Laser Probing of the Rotational Cooling of Molecular Ions by Electron Collisions

We present state-selected measurements of rotational cooling and excitation rates of ${\mathrm{CH}}^{+}$ molecular ions by inelastic electron collisions. The experiments are carried out at a cryogenic storage ring, making use of a monoenergetic electron beam at matched velocity in combination with state-sensitive laser dissociation of the ${\mathrm{CH}}^{+}$ ions for simultaneous monitoring of the rotational level populations. Employing storage times of up to 600 s, we create conditions where electron-induced cooling to the $J=0$ ground state dominates over radiative relaxation, allowing for the experimental determination of inelastic electron collision rates to benchmark state-of-the-art theoretical calculations. On a broader scale, our experiments pave the way to probe inelastic electron collisions for a variety of molecular ions relevant in various plasma environments.

Figure 1

(a) Schematic of the storage-ring section for laser probing and merged-beam electron-ion interaction. (b) Theoretical near-threshold photodissociation cross sections of ${\mathrm{CH}}^{+}$ ions [25] in $J\le 3$, weighted with a typical $J$ distribution during rotational relaxation in the CSR and convolved with the laser line shape (FWHM $6.1{\mathrm{cm}}^{-1}$). Horizontal brackets: wave number ranges between the thresholds for ${\text{C}}^{+}({}^2{P}_{1/2})$, lower, and ${\text{C}}^{+}({}^2{P}_{3/2})$, upper, for the indicated $J$. Thick vertical lines mark the wave numbers ${\overline{\nu }}_i$ ($i=0,\dots ,2$) and ${\overline{\nu }}_{b^{\prime }}$ where laser probing signals were accumulated. The probing wave numbers are Doppler shift corrected, as explained in the Supplemental Material [29]. Individual $J$ contributions (broken curves) add up to the total probed signal (full curve). The magnified contribution of $J=3$ is shown up to the onset of its continuum level only.

Figure 2

Measured and modeled ${\mathrm{CH}}^{+}$ rotational populations without electron interaction. Data $p_J$ at $t>40\mathrm{s}$ (filled symbols and one-sigma uncertainties) were determined from the signals $S_J$ at the $J$-specific laser-probing wavelengths ($J\le 2$) averaged over the probing time windows indicated at the top (horizontal bars). Specialized laser scans (see the text) yielded populations ${\tilde{p}}_J$ (unfilled symbols) at $t=21\mathrm{s}$ (arrow) for $J\le 3$. With these as initial conditions, the radiative model was fitted to the later $p_0$ and $p_2$ ($p_1$ follows as $1-p_0-p_2$) varying $T_{\mathrm{low}}$ and $\epsilon$. Light colored bands: one-sigma uncertainties of the fitted model populations (including the ${\tilde{p}}_J$ uncertainties).

Figure 3

Laser-probed ${\mathrm{CH}}^{+}$ rotational populations $p_J$ (symbols) with velocity-matched electrons applied in the shaded time windows. Thin full line: fitted $p_J(t)$ for radiative relaxation only from Fig. 2. The other lines show modeled evolutions starting from the $p_J(t=28\mathrm{s})$ measured here. Short-dashed, radiation only; dash-dotted, depletion by $J$-dependent DR also included; long-dashed line, additionally including inelastic collisions using cross sections ${\sigma }_{J,J^{\prime }}^{\mathrm{CB}}(E)$; thick full line, instead, using the $R$-matrix results [11] for the inelastic collisions cross sections. The red line and shaded area show the estimated maximum $J=3$ population. Data points with one-sigma uncertainties.

Figure 4

(a) Population ratios $p_1/p_0$ corresponding to Fig. 3 (electrons applied in shaded time windows) with modeled evolutions starting from the measured populations at $t=28\mathrm{s}$. Short-dashed, radiation only; dash-dotted, depletion by $J$-dependent DR also included; full line, additionally including inelastic collisions with the simplified ${\widehat{\sigma }}_{J,J^{\prime }}(E)$ and fitting for ${\widehat{\sigma }}_{0,1}^0$. (b) Plasma rate coefficients ${\alpha }_{1,0}(T)$ and ${\alpha }_{0,1}(T)$ as constrained by the fitted ${\widehat{\sigma }}_{0,1}^0$ (full lines and shaded one-sigma uncertainty), compared with $R$-matrix theory [11] (coalescing dots) and with the CB calculation (dashed line).