Dissociative Recombination Measurements of Chloronium Ions (D₂Cl⁺) Using an Ion Storage Ring

We performed electron–ion merged-beams DR measurements at the TSR storage ring of the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. Details on various aspects of the merged-beam technique as used at TSR have been described at length by, e.g., Amitay et al. (1996), Wolf (1999), and Novotný et al. (2013). Here we discuss only those aspects specific to this study.

D₂Cl⁺ ions were produced in a cold-cathode Penning ion source from a mixture of D₂ and HCl parent gases. A beam of ions was extracted from the source and brought to a kinetic energy of E_B = 2.3 MeV using a Pelletron-type accelerator. A beam of D${}_{2}{}^{37}$Cl⁺ was charge-to-mass selected using an analyzing dipole magnet and then injected into TSR, where it was stored for ≈50 s.

In the interaction region, the stored ions were merged for ∼1.6 m with a nearly monoenergetic electron beam, dubbed the Target (Sprenger et al. 2004). The mean electron beam velocity was matched to that of the ions for the entire storage time. For the first 30 s after injection, the ions underwent a process known as electron cooling (Poth 1990). During this time, elastic collisions of the ions with the low energy-spread (i.e., cold) electron beam transferred energy from the recirculating ions to the single pass electrons. This reduced the ion beam energy spread, thereby enhancing the energy resolution of the measurements. It also narrowed the beam diameter to <2 mm, improving the geometrical collection efficiency of the products.

Our work on D₂Cl⁺ is the first storage ring experiment where electron cooling of ions with a mass-to-charge ratio as high as 41 u/e has been demonstrated. Here u is the atomic mass unit, and e is the fundamental unit of electrical charge. In other storage ring studies much heavier molecules have been stored (e.g., OPCl₂⁺ by Zhaunerchyk et al. 2008), but in that work the ions were not electron cooled. Our success was enabled by the lower energy-spread of our photocathode-generated electron beam, compared to other electron coolers, and the correspondingly stronger cooling force (Orlov et al. 2004, 2009).

The electron beam is parameterized by effective temperatures ${T}_{\perp }$ and ${T}_{| | }$, perpendicular and parallel, respectively, to the bulk electron beam velocity. The magnetic field guiding the electrons expanded adiabatically from the photocathode to the interaction region by a factor of ξ = 20. For these conditions we expect ${k}_{{\rm{B}}}{T}_{\perp }=1.65\pm 0.35$ meV and ${k}_{{\rm{B}}}{T}_{\parallel }={25}_{-5}^{+45}$ μeV, based on precise fitting of resonance features in the dielectronic recombination measurement of Lestinsky et al. (2008) and on fragment-imaging spectra in the DR studies of Stützel (2011). The uncertainties quoted here and throughout are given at an estimated 1σ statistical confidence level. The Target was operated with typical electron densities of ${n}_{{\rm{e}}}\approx 2.5\,\times {10}^{6}$ cm⁻³.

The ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ ions produced in the discharge are expected initially to possess electronic, vibrational, and rotational excitation. We estimate that much of this excitation radiatively relaxes during the 30 s of electron cooling. We are not aware of any metastable electronic states for ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$, and any bound excited electronic states are expected to quickly relax to the ground electronic state. Vibrationally, we expect that the molecule will rapidly relax to the v = 0 vibrational level. Vibrational decay times for asymmetric triatomic molecules are typically in the millisecond range (e.g., H₂D⁺; Miller et al. 1989). Slower decay times are expected for symmetric molecules, but even in those cases laboratory studies find that the molecules radiatively relax to v = 0 within a few seconds (e.g., ${{\rm{H}}}_{3}^{+}$; Kreckel et al. 2002). Lastly, while the rotational excitation can potentially radiatively cool into equilibrium with the 300 K blackbody radiation of the TSR chamber, this may not be the case for D₂Cl⁺. Studies on other polyatomics at TSR, such as D₃O⁺ (Buhr et al. 2010a), have found rotational excitations significantly higher than 300 K.

After cooling, the Target was used to measure the DR reaction. The resulting neutral products were not deflected by the first dipole magnet downstream of the Target, but rather continued ballistically into a detector that collected most of the neutrals. For the rate coefficient measurements we used a nonsegmented silicon surface-barrier detector. For the fragment-imaging studies we used a segmented silicon surface-barrier detector.

After ∼20 s of measurement (i.e., ∼50 s after injection), the beam intensity became too low to collect a meaningful signal. At that point the current was renewed with a new injection of ions. The injection-cooling-measurement cycle was repeated for several hours, until the desired statistical level was achieved for the data.

Here we present results for ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ DR only at matched mean electron and ion beam velocities, i.e., near-zero relative energy. The DR signal, which generally decreases with increasing relative energy, was sufficiently large to separate from the background only for matched velocities. This background predominantly arises from neutrals generated by collision-induced dissociation of the parent ions on the residual gas in TSR and decreases with increasing ion velocity. However, the high mass of ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ and the magnetic deflection power of TSR limited the ion velocity achievable. This is to be contrasted with DR studies using lighter ions, for which sufficiently high velocities could be used to reduce the dissociation background to a level where DR measurements versus relative energy are possible.

We determined the absolute DR rate coefficient using the ion-beam-lifetime method described at length by Novotný et al. (2012). In short, at a fixed center-of-mass collision energy (here zero, i.e., matched ion and electron beam velocities), we compare the exponential ion beam storage lifetime with the Target electron beam on, ${\tau }^{\mathrm{on}}$, to the lifetime with the electron beam off, τ^off. As long as DR is the dominant electron-driven process, then the difference in beam lifetimes is due solely to DR and the experimental merged-beams DR rate coefficient α_mb is given by

$$\begin{eqnarray}&&{\alpha }_{\mathrm{mb}}=\displaystyle \frac{1}{{n}_{{\rm{e}}}\,\eta }\left(\displaystyle \frac{1}{{\tau }^{\mathrm{on}}}-\displaystyle \frac{1}{{\tau }^{\mathrm{off}}}\right).\end{eqnarray} \tag{ 12 }$$

Here $\eta =L/C$ is the overlap length L of the ion and electron beams in the interaction region normalized by the total storage ring circumference C.

The ion beam lifetimes were determined using as a proxy the neutral fragments coming from the beam. The dominant neutralization process is DR, but there is also a smaller contribution due to neutralizing collisions with the residual gas. The neutrals were detected with a nonsegmented 10 × 10 cm² silicon surface-barrier detector located ∼12 m downstream of the Target center. The rate coefficients for all neutralizing processes are assumed to be constant versus storage time, along with the detector counting efficiency. Thus, the detector signal versus storage time yields the desired ion beam lifetimes with the Target on and off. Results will be presented in Section 4.1.

Although we have directly measured the absolute DR rate coefficient only at matched electron and ion velocities in merged beams, we can still derive a plasma rate coefficient for a plasma with a Maxwell–Boltzmann distribution for a range of temperatures using the general method described in detail by Novotný et al. (2013). First, we deconvolve the measured DR data, accounting for the effects of the electron beam velocity spread and the beam overlap geometry, and extract the DR cross section. Then, we reconvolve the product of the derived cross section and the collision velocity with a Maxwell–Boltzmann distribution to generate a DR plasma rate coefficient.

The method of Novotný et al. (2013) numerically evaluates a model experimental merged-beams rate coefficient ${\alpha }_{\mathrm{mb}}^{{\prime} }$ given by

$$\begin{eqnarray}&&{\alpha }_{\mathrm{mb}}^{{\prime} }=\int {\sigma }^{{\prime} }(E)v\,{f}_{\mathrm{mb}}(E){dE}.\end{eqnarray} \tag{ 13 }$$

Here ${\sigma }^{{\prime} }(E)$ is the model DR cross section as a function of center-of-mass collision energy E, and v is the electron–ion collision velocity. The term ${f}_{\mathrm{mb}}(E)$ is the merged-beams energy distribution in the overlap region of the Target. It is evaluated numerically using a Monte Carlo method and reflects both the beam velocity spreads and the interaction region geometry. To solve for ${\sigma }^{{\prime} }(E)$, we parameterize the model cross section and iteratively modify the parameters until the resulting ${\alpha }_{\mathrm{mb}}^{{\prime} }$ fits the experimental α_mb. The derived ${\sigma }^{{\prime} }(E)$ is then taken as the experimental cross section.

The number of free parameters used to describe ${\sigma }^{{\prime} }$ is limited by the number of center-of-mass energies at which α_mb was measured. Since for D₂Cl⁺ we only collected data for matched beam velocities, ${\sigma }^{{\prime} }(E)$ can be parameterized by one free parameter only. Here we adopt a functional form to reflect the typical low-energy DR behavior, namely,

$$\begin{eqnarray}&&{\sigma }^{{\prime} }(E)=\displaystyle \frac{A}{{E}^{s}},\end{eqnarray} \tag{ 14 }$$

where A is the free parameter and s is a fixed slope. Below we adopt a value of s = 1, which is expected for a direct DR process (Larsson & Orel 2008). However, we also explore a range of possible values, as we discuss in more detail in Section 4.2.

The desired plasma DR rate coefficient versus plasma temperature T can then obtained via numerical integration of

$$\begin{eqnarray}&&{\alpha }_{\mathrm{pl}}(T)=\int {\sigma }^{{\prime} }(E)v\,{f}_{\mathrm{pl}}(E,T){dE}.\end{eqnarray} \tag{ 15 }$$

Here ${f}_{\mathrm{pl}}(E,T)$ is the Maxwell–Boltzmann collision energy distribution at T.

As we show later in Section 4.1, the resulting ${\alpha }_{\mathrm{pl}}(T)$ depends only weakly on the value of s for plasma temperatures T ≲ 20 K. This is due to the fact that our measurements were performed at relative velocities corresponding to these low temperatures, with the collision energy spread being dominated by the transverse electron temperature ${k}_{{\rm{B}}}{T}_{\perp }\approx 1.65$ meV (see Section 3.1). Therefore, our plasma rate coefficient is most reliable at the low temperatures most relevant for astrochemical applications. This is in contrast to other experiments performed at room temperatures that extrapolate their results down to 10 K. Our results will be given in Section 4.2.

3.4.1. Overview

3.4.2. Fragmentation Model

The Monte Carlo fragmentation model is constructed by stochastically simulating DR event positions within the interaction region. The positions of the center of mass are randomized within the ion beam profile as projected on the detector. The measured distribution of the transverse center-of-mass positions for nonambiguous DR events (e.g., assigned D + D + Cl) serves to model this ion beam profile.

The longitudinal dissociation positions are distributed homogeneously throughout the interaction region. We neglect the effects of the merging and de-merging regions, as the collision energy in these edge regions is significantly larger than that in the bulk of the interaction region. This higher energy is due to the nonzero collision angle between the electron and ion beams in the edge regions. Since the DR cross section rapidly decreases with increasing collision energy, DR in these edge regions is greatly suppressed relative to that in the straight portion of the interaction region. The error introduced by this approximation is estimated to be small.

At the near-zero collision energy measured here, the electron–ion collision vector is randomly oriented with respect to the beam direction. Additionally, the molecules are randomly oriented in space. As a result, there is no preferred orientation for the fragmentation. The relative orientation of the fragments at the time of dissociation is determined by the orientation of the molecule at that time. Since these are random, for the two-body fragmentation channels we homogeneously randomize the orientation of the vector between the two fragments. For the three-body channel we randomize the normal vector of the dissociation plane and the rotation of the plane around this normal vector.

Another parameter to vary is the KER, E_k, for each simulated event. For all event types, E_k is given by the sum of the fragment i kinetic energies, ${E}_{{\rm{k}},i}$, in the center-of-mass frame

$$\begin{eqnarray}&&{E}_{{\rm{k}}}=\sum {E}_{{\rm{k}},i}.\end{eqnarray} \tag{ 16 }$$

In the two-body channels E_k is the only remaining parameter to vary. There, by specifying E_k, the ${E}_{{\rm{k}},i}$ components are set by energy and momentum conservation, which also yield the relative velocities of the fragments. The resulting transverse distance d between the fragments, as measured at the detector, can then readily be determined for the model from the orientation of the fragmentation vector and the relative velocities. The KER distributions $f({E}_{{\rm{k}}})$ are generally not known a priori and must be determined from the measured data. We follow a method similar to that of Buhr et al. (2010b) and use the fit of our modeled distribution f(d) to the data to find $f({E}_{{\rm{k}}})$. In short, we divide the KER distribution into a number of narrow energy ranges, each with an arbitrary amplitude. We next use the fragmentation and detector models to generate fragment distance distributions for each KER range. The amplitude for each of these distributions is used as a fitting factor, and the sum of these distributions is then fitted to the experimental data, thereby yielding $f({E}_{{\rm{k}}})$. Additional details are given in Sections 4.3–4.5, where we also outline how we account for channel mixing.

Our simulations for the three-body channel model the momentum distribution of the fragments in the dissociation plane. Conservation of energy and momentum enables us to split this problem into two parts: the KER distribution and the correlation between the momenta of the fragments. Below we describe how we determine both of these from the experimental data.

The KER distribution is inferred from the fragment kinetic energies ${E}_{{\rm{k}},i}^{\perp }$ projected onto the detector plane. We calculate these using the distances d_i between the fragment impact positions and the center of mass, both as projected onto the detector plane. Following the procedure of Buhr et al. (2010b), the relation between ${E}_{{\rm{k}},i}^{\perp }$ and d_i is given by

$$\begin{eqnarray}&&{E}_{{\rm{k}},i}^{\perp }={E}_{{\rm{B}}}\displaystyle \frac{{M}_{i}}{M}\displaystyle \frac{{d}_{i}^{2}}{{S}^{2}},\end{eqnarray} \tag{ 17 }$$

where M_i is the mass of the $i\mathrm{th}$ fragment, $M=\sum {M}_{i}$, ${E}_{{\rm{B}}}$ is the ion beam energy, and S = 9.41 m is the distance from the center of the interaction zone to the EMU detector. The total projected KER is then defined as ${E}_{{\rm{k}}}^{\perp }=\sum {E}_{{\rm{k}},i}^{\perp }$. The measured distribution of projected energies $f({E}_{{\rm{k}}}^{\perp })$ reflects the physical $f({E}_{{\rm{k}}})$ distribution but is strongly modified by observational effects, i.e., the projection of three-dimensional fragment coordinates onto the detector plane, the counting efficiencies of individual strips of the detector, the spread of flight distances due to the finite length of the interaction zone, and so on. These effects are taken into account when the event coordinates are generated by the Monte Carlo model. Moreover, an experimentally determined fragment angular correlation, assumed to be independent of the KER, is applied in this model.

The fragment momenta correlation of a three-body decay can be represented by the two-dimensional distribution of the Dalitz coordinates (Dalitz 1953). Dalitz introduced the coordinates η₁ and η₂ as linear combinations of the kinetic energies ${E}_{{\rm{k}},i}$ of the three fragments in the center-of-mass frame, taking into account conservation of energy and momentum. For the case of D + D + Cl, with one fragment having a mass different from the others, the coordinates are defined as (Strasser et al. 2004; Lammich 2004)

$$\begin{eqnarray}&&{\eta }_{1}=\sqrt{\displaystyle \frac{M}{{M}_{3}}}\displaystyle \frac{{E}_{{\rm{k}},2}-{E}_{{\rm{k}},1}}{3{E}_{{\rm{k}}}},\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&{\eta }_{2}=\displaystyle \frac{M}{3{M}_{1}}\displaystyle \frac{{E}_{{\rm{k}},3}}{{E}_{{\rm{k}}}}-\displaystyle \frac{1}{3},\end{eqnarray} \tag{ 19 }$$

where ${M}_{1}={M}_{2}\ne {M}_{3}$. For a phase-space-dominated breakup without correlations (i.e., with all dissociation geometries equally likely), the distribution of η₁ versus η₂ (a Dalitz plot) is homogeneous (i.e., flat). Any inhomogeneities in the Dalitz plot indicate preferred or forbidden dissociation geometries.

We determine the distribution $f({\eta }_{1},{\eta }_{2})$ by using a parameterized representation of it in the Monte Carlo model and by calculating the corresponding distribution $f({Q}_{1},{Q}_{2})$ suitable for a fit to the detector data. Adapted to the transverse coordinates measured, this uses the modified Dalitz coordinates Q₁ and Q₂ defined as (Strasser et al. 2002, 2004)

$$\begin{eqnarray}&&{Q}_{1}=\sqrt{\displaystyle \frac{M}{{M}_{3}}}\displaystyle \frac{{E}_{{\rm{k}},2}^{\perp }-{E}_{{\rm{k}},1}^{\perp }}{3{E}_{{\rm{k}}}^{\perp }},\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&{Q}_{2}=\displaystyle \frac{M}{3{M}_{1}}\displaystyle \frac{{E}_{{\rm{k}},3}^{\perp }}{{E}_{{\rm{k}}}^{\perp }}-\displaystyle \frac{1}{3}.\end{eqnarray} \tag{ 21 }$$

Unlike $f({\eta }_{1},{\eta }_{2})$, the distribution $f({Q}_{1},{Q}_{2})$ is no longer flat for an isotropic breakup. Therefore, the measured $f({Q}_{1},{Q}_{2})$ is first divided by a simulated one assuming isotropic (phase-space-dominated) breakup in order to compensate for possible detection efficiency variations and to regain a uniformly populated Dalitz plot in case there are no momentum correlations between the fragments. From here on $f({Q}_{1},{Q}_{2})$ stands for such a normalized distribution.

This resulting $f({Q}_{1},{Q}_{2})$ is related nonlinearly to the underlying $f({\eta }_{1},{\eta }_{2})$ distribution. As a result, any sharp features in $f({\eta }_{1},{\eta }_{2})$ are smoothed out when plotted in the experimentally accessible $f({Q}_{1},{Q}_{2})$ representation. To extract the underlying dissociation data, we use a parameterized model ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ distribution as the input for the simulated fragmentation and detector model. The resulting model distribution ${f}^{{\prime} }({Q}_{1},{Q}_{2})$ is fitted to the measured $f({Q}_{1},{Q}_{2})$ by iteratively changing the parameters of ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$. The optimized ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ is then taken as a representation of the real $f({\eta }_{1},{\eta }_{2})$. The specific parameterization of ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ is discussed below in Section 4.3.

3.4.3. Detector Model

The detector model includes the geometric cutoff (due to the detector size and location), the detection energy thresholds for D fragments on each strip, the energy resolution for the various fragment masses, the effects of coincident multi-hits on any given single strip, the signal amplification functions for each strip, the signal dependence on the thickness of various strip parts, signal splitting between strips (when hitting the 30 μm gap between the strips), and so on. The implementation of most of these effects has been described previously by Buhr et al. (2010b). The parameters entering the model are based partly on our ab initio understanding of the detector structure (e.g., the strip-to-gap area ratio) and partly on empirical adjustments to match the measured data (e.g., the energy resolution for the various fragments). It is beyond the scope of this paper to describe the detector model in more detail. Instead, we demonstrate the quality achieved for the detector model by comparing the measured and modeled data.

The measured pulse height distributions for the three-body DR channel are shown in Figure 1 for both the front side and back side of the EMU detector. The histograms plot the number of counts versus channel number of the analog-to-digital converter (ADC), i.e., the pulse height. The data have been summed over all strips for each side. Only the assigned three-body data are presented here in order to avoid issues of channel mixing and simplify the comparison between the data and the model.

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Overall, we find good agreement between the data and model for most of the ADC range. The peaks corresponding to the D and D₂ kinetic energies are well separated at ADC channel numbers of ∼80 and ∼130, while the pulse heights from the Cl, DCl, and D₂Cl fragments are unresolved, forming one broad peak at ∼800.

We use the signal from the heavy fragment on the front side of the detector to trigger a readout of the data whenever an event has an ADC channel number above 650. As a result, there is no signal on the front side between ∼150 and 650 (with channel numbers below 150 corresponding to D and D₂ fragments that do not trigger a readout but are recorded if accompanied by a heavy particle impact above channel 650). The signal on the back side in this range we attribute to a heavy fragment hitting a gap between back-side strips. The resulting charge appears to diffuse to a larger area on the back side, where it is collected by one or two strips. Additionally, our modeling indicates that the enhancement on the back side at ∼600 arises from the particles hitting thicker parts on the front side of the detector electrodes, thus losing more energy before hitting the back-side strip. Lastly, an enhancement in the pulse height distribution above 900 was seen in both the DR data and the non-DR background. The effect likely originates from the amplification electronics chain. However, the ratio of the area in this high-end shoulder relative to the main peak was the same for both the DR and non-DR signal. Hence, including or excluding this range had no effects on our data analysis below. We found that this feature is insensitive to impact position, storage time, and other possible systematic effects.

3.4.4. Non-DR Background Subtraction

3.4.5. DR Branching Ratios

As mentioned above, mixing of the different physical DR channels in some of the experimentally assigned channels can be modeled by the Monte Carlo procedure once the fragmentation energetics and angular geometries are specified. This model can then predict how many events from a given physical DR channel j will be assigned to an observed channel i. We quantify the matrix describing this mixing through a Monte Carlo simulation of 10⁶ events for each DR channel j, using the fragmentation and detector models described above. From the resulting mixing coefficients, we can obtain the desired DR branching ratio R_j for channel j.

As mixing coefficients, the matrix elements A_ij relate the number of actual events n_j from channel j and the number of observed events o_i assigned to channel i by the reconstruction procedure as

$$\begin{eqnarray}&&{o}_{i}=\displaystyle \sum _{j}{A}_{{ij}}{n}_{j}.\end{eqnarray} \tag{ 22 }$$

To obtain the DR branching ratios R_j, we rewrite Equation (22) in matrix form and solve for n_j as

$$\begin{eqnarray}&&{\boldsymbol{n}}={{\boldsymbol{A}}}^{-1}{\boldsymbol{o}}.\end{eqnarray} \tag{ 23 }$$

The resulting branching ratios are given by

$$\begin{eqnarray}&&{R}_{j}=\displaystyle \frac{{n}_{j}}{{\displaystyle \sum }_{{j}^{{\prime} }}{n}_{{j}^{{\prime} }}}.\end{eqnarray} \tag{ 24 }$$

To verify the accuracy of the branching ratio analysis, we have performed measurements for two very different ion beam configurations. For the first case the ion and electron beams were aligned in the interaction zone so that the ion beam axis pointed to the center of the detector. This is the same arrangement as for the rate coefficient measurements, and it was also used to determine the KER distributions and angular correlation function for the physical DR reactions. In the second configuration we moved both beams so that, while they remained aligned, the ion beam axis pointed ∼23 mm away from the center of the detector. These two configurations, which we dub as centered and off-center, lead to very different results for the channel mixing. For example, the geometric cutoff is asymmetric for the second configuration and thus more sensitive for the input $f({E}_{{\rm{k}}})$ distributions in the individual fragmentation channels. As a result, the mixing matrices ${\boldsymbol{A}}$ are very different for the two configurations.

As we will show in Section 4.5, for both the centered and off-centered configurations we find the DR branching ratios to agree within their mutual uncertainties. This gives us a high degree of confidence in our analysis.

We determine the absolute merged-beams rate coefficient α_mb using the detector count rate versus storage time from the nonsegmented silicon surface-barrier detector (see Section 3.2). An example of the measured signal versus storage time is shown in Figure 2. For this particular run the Target beam was on during ion storage times from t = 0 to ≈33 s, off for t ≈ 33–42 s, and on again for t ≈ 42–52 s. During the electron-on phases, the electron and ion beams were matched in velocity. The fitted exponential decay times τ are given in the figure. The other parameters used for determining α_mb were ${n}_{{\rm{e}}}=2.39\times {10}^{6}$ cm⁻³, L = 1.57 m, and C = 55.4 m.

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To test for systematic effects, we varied the time at which the Target was turned off, the time at which it was turned back on, and the length of each of these two periods. The resulting values for α_mb all agreed to within their statistical uncertainties. This supports our assumption that the rate coefficients for all neutralizing processes that significantly contribute to our detector signal are constant versus storage time.

The resulting merged-beams rate coefficient for DR of D${}_{2}{}^{37}$Cl⁺ at matched mean electron and ion beam velocities is

$$\begin{eqnarray}&&{\alpha }_{\mathrm{mb}}=(2.07\pm 0.25)\times {10}^{-6}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 25 }$$

The total uncertainty amounts to 12%. It is dominated by the 11% error on the fitting of the ion beam lifetime. Additional contributions to the uncertainty are due to the electron density (∼4%) and the L/C ratio (≲2%).

We have converted α_mb to the plasma rate coefficient α_pl using the procedure described in Section 3.3 for s = 1. The resulting α_pl is displayed in Figure 3 for the plasma temperature range of T = 5–500 K. The rate coefficient can be represented as

$$\begin{eqnarray}&&{\alpha }_{\mathrm{pl}}(T)=4.3\times {10}^{-7}{\left(\displaystyle \frac{300}{T}\right)}^{0.5}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1},\end{eqnarray} \tag{ 26 }$$

a form that can readily be incorporated into common astrochemical databases.

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There are several sources of uncertainty in α_pl. Here we discuss only the most important ones. The 12% uncertainty in α_mb translates into a temperature-independent uncertainty of 12% in α_pl. Extracting the DR cross section introduces an uncertainty dominated by the error in ${f}_{\mathrm{mb}}(E)$, which in turn is dominated by the uncertainty of ${k}_{{\rm{B}}}{T}_{\perp }$. Taking the outermost values of ${k}_{{\rm{B}}}{T}_{\perp }=1.3$ and 1.9 meV results in changes to α_pl of −9.7% and +6.2%, respectively. These values are not dependent on T. The effect of the uncertainty in ${k}_{{\rm{B}}}{T}_{\parallel }$ is negligible.

The largest uncertainty in α_pl arises from our adoption of s = 1 for the cross-section slope (Larsson & Orel 2008). However, the slopes for molecules similar to ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ have been found experimentally to vary from s ≈ 0.75 to 1.4 (Florescu-Mitchell & Mitchell 2006). This propagates into a temperature-dependent uncertainty in α_pl. For the temperature range considered here, the change is ${}_{-15}^{+10} \%$ at T = 5 K. It drops to ${}_{-5.4}^{+0.0} \%$ at T ≈ 8 K and then increases to ${}_{-61}^{+75} \%$ at T = 100 K and further to ${}_{-97}^{+160} \%$ at T = 500 K.

We find that the adopted value of s has the smallest effect on α_pl at T ≈ 8 K. This is because the distribution of collision energies E contributing to the measured α_mb is comparable to those contributing to α_pl at this temperature. Hence, our results are particularly reliable for the typical molecular cloud temperatures of ≈10 K.

Understanding the three-body dissociation channel in detail subsequently enables us to accurately model the mixing of this channel into any other one. For the outgoing D + D + Cl channel, we determine the geometry of the fragments after dissociation (i.e., the dissociation velocity vectors) using the EMU detector (Section 3.4). Mixing into this fragmentation channel from either of the two-body channels is negligibly small, less than 0.1%, and we do not account for it in our analysis. Non-DR background into this channel is also low, but we correct for it as described in Section 3.4.4.

In Figure 4 we plot the measured and modeled Dalitz plots for this dissociation channel. Panel (a) shows the measured data in the projected representation $f({Q}_{1},{Q}_{2})$. The corresponding model distribution ${f}^{{\prime} }({Q}_{1},{Q}_{2})$ is presented in panel (b). This distribution, in turn, is derived from a convolution of the parameterized model ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ with the detector model. Both distributions have mirror symmetry with respect to Q₁ = 0.

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In Figures 4(c) and (d) we use the [η₁, η₂] dependencies. The results shown in each panel have mirror symmetry with respect to η₁ = 0. Panel (c) shows for various regions of the Dalitz plot the corresponding geometry of the fragments after dissociation. The vectors show the relative velocity of the fragments relative to the dissociation origin, which falls under the Cl atom marker in the figure.

We have parameterized our ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ model using a grid of 10 fixed points and varying the amplitude at each of these (η₁, η₂) coordinates, which are indicated in panel (d). These points have been chosen to best reproduce the largest variations in the measured $f({Q}_{1},{Q}_{2})$. We limited the number of points to keep the model calculations tractable and linearly interpolated the amplitude between these 10 data points to fill in the rest of the (η₁, η₂) plane. The amplitudes of ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ were varied to minimize the difference between the measured $f({Q}_{1},{Q}_{2})$ and the model ${f}^{{\prime} }({Q}_{1},{Q}_{2})$.

The KER for each fragmentation channel, E_k, is given by Equation (7). Our measurements were performed for matched electron and ion velocities. Under these conditions, the width of the electron energy distribution determines the typical DR collision energy, here $E\sim {k}_{{\rm{B}}}{T}_{\perp }\approx 1.65$ meV. This energy is much smaller than the other three terms contributing to E_k and can be neglected for the discussion below. We infer the values for these other three components using the distribution of fragment kinetic energies $f({E}_{{\rm{k}}})$ that fits the observed kinematical distribution, i.e., $f({E}_{{\rm{k}}}^{\perp })$ or f(d) for the three-body channel or the two-body channels, respectively.

4.4.1. D + D + Cl

Figure 5 shows the measured $f({E}_{{\rm{k}}}^{\perp })$ for the three-body channel and compares it to a model ${f}^{{\prime} }({E}_{{\rm{k}}}^{\perp })$. The model uses the fragmentation geometries ${f}^{{\prime} }({\eta }_{1},{\eta }_{2})$ as determined above for this channel. The exothermicity of the ground-state molecule is ${E}_{0}\approx 3.5\,\mathrm{eV}$. The internal energy of the parent ion is expected to be rotational only (see Section 3.1). We approximate this using a Boltzmann distribution of energies with a temperature T_rot, which we convolve to yield the modeled ${f}^{{\prime} }({E}_{{\rm{k}}})$ distribution.

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The only excited product accessible at the near-zero relative collision energy measured here is the fine-structure Cl(${}^{2}{P}_{1/2}$), lying ∼0.11 eV above the Cl(${}^{2}{P}_{3/2}$) ground level. The energy difference between these two levels is too small for us to experimentally distinguish them and to derive their population ratio. To account for this, we assume that the J = 3/2 and 1/2 fine-structure levels are populated according to their statistical weights with a 2:1 ratio, respectively. Thus, in our modeled distributions, we treat two-thirds of the Cl as being in their ground level and one-third as being excited such that ${E}_{\mathrm{exc}}^{\mathrm{prod}}=0.11\,\mathrm{eV}$ in Equation (7).

We calculate the model ${f}^{{\prime} }({E}_{{\rm{k}}}^{\perp })$ distribution using a Monte Carlo approach combined with the fragmentation and detector models described earlier. In the fit we keep the rotational temperature ${T}_{\mathrm{rot}}$ of the ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ as a free parameter. Additionally, due to the uncertainty in the estimated value of E₀ = 3.5 eV (see Section 2), we also treat E₀ as a free parameter. The best agreement between the measured $f({E}_{{\rm{k}}}^{\perp })$ and modeled ${f}^{{\prime} }({E}_{{\rm{k}}}^{\perp })$ distributions, shown in Figure 5, was found for T_rot = 1200 ± 1000 K and ${E}_{0}({\rm{D}}+{\rm{D}}+\mathrm{Cl})=3.22\pm 0.06\,\mathrm{eV}$. We note that the derived T_rot is far from the the wall temperature of TSR at ≈300 K, indicating that the ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ ions did not reach equilibrium with the blackbody radiation. For such a nonequilibrium case, a Boltzmann distribution may not describe the rotational population correctly. Nevertheless, our simplified cooling models have shown that this deficiency is negligible compared to the T_rot uncertainty, which is dominated by other systematic errors in the model. These errors are discussed in more detail in Section 4.5.

4.4.2. D₂ + Cl

Mixing into the D₂ + Cl channel from the other fragmentation channels is estimated by our models to be less than 0.2%. Hence, the data for this channel can be easily filtered from that for the other two channels.

Figure 6(a) shows the projected fragment distance distribution f(d) for this two-body channel. We have fitted the measured data using the model distribution ${f}^{{\prime} }(d)\,={\sum }_{i}{S}_{i}{f}_{i}^{{\prime} }(d)$. Each ${f}_{i}^{{\prime} }(d)$ represents the modeled subdistribution for fragment kinetic energies uniformly distributed within a narrow E_k range chosen to represent a bin in the $f({E}_{{\rm{k}}})$ distribution. These subdistributions are each normalized to unity and multiplied by a scaling factor S_i, derived by fitting ${f}^{{\prime} }(d)$ to the measured f(d). The resulting model distributions ${f}^{{\prime} }(d)$ and ${f}_{i}^{{\prime} }(d)$ are indicated in Figure 6(a). We note that the model distributions already include rotational excitation of the ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ parent ions with the value of T_rot determined in Section 4.4.1.

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Using these distributions, we can derive the binned $f({E}_{{\rm{k}}})$ distribution, as shown in Figure 6(b). From this, using Equation (7), we can infer the internal energy distribution of the product D₂ molecule, as the Cl cannot be excited to higher terms by the energy released in the dissociation process. In this model, the bin widths were chosen as narrow as possible while still enabling the fitting algorithm to converge. We note that these widths are much broader than the energy spacing of the rovibrational levels in the product D₂. The amplitude for each bin corresponds to the respective value of S_i for that subdistribution. The error bars plotted present the statistical uncertainty of the fit for each bin.

4.4.3. D + DCl

Mixing into the D + DCl channel is strong. The dominant contamination is from the D + D + Cl channel, due to one of the D fragments not being detected. This results either from the geometrical limits of the detector or from an electronic signal in one of the detector strips that is too low to be detected. We correct the measured fragment distance distribution f(d) for this contamination by modeling the contribution from the three-body channel.

In Figure 7(a) we plot the measured f(d) distribution assigned by the reconstruction procedure to the ${\rm{D}}+\mathrm{DCl}$ channel together with the simulated, large contribution from the D + D + Cl channel. We simulate mixing into the ${\rm{D}}+\mathrm{DCl}$ channel from the D + D + Cl channel using the parameters for the three-body dissociation channel that we have experimentally determined above, i.e., $f({\eta }_{1},{\eta }_{2})$, ${T}_{\mathrm{rot}}$, and ${E}_{0}({\rm{D}}+{\rm{D}}+\mathrm{Cl})$. We have also scaled the model so that the number of unambiguous three-body dissociation events matches the number of experimental three-body events assigned by the reconstruction procedure. The difference between the two curves then represents the transverse distance distribution caused by the physical D + DCl channel alone. Using the same procedure as for the ${{\rm{D}}}_{2}+\mathrm{Cl}$ channel above, we can infer the corresponding internal energy of the product DCl. This is shown in Figure 7(b).

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Section 3.4.5 describes our procedure for determining the DR fragmentation branching ratios. The specific model we have used includes four outgoing channels: three for the expected DR fragmentation channels and one for nondissociative recombination forming D₂Cl. This last channel is included because it can be assigned for events in which one or both light fragments (essentially D) escape observation. The branching ratio for this nondissociative channel, as we will show later, is consistent with the expected value of zero. Using this four-channel model, we have determined the mixing coefficients A_ij between the four channels for both the centered and off-center beam configurations.

In the model used the parameters for the three DR fragmentation channels include ${T}_{\mathrm{rot}}$, the three-body dissociation distribution $f({\eta }_{1},{\eta }_{2})$, and the KER distribution $f({E}_{{\rm{k}}})$ for each of the outgoing DR channels. The determination of these parameters has been described above. For the nondissociative recombination channel, we treat the neutral D₂Cl molecule as propagating along the velocity vector of the parent ion at the point where recombination occurs.

Starting with the measured fragment-imaging data, we use the event reconstruction procedure described in Section 3.4 to determine the total number of observed events assigned to each of the four outgoing channels, o_i. The branching ratios R_j are then derived by solving Equations (23) and (24). Table 1 presents the results for both the centered and off-center beam configurations. The branching ratios are given in percentage, followed by their statistical uncertainty and then their systematic error. We have combined these two data sets using a statistically weighted average, which is also given in the table along with the corresponding systematic error. The branching ratio for the nondissociative channel is consistent with zero. As will be discussed in Section 5.4, we find no evidence in our imaging data for this channel. So we present in the final line of the table the branching ratios corrected for the nondissociative channel branching ratio being zero.

The dominant source of statistical uncertainty in the branching ratios arises from the counting statistics for the number of counts assigned to each channel (the o_i values). We determined the statistical uncertainties of the branching ratios using a sensitivity analysis. The o_i values are assumed to follow normal distributions with a 1σ width of $\sqrt{N}$, where N is the number of counts. Starting with the measured o_i values, we randomly and independently varied the number of counts for each channel using a normal distribution. Each trial resulted in new o_i values and correspondingly modified branching ratios. This process was repeated for 1000 trials. The resulting branching ratio distribution for each channel was fit using a Gaussian to estimated 1σ statistical uncertainty in the measurement.

We have estimated the systematic uncertainties by calculating how the derived branching ratios change as a result of systematic shifts in various input parameters. The parameters that we varied include as follows: the mass-assignment window sizes, i.e., the range of signal amplitudes assigned to a certain mass; the ion beam width; $f({\eta }_{1},{\eta }_{2});$ ${E}_{0}({\rm{D}}+{\rm{D}}+\mathrm{Cl})$ and T_rot, which, together with $f({\eta }_{1},{\eta }_{2})$, determine the fragment kinetic energy distribution for the three-body channel; $f({E}_{{\rm{k}}})$ for the two-body channels; and the scaling of the non-DR distributions for background subtraction. We combine the resulting shifts in R_j in quadrature and give the resulting estimated systematic uncertainties in Table 1.

As a final note in this section, we point out that for any given channel in Table 1 the branching ratios for the centered and off-center beam configurations lie well within the corresponding systematic uncertainties. This demonstrates the reliability of our fragmentation and detection models and the accuracy of the resulting branching ratios.

Figure 3 shows our experimentally derived plasma rate coefficient. Our result is most accurate for a translational temperature of T ≈ 8 K, i.e., similar to typical dense molecular cloud temperatures. We have extrapolated to lower and higher temperatures using typical DR translational-temperature dependencies.

Also shown in Figure 3 are the results from other experimental groups. W. Geppert et al. (2009, private communication) measured ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ DR using the CRYRING ion storage ring. Within the mutual error bars, their results and ours are in agreement. This is expected, given the similar systematics of the CRYRING and TSR experiments and also due to the expected similar levels of internal excitation of the parent ${{\rm{D}}}_{2}{}^{37}{\mathrm{Cl}}^{+}$ ions.

Wiens et al. (2016) measured DR for ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ and ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ in a flowing afterglow experiment for translational kinetic temperatures of T = 300–500 K. They estimate the accuracy of their results to be ±30%. Our extrapolated ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ results agree well with their measured results, to within the respective error bars. Their results are also in good agreement with the ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ results of W. Geppert et al. (2009, private communication). We note that the rate coefficient temperature dependencies of Wiens et al. (2016) suffer from large uncertainties. Moreover, the internal and translational temperatures in their experiment are coupled, which is in contrast to our storage ring measurement. Hence, one cannot reliably extrapolate the rate coefficient results of Wiens et al. (2016) to low temperatures to compare to our data.

Using a pulsed discharge source combined with infrared time-resolved spectroscopy, Kawaguchi et al. (2016) derived the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ DR rate coefficient for an estimated T = 209 K. These results are nearly an order of magnitude below the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ results of Wiens et al. (2016). One possible explanation for the discrepancy may be an error in the translational temperature. Kawaguchi et al. assumed this temperature to be equal to the ${{\rm{H}}}_{3}^{+}$ rotational temperature that they determined in a separate experiment under similar conditions. Another possible source of error may arise from additional chemical processes occurring in the plasma. The stated electron density is much higher than that of ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$. Since the overall plasma is expected to be neutral, this implies the presence of other ions and other reactions that may affect the inferred ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ DR rate coefficient.

For the three-body D + D + Cl channel, the KER distribution $f({E}_{{\rm{k}}})$ is expected to be narrow in energy, broadened only by the rotational excitation of the parent ions and by the fine-structure splitting in the Cl product. The latter is too small for us to resolve, and we have assumed that the fine-structure levels are populated according to their statistical weights. (Note that $f({E}_{{\rm{k}}})$ appears broadened when transformed into $f({E}_{{\rm{k}}}^{\perp })$, as shown in Figure 5.) The inferred exothermicity is ${E}_{0}({\rm{D}}+{\rm{D}}+\mathrm{Cl})=3.22\pm 0.06\,\mathrm{eV}$. This available energy is insufficient to excite either the D or Cl products into the first term above the ground term. This energy also differs from the 3.5 ± 0.1 eV calculated for the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ isotopologue (i.e., Equation (10)). A part of this difference (≈0.1 eV) can be explained by the lowering of the zero-point energy in ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ versus ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$. The remaining ≈0.1 eV difference is comparable to the error bars of the result.

For each of the two-body fragmentation channels, D₂ + Cl and DCl + D, we observe broad KER distributions, Figures 6(b) and 7(b), respectively. Each of these span from the expected maximum KER (i.e., the E₀ = 7.9 eV exothermicity for each reaction) and extend downward to lower energies. The maximum KER corresponds to the daughter products being in their lowest energy levels of their ground electronic states. As the KER decreases, the "missing" energy goes into internal excitation of the DR products. Each of these KER distributions turns off for energies below ∼3 eV. We attribute this to the internal excitation being sufficient to dissociation of the daughter molecular products, i.e., to the opening up of the three-body DR channel. This ∼3 eV corresponds well to the E₀ of the three-body channel, to within the energy resolution of our KER distribution analysis for the two-body channels. Similar KER distributions, extending from the two-body E₀ value and going down to the three-body fragmentation E₀ value, have been observed in DR of ${{\rm{H}}}_{3}^{+}$, D₂H⁺, D₃O⁺, and DCND⁺ (Strasser et al. 2002; Buhr et al. 2010a, 2010b; Mendes et al. 2012).

The maximum energy released here by either two-body DR channel at matched beams' velocities is 7.9 eV. This available energy is insufficient to excite either the D or Cl products into the first term above the ground term. It is also not sufficient to excite the daughter D₂ or DCl to their lowest bound electronic states above their ground levels. In H₂ (and similarly D₂) the first excited bound electronic state lies ∼10.5 eV above the ground electronic state (Field et al. 1966). For HCl (DCl) this occurs at ∼9.5 eV (Alexander et al. 1998). Thus, we expect the D₂ and DCl daughter products to be formed in their ground electronic states and attribute the observed spread in the KER distributions to rovibrational excitation of the daughter molecules.

Our DR results also demonstrate that the dissociation occurs soon after recombination, on a timescale much shorter than the ∼3 μs time of flight between the electron–ion interaction zone and the detector. If the dissociation proceeded more slowly, then we would expect some of the recombined parent molecules to dissociate downstream of the electron–ion interaction region. This would result in smaller fragment distances d at the detector and correspondingly smaller inferred values of E_k. The absence of any two-body DR events observed with E_k below the expected three-body dissociation limit demonstrates that dissociation occurs soon after electron capture, which is as we assume in our dissociation model.

Using the Dalitz plots shown in Figure 4, we can determine the most likely fragmentation geometries for the D + D + Cl dissociation channel. Figure 4(d) shows the inferred data for the f(η₁, η₂) representation after deconvolving the experimental effects. We have parameterized f(η₁, η₂) using 10 pairs of [η₁, η₂] coordinates and linearly interpolated between the points in radial coordinates. The peak at (η₁, η₂) ≈ (0, −0.3) corresponds to dissociation in a linear D – Cl – D geometry and accounts for ∼40% of the dissociations. The peak at (η₁, η₂) ≈ (0, 0) corresponds to dissociation in an equilateral triangle geometry and accounts for ∼30% of the dissociations. The remaining area in the Dalitz plot corresponds to dissociations into all other geometries and accounts for the remaining ∼30% of the dissociations. However, given that we only use 10 pairs of coordinates in our model for f(η₁, η₂), it is possible that this third component may be an artifact from the numerical processing of our data.

It is interesting to note that the linear dissociation channel is so strong. The parent ion has a bent geometry with an equilibrium angle of 94° (Chattopadhyay 2010). This suggests that the dissociation triggered by the capture of a low-energy electron occurs along one or several repulsive potential surfaces of complex shape, so that the dissociation velocity vectors do not represent the original physical arrangement of the atoms. Consistent with earlier observations on, e.g., ${{\rm{O}}}_{3}^{+}$ (Zhaunerchyk et al. 2007), this contradicts a simple "bond-breaking" picture of the DR process.

Table 1 gives the statistically weighted averages for the experimental branching ratios of the outgoing channels for electrons recombining with ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$. At this step of the analysis we have included the nondissociative channel leading to D₂Cl as a possible physical recombination channel. As expected (see next paragraph), we find that the branching ratio for this nondissociative channel is consistent with zero, to within the experimental uncertainties, and set the branching ratio for this channel to zero. The resulting final branching ratios for the remaining three DR channels are listed in the last row of Table 1.

For the nondissociative channel to be nonzero the unlikely scenario would be required that the recombined D₂Cl molecules remain internally excited by >12 eV for the ∼3 μs flight time from the interaction zone to the detector. However, this excitation energy lies ∼4.4 eV above the D₂Cl dissociation energy. Thus, even if metastable D₂Cl existed, we would expect some fraction of the molecules to dissociate during this time interval. These delayed dissociations would result in an enhancement in the measured signal at low fragment distances d, resulting in values for E_k or ${E}_{{\rm{k}}}^{\perp }$ that would be significantly lower than those derived from the molecular energetics of Equations (8)–(10). We find no such signatures in any of the $f({E}_{{\rm{k}}})$ and $f({E}_{{\rm{k}}}^{\perp })$ distributions for any fragmentation channel. Thus, we conclude either that the nondissociative recombination channel of ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ (Equation (11)) is indeed closed or that its rate coefficient is negligible in comparison to the DR channels (Equations (8)–(10)).

To the best of our knowledge, there are no published experimental or theoretical branching ratios for DR of any of the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ isotopologues. There are, however, two estimates. Astrochemists have long assumed a branching ratio of 10% for the HCl+H fragmentation channel, largely motivated by their attempts to match the small HCl abundances observed in diffuse clouds (e.g., Neufeld et al. 2015, and references therein). Interestingly, this observationally motivated estimate agrees reasonably well with our results for the DCl + D channel. Conversely, Roueff & Herbst (2011) estimate the branching ratio for the H + H + Cl fragmentation channel to be 56%. They base their estimate on the apparent correlation between the three-body DR fragmentation branching ratio and the reaction exoergicity E₀ observed for DR of other dihydride ions. However, there is a large scatter in the data of their correlation plot, suggesting that any correlation is very weak, at best. Our ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ result of ≈86% for the D + D + Cl channel lies well above their estimated branching ratio and further adds to the scatter of the data on their correlation plot.

Our results appear unlikely to explain the discrepancy between the observationally inferred HCl and H₂Cl⁺ abundances and the ∼3–5 times smaller predicted abundances (De Luca et al. 2012; Monje et al. 2013; Neufeld et al. 2015). The astrochemical models of Neufeld et al. (2015) use the DR rate coefficient for ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ from W. Geppert et al. (2009, private communication), with which our results are in good agreement. If the DR rate coefficient for ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ were smaller than that for ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$, as suggested by the work of Kawaguchi et al. (2016), then that could account for some of the discrepancy. However, the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ DR rate coefficient of Wiens et al. (2016) is an order of magnitude larger than that of Kawaguchi et al. (2016) and a factor of ≈2 larger than the DR rate coefficient for ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ reported by us and by W. Geppert et al. (2009, private communication). Given the good agreement between the work of Wiens et al. (2016), W. Geppert et al., and us for DR of ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$, we favor the ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ DR rate coefficient from Wiens et al. (2016). If that is the case, then DR appears to be unable to explain the observed discrepancies.

Additionally, as noted above, we find good agreement between our measured branching ratio for DR of ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ forming DCl + D and the branching ratio currently being used by astrochemists for DR of H₂Cl⁺ forming HCl + H, which is assumed to be the dominant HCl formation channel. Given the nearly identical structures of the various ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ isotopologues, we expect that our results on ${{\rm{D}}}_{2}{\mathrm{Cl}}^{+}$ are a good proxy for those of ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$. Hence, the branching ratio also appears not to be the explanation for the observed HCl discrepancy.

It seems to us that at this point there are two issues to resolve. The first is for DR measurements on ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ rather than any isotopologues. The second is to measure DR for internally cold molecules. Our results here are valid for T_rot ∼ 1200 K. But molecules in diffuse clouds radiatively relax to their ground vibrational and rotational states, since their radiative decay rates are faster than the typical collisional excitation rates (Spitzer 1978). To address these questions, we plan to perform DR studies on internally cold ${{\rm{H}}}_{2}{\mathrm{Cl}}^{+}$ using the recently commissioned heavy-ion Cryogenic Storage Ring (CSR) located at the Max Planck Institute for Nuclear Physics (MPIK) in Heidelberg, Germany (von Hahn et al. 2016).