Dissociative recombination of rotationally cold $\mathrm{H}_3{}^{+}$

This paper presents the first dissociative recombination (DR) measurement of electrons with rotationally and vibrationally cold $\mathrm{H}_3{}^{+}$ ions. A dc discharge pinhole supersonic jet source was developed and characterized using infrared cavity ringdown spectroscopy before installation on the CRYRING ion storage ring for the DR measurements. Rotational state distributions $\left(T_{\mathrm{rot}}\sim 30\mathrm{K}\right)$ produced using the source were comparable to those in the diffuse interstellar medium. Our measurement of the electron energy dependence of the DR cross section showed resonances not clearly seen in experiments using rotationally hot ions, and allowed calculation of the thermal DR rate coefficient for ions at interstellar temperatures, ${\alpha }_{\mathrm{DR}}\left(23\mathrm{K}\right)=2.6\times {10}^{-7}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. This value is in general agreement with recent theoretical predictions by Kokoouline and Greene [Phys. Rev. A 68, 012703 (2003)]. The branching fractions of the two breakup channels, $\mathrm{H}+\mathrm{H}+\mathrm{H}$ and $\mathrm{H}+{\mathrm{H}}_2$, have also been measured for rotationally and vibrationally cold $\mathrm{H}_3{}^{+}$.

Figure 1

Cross section of the Berkeley cold-ion pinhole source used to produce rotationally cold $\mathrm{H}_3{}^{+}$. The ground electrode and entire source assembly is floated at a voltage of $+30\mathrm{kV}$ on the CRYRING endstation. The values of the ${\mathrm{H}}_2$ gas pressure and dc discharge voltage were typical of those used during DR experiments (see text). Figure is not to scale.

Figure 2

Cavity ringdown spectra of the $R\left(1,0\right)$ and $R{\left(1,1\right)}^u$ lines of $\mathrm{H}_3{}^{+}$ as a function of dc discharge voltage. Temperatures (listed in parentheses) were determined from the ratio of the integrated areas of the two peaks. Spectra have been background subtracted, and shifted vertically for clarity.

Figure 3

A simplified energy level diagram of $\mathrm{H}_3{}^{+}$. Energy levels are plotted versus the quantum number $G\equiv \mid k-\ell \mid$, where $k$ is the projection of $J$ onto the molecular symmetry axis and $\ell$ is the vibrational angular momentum associated with the ${\nu }_2$ mode. Each level is labeled on the right as $\left(J,G\right)$, with superscript $u$ and $l$ to indicate the upper and lower levels of doublets. A complete explanation of the notation and energy level structure of $\mathrm{H}_3{}^{+}$ can be found in [34]. The infrared transitions used are shown by upward-going thin arrows, and the allowed electron-impact excitation transitions are shown as thick arrows. The downward-going dashed arrows indicate the radiative relaxation pathways for the small fraction of ions produced in vibrationally excited (yet rotationally cold) states.

Figure 4

Ramping schemes used for DR measurements. Ramp (a), shown by a dotted line, spans detuning energies from 0 to $20\mathrm{eV}$. Ramp (b) covers detuning energies from $+1$ to $-1\mathrm{eV}$. In ramp (c), the ion beam was heated for $1.5\mathrm{s}$ by exposing it to electrons just above the threshold for the $\left(3,0\right)\leftarrow \left(1,0\right)$ transition, before making DR measurements at detuning energies from $+1$ to $-1\mathrm{eV}$. In ramp (d), low energy DR measurements were performed without exposing the ion beam to electrons above the $\left(2,1\right)\leftarrow \left(1,1\right)$ threshold (for $t<6\mathrm{s}$) or the $\left(3,0\right)\leftarrow \left(1,0\right)$ threshold (for $t<6\mathrm{s}$), as discussed in Sec. 4B. Ramps (b)–(d) have been offset vertically for clarity, and ramps (c) and (d) have been vertically expanded to show detail. In all experiments, the ion beam was stored for at least four seconds ($t=0$ corresponds to injection into the ring).

Figure 5

Measured dissociative recombination rate as a function of detuning energy. The curve with dots is the data obtained in this work using the Berkeley supersonic expansion ion source. For comparison, the curve without dots is from a run using the JIMIS hollow cathode source, as reported in [28].

Figure 6

Derived thermal rate coefficient as a function of electron temperature, for rotationally cold $\mathrm{H}_3{}^{+}$ ions. Markers indicate $23\mathrm{K}$ (rotational temperature of $\mathrm{H}_3{}^{+}$ towards $\zeta$ Persei) and $300\mathrm{K}$. The dotted line is a power law fit [Eq. (7)].

Figure 7

Energy level diagram for $\mathrm{H}_3{}^{+}$ and ${\mathrm{H}}_3$ (adapted from [45]). The energy, relative to ${\mathrm{H}}_2\left[{}^1\sum _g^{+}\right]+\mathrm{H}\left[n=1\right]$, is shown as a function of the distance between the ${\mathrm{H}}_2$ subunit (with $r_e=1.65a_0=0.873\mathrm{\AA }$ for $\mathrm{H}_3{}^{+}$) and $\mathrm{H}$, for a $C_{2v}$ symmetry structure. ${\mathrm{H}}_3$ states that do not cross the $\mathrm{H}_3{}^{+}$ surface are omitted, with the exception of the dissociative ground state. The energy levels of possible products are shown on the right.

Figure 8

Comparison between the measured dissociative recombination cross section (curve with dots, obtained using the Berkeley source), and theoretical calculations (grey curve) by Kokoouline and Greene [49]. See text for details.