Independent-atom-model description of multiple ionization of water, methane, and ammonia molecules by proton impact

We study multiple ionization in proton collisions with water, methane, and ammonia molecules using an independent-atom model. Previous work on total (net) capture and ionization cross sections is extended to treat the multiple-ionization channels explicitly. We present the theoretical framework to treat charge-state correlated processes within the independent-atom-model approach, which uses the geometric screening introduced for different molecular geometries and orientations. A comparison of results is made for the target molecules ${\text{H}}_2\text{O}, {\text{CH}}_4$, and ${\text{NH}}_3$ with an emphasis on $q$-fold electron removal. Coincident measurements of produced molecular fragments can be used to estimate this quantity. We find very good agreement for the model calculations for the water molecule, where data exist for $q=1–4$. For methane we observe reasonable agreement for $q=1,2$ and for ammonia only for $q=1$, i.e., the experimental data show little support for a direct multiple-ionization channel in the latter case.

Figure 1

(a) Scattering geometry and (b) projection on the impact parameter plane for a collision involving the CO molecule as an example.

Figure 2

Total cross sections for proton collisions with water molecules as functions of impact energy: (a) for net removal and $q=1,2,3,4$ charge-state production and (b) the case of $q=1$ compared to the production of ${\mathrm{H}}_2{\mathrm{O}}^{+}$. In (a) the solid curves show the total (net) removal in the MO IEM (black, Ref. [16]) and IAM-PCM frameworks (green, marked with crosses, present work) in comparison to the fragmentation data of Werner et al. [17] (black squares), Gobet et al. [18] (blue triangles), Luna et al. [19] (red diamonds), and Tavares et al. [20] (purple circles). The broken lines are for $q=1$ (short-dashed), $q=2$ (dash-dotted), $q=3$ (dotted), and $q=4$ (long-dashed). The experimental data should be lower bounds for the $q$-fold electron removal cross sections (cf. the text). In (b) the legend for the experimental data for the production of ${\mathrm{H}}_2{\mathrm{O}}^{+}$ corresponds to those in (a), while the dashed line is the IAM-PCM estimate for this channel.

Figure 3

Charge-state correlated cross sections ${\sigma }_{kl}$ for proton collisions with water molecules versus impact energy. The IAM-PCM results are shown as curves: red solid line with crosses, pure single capture; green solid line with crosses, transfer ionization; green dashed line with crosses, transfer ionization with two electrons in the continuum; blue solid line, pure single ionization; blue dashed line, pure double ionization; blue short-dashed line, pure triple ionization. Shown as closed squares are the experimental pure single-ionization data (exclusively) for the ${\mathrm{H}}_2{\mathrm{O}}^{+}$ channel and as diamonds the pure double-ionization data from Tavares et al. [20] based on coincidence measurements ${\mathrm{H}}^{+}+{\mathrm{OH}}^{+}$ and ${\mathrm{H}}^{+}+{\mathrm{O}}^{+}$, but ignoring the ${\mathrm{H}}^{+}+{\mathrm{H}}^{+}$ with neutral channel. The open symbols represent the derived net capture cross sections from experiments: circles, Toburen et al. [32]; triangles, Rudd et al. [21]. The red dotted line is the IAM-PCM net capture result [8].

Figure 4

(a) Net ionization cross section as a function of collision energy for proton-methane collisions. The present IAM-PCM calculation is based on the ground-state carbon atom $\left[\text{C}\left(1s^{2}2s^{2}2p^2\right)\right]$ input (red dashed line) and on the excited carbon atom $\left[\text{C}\left(1s^{2}2s2p^3\right)\right]$ input (black solid line). Experimental data are from Rudd et al. [33] (blue circles) and from Luna et al. [34] (black squares) which were normalized to the original measurements of Ref. [35]. (b) Total cross sections for $l$-fold ionization (${\sigma }_{0l}$ shown as blue curves) and total ion production (${\sigma }_q$ shown as green curves with crosses) as functions of impact energy in proton-methane collisions. Equations (15) and (16) are used to define the cross sections with electron capture which enter ${\sigma }_q$ according to Eq. (17). The experimental data are from Luna et al. [34]. The squares denote ${\sigma }_1\approx {\sigma }_{01}$ and the circles ${\sigma }_2\approx {\sigma }_{02}$. The IAM-PCM results for net electron production (${\sigma }^{-}$) are shown as a blue solid line, ${\sigma }_{01}$ as a blue dashed line, and ${\sigma }_1$ as a green dashed line, followed by dash-dotted and dotted corresponding lines for the channels involving $l=2,3$ and $q=2,3$, respectively.

Figure 5

Total cross sections for $l$-fold ionization (${\sigma }_{0l}$) and total ion production (${\sigma }_q$) as functions of impact energy in proton-ammonia molecule collisions. Equations (15) and (16) are used to define the cross sections with electron capture which enter ${\sigma }_q$ according to Eq. (17). The experimental data are from Wolff et al. [39]. The squares denote ${\sigma }_1\approx {\sigma }_{01}$, the circles ${\sigma }_2\approx {\sigma }_{02}$, and triangles show ${\sigma }_3\approx {\sigma }_{03}$. The IAM-PCM results for net electron production (${\sigma }^{-}$) are shown as a blue solid line, ${\sigma }_{01}$ as a blue dashed line, and ${\sigma }_1$ as a green dashed line with crosses, followed by dash-dotted and dotted corresponding lines for the channels involving $l=2,3$ and $q=2,3$ respectively.

Figure 6

Ratios of $q$-fold electron removal cross sections ${\sigma }_2/{\sigma }_1$ (solid lines) and ${\sigma }_3/{\sigma }_1$ (dashed lines) vs energy as calculated in the IAM-PCM approach for proton collisions with water (blue), methane (red with crosses), and ammonia (green with asterisks) collisions. Experiments with ${\mathrm{H}}_2\mathrm{O}$ are from Werner et al. [17] (blue squares) and Tavares et al. [20] (blue circles), with ${\mathrm{CH}}_4$ are from Luna et al. [34] (red triangles), and with ${\mathrm{NH}}_3$ are from Wolff et al. [39] (green diamonds).