${\mathrm{H}}_2$-assisted ternary recombination of ${\text{H}}_3{}^{+}$ with electrons at 300 K

Stationary afterglow measurements in conjunction with near-infrared absorption spectroscopy show that the recombination of the ${\text{H}}_3{}^{+}$ ion with electrons in ionized gas mixtures of He, Ar, and ${\text{H}}_2$ at 300 K is strongly enhanced by neutral helium and by molecular hydrogen. The ${\text{H}}_2$-assisted ternary recombination coefficient $K_{{\text{H}}_2}=(8.7\pm 1.5)\times {10}^{-23}{\text{cm}}^6{\text{s}}^{-1}$ substantially exceeds the value measured for ${\text{H}}_3{}^{+}$ in ambient helium $(K_{\mathrm{He}}\sim {10}^{-25}{\text{cm}}^6{\text{s}}^{-1})$ or predicted by the generally accepted classical theory of Bates and Khare $(\sim {10}^{-27}{\text{cm}}^6{\text{s}}^{-1})$ for atomic ions. Because of the extremely large value of $K_{{\text{H}}_2}$ in a hydrogen plasma the ternary recombination dominates over binary recombination already at pressures above 3 Pa. This can have consequences in plasma physics, astrophysics, recombination pumped lasers, plasma spectroscopy, plasmatic technologies, etc. The ternary processes provide a plausible explanation for the discrepancies between many earlier experimental results on ${\text{H}}_3{}^{+}$ recombination. The observation that the ternary process saturates at high He and ${\text{H}}_2$ densities suggests that recombination proceeds by a two-step process: formation of a long-lived complex [with a rate coefficient ${\alpha }_{\mathrm{F}}=(1.5\pm 0.1)\times {10}^{-7}{\text{cm}}^3{\text{s}}^{-1}]$ followed by collisional stabilization.

Figure 1

The scheme of the proposed ${\text{H}}_3{}^{+}$ recombination mechanism. Used symbols are explained in the text.

Figure 2

The decay curves measured for (1,0), (1,1), and (3,3) states of ${\text{H}}_3{}^{+}$ at 300 K and number densities $\left[\text{He}\right]=8\times {10}^{17}{\text{cm}}^{-3},\left[{\text{H}}_2\right]=2\times {10}^{16}{\text{cm}}^{-3}$, and $\left[\text{Ar}\right]=7\times {10}^{14}{\text{cm}}^{-3}$. The total number density of ${\text{H}}_3{}^{+}$ ions, calculated from the measured data under assumption of LTE, is shown as a full line. Calculated evolutions of the number densities of ${\text{H}}_3{}^{+},{\text{H}}_5{}^{+}$, and ${\text{He}}^{\mathrm{m}}$ are indicated as dashed, dotted, and dash-dotted lines, respectively.

Figure 3

The dependencies of $({\alpha }_{\mathrm{eff}\text{−}\mathrm{ion}}-{\alpha }_{\mathrm{bin}})$ on $\left[{\text{H}}_2\right]$ measured at indicated [He]. Full diamond: measurements in pure ${\text{H}}_2$. Dashed lines: fits of Eq. (3) to the data, using the parameters mentioned in the text. Double-dot-dashed line: three-body recombination in pure ${\text{H}}_2$ . Solid line $\left({\text{LTE}}_{{\text{H}}_5}\right)$: approximate ${\text{H}}_5{}^{+}\mathrm{contribution}$, ${\alpha }_5{K}_{\mathrm{C}}\left[{\text{H}}_2\right]$. Dash-dotted line $\left({\text{M}}_{{\text{H}}_5}\right)$: ${\text{H}}_5{}^{+}\mathrm{contribution}$ obtained from the kinetic model for $\left[\text{He}\right]=2.1\times {10}^{17}{\text{cm}}^{-3}$. Dotted horizontal line: data obtained by Amano [34] in pure ${\text{H}}_2$ at 273 K, after subtracting ${\alpha }_{\mathrm{bin}}=6\times {10}^{-8}{\text{cm}}^3{\text{s}}^{-1}$.

Figure 4

Measured dependence of $({\alpha }_{\mathrm{eff}\text{−}\mathrm{ion}}-{\alpha }_{\mathrm{bin}})$ on He number density at 300 K for $\left[{\text{H}}_2\right]=2\times {10}^{14}{\text{cm}}^{-3}$ (open circles) and for $\left[{\text{H}}_2\right]=2\times {10}^{16}{\text{cm}}^{-3}$ (closed circles). The values of $({\alpha }_{\mathrm{eff}\text{−}\mathrm{ion}}-{\alpha }_{\mathrm{bin}})$ measured in pure ${\text{H}}_2$ at $(270\pm 5)$ K are denoted by full diamonds (see also Fig. 3). The values measured in other experiments [18, 22, 23, 26, 34, 39, 41, 42, 43] are plotted for comparison. Values indicated by open symbols were measured for $\left[{\text{H}}_2\right]<5\times {10}^{14}{\text{cm}}^{-3}$. All experiments were performed with helium as a buffer gas with the exception of data in [18, 34, 39] where no buffer gas, pure ${\text{H}}_2$, or neon buffer gas was used, respectively. The dot-dashed lines denote values given by Eq. (3) for $\left[{\text{H}}_2\right]=2\times {10}^{14}$ and $2\times {10}^{16}{\text{cm}}^{-3}$ and with parameters written in the text.

Figure 5

Measured dependence of the effective recombination rate coefficient on ${\text{H}}_2$ (full squares, with $\left[\text{He}\right]=2\times {10}^{17}{\text{cm}}^{-3})$ and He number density (open squares, with $\left[{\text{H}}_2\right]=2\times {10}^{14}{\text{cm}}^{-3})$ measured at 300 K. The full lines are fit to the data from Figs. 3 and 4. The horizontal dotted line shows the value of the binary recombination rate coefficient ${\alpha }_{\mathrm{bin}}$ of ${\text{H}}_3{}^{+}$ ions at 300 K. The dashed line shows the sum $\left({\alpha }_{\mathrm{bin}}+{\alpha }_{\mathrm{F}}\right)$, i.e., maximum rate coefficient given by the sum of contributions from binary and saturated ternary recombination. The dot-dashed lines (A, B, and C) denote the sum of ${\alpha }_{\mathrm{bin}}$ and the contribution of the ${\text{H}}_2$-assisted process only (A), the sum of ${\alpha }_{\mathrm{bin}}$ and the contribution of the He-assisted process only (B), and the ${\alpha }_{\mathrm{eff}}$ arising from ternary helium-assisted recombination as predicted by the theory of Bates and Khare [24] with the ternary recombination rate coefficient of $1.2\times {10}^{-27}{\text{cm}}^6{\text{s}}^{-1}$ (C). The dotted lines denoted ${\mathrm{A}}_{\mathrm{T}}$ and ${\mathrm{B}}_{\mathrm{T}}$ indicate the contributions to the measured ${\alpha }_{\mathrm{eff}}$ arising from the ${\text{H}}_2$ - and He-assisted ternary process, respectively. Values from other afterglow experiments are plotted using the same notation as in Fig. 4.