentheses. The measured data are indicated as gray diamonds. In (a) CTMC results for target and total (target + projectile) ionization are displayed by dash-dotted and solid lines, respectively. In (b) experiment is compared with CDW-EIS results for target and total ionization with the same notations.

Figure 10

Double-differential electron emission cross section for the 650 keV ${\mathrm{N}}^{+}+\mathrm{C}{\mathrm{H}}_4$ collision at different observation angles. The multiplying factors are shown in parentheses. The measured data are indicated as gray diamonds and are compared with the CDW-EIS results. The calculations for the target and the total (target+projectile) ionization are displayed by dash-dotted and solid lines, respectively.

Figure 11

The CTMC calculations for 46 keV/u ${\mathrm{N}}^{+}+{\mathrm{H}}_2\mathrm{O}$ collision divided by the result of the first order Born (B1) approximation for the 46 keV/u ${\mathrm{H}}^{+}+{\mathrm{H}}_2\mathrm{O}$ collision system at different observation angles: 20°, dotted line; 45°, dash-totted line; 160°, solid line. The ratios highlight the contributions of higher-order processes as wide humps at higher energies. Multiple electron scattering (Fermi shuttle) occurs even at backward angles.