Vibronic treatment of vibrational excitation and electron capture in ${\mathrm{H}}^{+}+{\mathrm{H}}_2$ (HD, ${\mathrm{D}}_2$, …) collisions at low impact energies

We present ab initio calculations of cross sections for vibrational excitation and electron capture in collisions of ${\mathrm{H}}^{+}$ with ${\mathrm{H}}_2$ and its isotopical variants at impact energies between $10\mathrm{eV}$ and $10\mathrm{keV}$. Calculations have been carried out by means of a vibronic close-coupling expansion in both quantal and semiclassical treatments to evaluate vibrationally resolved total cross sections. We also report total cross sections and spectra for dissociative capture and ${\mathrm{H}}_2$ dissociation.

Figure 1

Contour plot of the difference between the two lowest PES’s of $\mathrm{H}_3{}^{+}$ for $\theta =60°$. Energy differences smaller than $0.01\mathrm{a.u.}$ are not shown.

Figure 2

Contour plots of the vibrational (top panels) and radial couplings (bottom panels) between the two lowest states of $\mathrm{H}_3{}^{+}$ for $\theta =60°$. Left panels are the couplings between the adiabatic states and right panels between the diabatic states defined through Eqs. (27, 31).

Figure 3

(Color online) Total cross sections for vibrational excitation and electron capture processes. Solid line: present VCC eikonal calculation. Calculations using additional approximations for electron capture: solid line labeled Sudden, SEIKON approximation; dashed line labeled FC, FC approximation. Previous theoretical results: ◻ [11] and × [14]. Experimental results: ● [8], ▴ [10], and ∎ [40]. Dotted lines: recommended data of Ref. 6.

Figure 4

(Color online) (a) Total cross sections for vibrational excitation and electron capture processes. Solid lines: quantal calculation. Dashed line: eikonal approximation. (b) Electron-capture total cross section for several values of angle $\theta$ and angular average.

Figure 5

(Color online) Partial cross sections. Solid lines: VCC. Dashed lines: sudden approximation. Dotted lines: Franck-Condon approximation.

Figure 6

(Color online) Cross sections for excitation to the ${\mathrm{H}}_2$ vibrational states with $\nu =1–5$. Solid line: present calculation. Dashed line: classical calculation of Ref. 42. Squares: IOSA calculation of Ref. 11.

Figure 7

(Color online) Energy curves of the 50 lowest-lying vibronic states of the $\mathrm{H}_3{}^{+}$ quasimolecule for $\theta =60°$. The dashed lines are the energies of the states that correlate to $\mathrm{H}\left(1s\right)+\mathrm{H}_2{}^{+}(\nu =0)$ and ${\mathrm{H}}^{+}+{\mathrm{H}}_2(\nu =4)$ in the limit $R\to \infty$.

Figure 8

(Color online) Total cross section for electron capture from several vibrational states of ${\mathrm{H}}_2$.

Figure 9

(Color online) Dissociation spectra for three impact energies as indicated in the figure. Solid lines: VCC with ${\rho }_{\max }=10\mathrm{a.u.}$, $k_{\max }=40\mathrm{a.u.}$ (●) VCC with ${\rho }_{\max }=20\mathrm{a.u.}$, $k_{\max }=40\mathrm{a.u.}$ (×) VCC with ${\rho }_{\max }=10\mathrm{a.u.}$, ${\rho }_{\max }=30\mathrm{a.u.}$ Dashed line: SEIKON approximation.

Figure 10

(Color online) Spectra for dissociative capture in ${\mathrm{H}}^{+}+{\mathrm{H}}_2\left(\nu \right)$ collisions at $E=250\mathrm{eV}$. Dotted line: SEIKON result for $\nu =4$. Dashed line: semiclassical VCC result for $\nu =4$. Dot-dashed line: semiclassical VCC result for $\nu =0$. Solid line: quantal VCC result for $\nu =0$. (●) Semiclassical VCC result for $\nu =0$ including only trajectories with $b>1\mathrm{a.u.}$

Figure 11

(Color online) Total cross sections for electron capture in collisions of ${\mathrm{H}}^{+}$ with different isotopical variants of the hydrogen molecule, as indicated in the figure. The experimental cross sections have been reported in Ref. [10].