DISSOCIATIVE RECOMBINATION MEASUREMENTS OF NH⁺ USING AN ION STORAGE RING

Data were collected in 2010 July using the TSR storage ring located at the Max Planck Institute for Nuclear Physics (MPIK) in Heidelberg, Germany. Details on various aspects of this merged-beams experimental setup have been described in more detail by Amitay et al. (1996a), Wolf (1999), and Novotný et al. (2013). Here, we discuss only those aspects specific to this study.

To generate the NH⁺ ion beam, we first produced NH$_3^-$ in a cesium sputtering source with a molybdenum target and ammonia as the parent gas. The negative ions were accelerated and then directed through a nitrogen gas stripping curtain. The resulting NH⁺ ions were further accelerated to a final energy of E_i ≈ 6.2 MeV and injected into the storage ring. Typical stored ion currents were ∼0.3 nA during data acquisition.

The stored ion beam was merged with two nearly mono-energetic electron beams, dubbed the Target (Sprenger et al. 2004) and the Cooler (Steck et al. 1990). Starting after ion injection at time t = 0, both electron beams were velocity matched to the ions until t = 6 s. During this time, elastic collisions of the ions with the low energy spread electron beams transferred energy from the recirculating ions to the single pass electrons, a process known as electron cooling (Poth 1990). This reduced the energy spread of the ions and resulted in a narrow ion beam diameter (<1 mm). Data were collected from t = 6 s to t = 16.5 s. This was then followed by ion injection, and the cycle repeated.

The energy spread of each electron beam is critical for the energy resolution of the experiment. The energy distribution is parameterized by the effective temperatures, T_⊥ and T_||, respectively perpendicular and parallel to the bulk electron beam velocity. The Target electron beam was produced using a photocathode in transmission mode (Orlov et al. 2004, 2009) and expanded adiabatically by a factor of 20. For these conditions, we expect $k_{\rm B}T_{\hspace{-1.49994pt}{\perp }}^{\rm T}=1.65\pm 0.35$ meV and $k_{\rm B}T_{\parallel }^{\rm T}= 25^{+45}_{-5} \ \mu$eV (Novotný et al. 2013), where k_B is the Boltzmann constant. Here, and throughout, all uncertainties are quoted at an estimated 1σ statistical confidence level. The Cooler uses a thermionic emission cathode and expansion factor of 9.6. The corresponding electron beam temperatures are $k_{\rm B}T_{\parallel }^{\rm {C}}\approx 180 \ \mu$eV and $k_{\rm B}T_{\hspace{-1.49994pt}{\perp }}^{\rm {C}}\approx 13.5$ meV (Lestinsky et al. 2008).

After the cooling phase, the Target electron beam was used as a probe to measure DR over a range of electron–ion center-of-mass collision energies. This was accomplished by varying the laboratory energy of the Target. While this was happening, the Cooler beam remained velocity matched with the ions at all times. In this way, the ion beam was continuously cooled and did not expand in size or shift in energy as the Target beam was detuned. The Target and Cooler were operated with typical electron beam densities of $n_{\rm e}^{\rm T}\approx 2.7\times 10^{6}$ cm⁻³ and $n_{\rm e}^{\rm C}\approx 2.5\times 10^{7}$ cm⁻³, respectively. Neutral DR products generated in the Target were not deflected by the first dipole magnet downstream of the Target and continued ballistically until they hit a detector. The detected signals provided the event count rates.

Ions produced by stripping are initially expected to possess electronic, vibrational, rotational, and fine-structure excitation. We estimate that radiative relaxation removes most of the NH⁺ internal excitation during the 6 s of electron cooling, resulting in a parent ion population far closer to astrophysical conditions than that which was achievable in the single pass results of McGowan et al. (1979). Below the first NH⁺ dissociation limit lie the a ⁴Σ⁻, A ²Σ⁻, and B ²Δ excited electronic states. The measurements of Brzozowski et al. (1974) yielded decay times for the A ²Σ⁻ and B ²Δ states of ∼1 μs. Thus, these states are expected to have fully decayed before the onset of data acquisition. To the best of our knowledge, there have been no such investigations into the radiative lifetime of the a ⁴Σ⁻ symmetry. Moreover, even if this state quickly relaxes into thermal equilibrium with the ∼300 K vacuum chamber, the expected Boltzmann distribution indicates that ∼15% of the NH⁺ will be in the a ⁴Σ⁻ state.

We are not aware of any theoretical or experimental investigations into radiative relaxation of the NH⁺ ro-vibrational levels and have therefore calculated them ourselves. We predict that all of the ions relax to their v = 0 level and that the rotational excitation comes into equilibrium with the ∼300 K blackbody radiation of the vacuum chamber during the initial electron cooling phase. To model this, we have calculated the ro-vibrational radiative lifetimes of X ²Π_1/2 for levels ranging from v = 1 to v = 5 and from J = 3/2 to J = 19/2. Higher levels are calculated to decay so rapidly that they are irrelevant for the model. Our approach uses a method similar to that of Amitay et al. (1994). The dipole moment for NH⁺ was taken from Cheng et al. (2007). With this as a guide, we have generated a radiative relaxation model using the calculated spontaneous radiative decay lifetimes, while also accounting for stimulated emission and absorption by the 300 K blackbody radiation. For the initial rotational excitation, we have taken a Boltzmann distribution at a temperature of 8000 K. This is approximately the excitation temperature derived in a similar DR experiment on CF⁺ (Novotný et al. 2009). After the initial 6 s of ion storage, the model predicts all vibrational levels decayed to v = 0. The remaining average rotational excitation energy exceeds the 300 K equilibrium by only 12%. The excitation energy averaged over the ion population during the measurement window, from t = 6.0 to 16.5 s, exceeds room temperature excitation by only 4.6%. This predicted level of excitation might be overestimated due to the omission of spin–orbit coupling and coupling to the a ⁴Σ⁻ state, both of which may result in extra decay pathways. The model also does not take into account additional acceleration of the rotational cooling from super-elastic ion collisions with electrons (e.g., Shafir et al. 2009).

The final excitation to consider is the fine structure splitting X ²Π_{1/2 − 3/2}. This is not expected to relax during ion storage. We are unaware of any published lifetime estimates for this transition. Moreover, the excitation energy of ∼13 meV is well within the energies accessible by the ∼300 K ambient radiation. Taking into account the Boltzmann distribution at 300 K for all the rotational levels in the X ²Π_1/2 and X ²Π_3/2 fine-structure levels (Kawaguchi & Amano 1988), we predict that the two fine-structure groups are statistically populated by ∼67% and ∼33%, respectively.

During the data acquisition phase of each injection cycle, the Target electron beam energy was stepped over a repeating set of three different energies. For the first step, cooling, the Target electrons were velocity matched to the ions at an electron energy of E_cool = 226.74 eV in the laboratory frame. Although the Cooler beam continuously cooled the ions, the much narrower energy spread of the Target beam provided even stronger cooling during this step. This helped to maintain a stable phase-space spread of the ions during storage.

In the next step, measurement, the Target beam was set to a mean energy of E_meas in the laboratory frame. The center-of-mass collision energy, the so-called detuning energy, E_d, can be calculated nonrelativistically from the mean electron and ion beam velocities, or from corresponding laboratory-frame ion beam energies as

$$\begin{equation} E_{\rm d} = (\sqrt{E_{\rm meas}} - \sqrt{E_{\rm cool}})^2. \end{equation} \tag{ 5 }$$

The count rate at the detector during this step was used to obtain the merged-beam DR rate coefficient at the calculated E_d. The measurement energy, and hence detuning energy, was changed for each injection cycle.

In the last step, reference, the Target beam energy was set to a detuning energy ${E}_{\rm d}^{\rm ref}\approx 29$ meV. This reference energy was identical for all injection cycles. The detector count rate during this step was used to monitor the ion beam intensity.

The laboratory frame electron beam energies for each step were obtained from the Target cathode voltage, which was then corrected for space-charge effects (Kilgus et al. 1992). The power supply providing the cathode voltage requires a short time to equilibrate. Thus, to ensure stable conditions during data acquisition at each step, we add 5 ms of settling time between setting the new cathode voltage and the start of the corresponding step. Excluding this settling time, the dwell times at the cooling, measurement, and reference steps were 40 ms, 30 ms, and 30 ms, respectively.

The count rate of the DR events was measured using a 10 × 10 cm² energy sensitive Si surface-barrier detector located ∼12 m downstream of the Target. For each DR event, the N and H fragments arrive at the detector with a time difference of only a few nanoseconds. Such a small delay cannot be distinguished by the detector, and hence only a single pulse is detected for each DR event, representing the total kinetic energy of the fragments.

Typically, both fragments reached the detector and the measured total kinetic energy corresponds to the original ion beam energy. However, DR of NH⁺ can release several eV in kinetic energy (see Table 1). Such a kick in the direction perpendicular to the parent ion beam can sufficiently deflect the light H fragments so that they miss the active area of the detector. On the other hand, the kinetic energy released has little effect on the heavier N fragments. They remain confined to a narrow cone, which is fully enclosed by the detector. The DR signal is therefore a sum of detections of both fragments and detections of only the N fragment.

A number of background processes can mimic our signal and must be accounted for. For example, electron-ion collisions can result in DE producing N and H⁺ fragments. The threshold for this DE channel is ∼3.5 eV. Thus, for E_d below this, to determine the DR signal we can use events with kinetic energies corresponding to capturing both fragments (N+H) and also those detecting only the N fragments. At higher energies, however, DE events could contaminate the DR data. Hence, above ∼3.5 eV, we used only events where both N and H reached the detector. These data then need to be adjusted to account for those DR events where the H fragment does not hit the detector due to the detector size. This correction was measured independently using a position sensitive detector (Buhr et al. 2010; B. Yang et al., in preparation). The resulting rescaling of the DR signal was less than 7% over the energy range studied.

The DR signal was also contaminated by reaction products from various collisions of the ions with the residual gas. Dissociative charge transfer produces neutral N and H fragments. Collision-induced dissociation can produce either N and H⁺ fragments or N⁺ and H fragments. In all of these cases, the resulting N + H and N events on the neutral-fragment detector can be misinterpreted as DR and need to be accounted for. To do this, we used the fact that the rate of these background events, R_BG, scales with the ion beam intensity and with the residual gas pressure, but—in contrast to DR—it does not depend on the electron density. Thus, any signal that does not depend on the electron beam density can be used as a proxy for the total DR background rate at the neutral-fragment detector induced by residual gas collisions. Here, we use the signal from N⁺ fragments produced in collision-induced dissociation to monitor the relative ion beam intensity. For this, we employ a detector located in the first dipole magnet downstream the Target (Lestinsky 2007). This detector was positioned such that only N⁺ fragments originating in the Target were deflected onto its active area. We used only the data from the reference step, which is at an energy below the threshold for DE forming N⁺ + H. A scaling factor, ξ, is needed to match the N⁺ count rate, $R_{{\rm N}^+}$, to the background count rate, R_BG, so that $R_{\rm BG} = \xi R_{{\rm N}^+}$.

We determined ξ independently using a special measurement scheme. After ion injection and the cooling phase, we switched off the Target electron beam. The ion beam was still cooled by the Cooler. With the Target off, the count rate at the neutral fragment detector originated only from residual gas-induced reactions and was thus equal to R_BG. Simultaneously, we also acquired the $R_{{\rm N}^+}$ signal. The scaling factor, ξ, was simply obtained by comparing R_BG to $R_{{\rm N}^+}$ at the same storage times.

We determined the measured merged-beams DR rate coefficient α_mb(E_d) by normalizing the recorded DR signal by the electron density and ion number (e.g., Amitay et al. 1996a). The electron beam density can be determined from the measured electron beam current, energy, and geometry (Sprenger et al. 2004). The number of interacting ions can be calculated from the ion beam current. However, the typical stored NH⁺ beam current was only a few nA. This is several orders of magnitude lower than what can be measured directly using the available DC current transformer (Unser 1981). Hence, we first determined a relative DR rate coefficient versus E_d using the $R_{{\rm N}^+}$ signal as a relative proxy for the ion beam current. We then scaled the whole curve to match the absolute rate coefficient value determined at E_d = 0 eV using an independent measurement technique based on comparing ion beam decay rates with and without the electron beam present in the interaction zone (Novotný et al. 2012).

In order to enable researchers to use our storage ring data in astrochemical models, we have converted the measured merged-beams DR rate coefficient into a plasma DR rate coefficient. The transformation is a two step process. First, the experimental collision energy distribution is deconvolved from α_mb(E_d) to obtain a cross section, σ(E), as a function of collision energy E. In the second step, the cross section is convolved with a Maxwell–Boltzmann distribution to generate a plasma rate coefficient, α_pl(T_pl), at the required collisional plasma temperature, T_pl. Here, T_pl reflects the collisional velocity spread in a plasma at given temperature, but not the internal excitation of the ions. We have recently developed a novel method for converting α_mb(E_d) to σ(E) and subsequently into α_pl(T_pl). The procedure also allows for propagating statistical and systematic uncertainties. The method is described in detail by Novotný et al. (2013).

Figures 1 and 2 present our merged-beams rate coefficient for DR of NH⁺. In Figure 1, we display the data on a log–log scale for the measured detuning energies E_d = 15 μeV to 12 eV. These data are also given in tabular form in Table 2. In Figure 2, we zoom in on the most pronounced rate coefficient structures in the detuning energy range from E_d = 40 meV to 5 eV and plot the data on a lin–log scale.

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The systematic uncertainty in the measured α_mb has several important components. The uncertainties from the ion beam storage lifetime measurements, and from the electron density, dominate the 8.4% uncertainty on the absolute scaling of α_mb. This value is independent of E_d. Another source of error is the background subtraction factor, ξ. At energies E_d < 0.01 eV, the corresponding uncertainty propagated to α_mb amounts to ≲ 1%. As the collision energy increases, the uncertainties are ∼5%, ∼10%, ∼50%, and ∼7% at E_d = 0.1 eV, 1.5 eV, 3.5 eV, and 10 eV, respectively. The energy dependence of the uncertainty is due to a decrease in DR up to 3.5 eV followed by an increase going to 10 eV, while the background stays constant. At E_d > 3.5 eV, an additional error originates from correcting for geometrical detector losses. We estimate this uncertainty to be less than 1%. The total systematic error is then ≲ 8.5%, ∼10%, ∼13%, ∼50%, and ∼11% at E_d ≲ 0.01 eV as well as E_d = 0.1 eV, 1.5 eV, 3.5 eV, and 10 eV, respectively.

For each data point in α_mb, the statistical uncertainty is given by the counting statistics from the number of signal and background counts. This error amounts to ≲ 4%, ∼10%, ∼50%, and ∼8% at E_d ≲ 1 eV as well as E_d = 1.5 eV, 3.5 eV, and 10 eV, respectively.

We have converted the experimental DR rate coefficient α_mb to a cross section σ. The result is plotted in Figure 3. These data are also given in tabular form in Table 3. The lower edge of the first energy bin is set to E = 0 and is not displayed on the logarithmic energy scale of the plot.

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Table 3. Cross Section σ for DR of NH⁺

Ecenter	Ewidth	σ	$U_{\rm stat}^{\rm lo}$	$U_{\rm stat}^{\rm hi}$	$U_{\rm syst}^{\rm lo}$	$U_{\rm syst}^{\rm hi}$
(eV)	(eV)	(cm2)	(cm2)	(cm2)	(cm2)	(cm2)
1.65(−5)	3.30(−5)	1.28(−10)	−4.38(−11)	+4.16(−11)	−2.76(−11)	+2.15(−10)
8.36(−5)	1.01(−4)	3.86(−11)	−5.16(−12)	+5.58(−12)	−7.80(−12)	+8.19(−12)
2.52(−4)	2.35(−4)	4.43(−12)	−6.96(−13)	+6.58(−13)	−1.77(−12)	+6.87(−13)
6.13(−4)	4.88(−4)	7.86(−13)	−9.02(−14)	+9.17(−14)	−1.37(−13)	+1.13(−13)
1.35(−3)	9.87(−4)	3.12(−13)	−1.89(−14)	+1.77(−14)	−3.09(−14)	+3.14(−14)
2.52(−3)	1.35(−3)	1.67(−13)	−6.70(−15)	+6.79(−15)	−1.64(−14)	+1.63(−14)
3.93(−3)	1.48(−3)	9.62(−14)	−3.31(−15)	+2.88(−15)	−1.02(−14)	+8.32(−15)
5.48(−3)	1.61(−3)	7.45(−14)	−1.88(−15)	+1.90(−15)	−6.90(−15)	+8.27(−15)
7.16(−3)	1.75(−3)	4.95(−14)	−1.26(−15)	+1.31(−15)	−5.36(−15)	+4.45(−15)
8.97(−3)	1.88(−3)	3.69(−14)	−1.21(−15)	+1.03(−15)	−3.26(−15)	+3.77(−15)
1.09(−2)	2.01(−3)	2.72(−14)	−9.67(−16)	+9.75(−16)	−2.92(−15)	+2.33(−15)
1.30(−2)	2.15(−3)	2.26(−14)	−7.54(−16)	+8.89(−16)	−1.93(−15)	+2.08(−15)
1.52(−2)	2.28(−3)	1.92(−14)	−7.69(−16)	+6.85(−16)	−1.70(−15)	+1.66(−15)
1.76(−2)	2.42(−3)	1.65(−14)	−6.76(−16)	+6.70(−16)	−1.44(−15)	+1.55(−15)
2.01(−2)	2.55(−3)	1.25(−14)	−5.19(−16)	+5.21(−16)	−1.19(−15)	+1.09(−15)
2.27(−2)	2.69(−3)	1.10(−14)	−4.55(−16)	+5.13(−16)	−9.54(−16)	+9.63(−16)
2.54(−2)	2.82(−3)	9.35(−15)	−4.00(−16)	+4.28(−16)	−8.38(−16)	+9.29(−16)
2.83(−2)	2.96(−3)	7.35(−15)	−4.21(−16)	+3.27(−16)	−9.52(−16)	+6.48(−16)
3.13(−2)	3.09(−3)	6.92(−15)	−4.04(−16)	+4.53(−16)	−6.32(−16)	+9.05(−16)
3.45(−2)	3.23(−3)	5.45(−15)	−3.72(−16)	+4.13(−16)	−6.10(−16)	+5.21(−16)
3.78(−2)	3.36(−3)	4.43(−15)	−3.42(−16)	+3.00(−16)	−4.35(−16)	+4.55(−16)
4.12(−2)	3.50(−3)	3.65(−15)	−1.68(−16)	+1.62(−16)	−5.36(−16)	+3.48(−16)
4.48(−2)	3.64(−3)	3.71(−15)	−1.57(−16)	+1.32(−16)	−3.65(−16)	+6.00(−16)
4.85(−2)	3.77(−3)	2.70(−15)	−1.26(−16)	+1.35(−16)	−4.08(−16)	+2.73(−16)
5.24(−2)	3.91(−3)	2.23(−15)	−1.28(−16)	+1.13(−16)	−2.36(−16)	+2.74(−16)
5.63(−2)	4.05(−3)	1.82(−15)	−9.06(−17)	+9.43(−17)	−2.21(−16)	+1.98(−16)
6.04(−2)	4.18(−3)	1.65(−15)	−8.59(−17)	+8.45(−17)	−1.84(−16)	+1.82(−16)
6.47(−2)	4.32(−3)	1.64(−15)	−1.08(−16)	+8.91(−17)	−1.84(−16)	+2.06(−16)
6.91(−2)	4.45(−3)	1.40(−15)	−1.06(−16)	+1.15(−16)	−2.46(−16)	+1.56(−16)
7.36(−2)	4.59(−3)	1.71(−15)	−1.09(−16)	+1.10(−16)	−1.84(−16)	+2.81(−16)
7.83(−2)	4.73(−3)	1.57(−15)	−1.68(−16)	+1.74(−16)	−2.40(−16)	+1.72(−16)
8.31(−2)	4.86(−3)	1.78(−15)	−1.41(−16)	+1.30(−16)	−1.88(−16)	+2.62(−16)
8.80(−2)	5.00(−3)	1.64(−15)	−1.07(−16)	+1.21(−16)	−2.80(−16)	+1.72(−16)
9.31(−2)	5.14(−3)	1.80(−15)	−1.62(−16)	+1.38(−16)	−1.85(−16)	+3.15(−16)
9.83(−2)	5.27(−3)	1.65(−15)	−8.93(−17)	+9.83(−17)	−3.37(−16)	+1.70(−16)
1.04(−1)	5.41(−3)	1.91(−15)	−1.28(−16)	+1.22(−16)	−1.95(−16)	+3.56(−16)
1.09(−1)	5.55(−3)	1.63(−15)	−7.99(−17)	+7.66(−17)	−3.02(−16)	+1.65(−16)
1.15(−1)	5.69(−3)	1.90(−15)	−1.04(−16)	+9.87(−17)	−1.83(−16)	+2.02(−16)
1.20(−1)	5.82(−3)	2.18(−15)	−7.33(−17)	+8.23(−17)	−2.06(−16)	+2.06(−16)
1.26(−1)	5.96(−3)	2.21(−15)	−9.81(−17)	+8.17(−17)	−2.09(−16)	+2.61(−16)
1.32(−1)	6.10(−3)	1.98(−15)	−7.74(−17)	+8.00(−17)	−2.56(−16)	+1.91(−16)
1.39(−1)	6.23(−3)	1.92(−15)	−7.52(−17)	+8.76(−17)	−1.84(−16)	+3.06(−16)
1.45(−1)	6.37(−3)	1.73(−15)	−8.21(−17)	+7.22(−17)	−3.74(−16)	+1.67(−16)
1.51(−1)	6.51(−3)	1.88(−15)	−7.06(−17)	+7.73(−17)	−1.82(−16)	+4.51(−16)
1.58(−1)	6.64(−3)	1.53(−15)	−8.57(−17)	+8.73(−17)	−4.03(−16)	+1.52(−16)
1.65(−1)	6.78(−3)	1.52(−15)	−6.82(−17)	+6.45(−17)	−1.51(−16)	+3.14(−16)
1.71(−1)	6.92(−3)	1.35(−15)	−1.07(−16)	+9.58(−17)	−2.62(−16)	+1.36(−16)
1.78(−1)	7.06(−3)	1.32(−15)	−6.06(−17)	+6.17(−17)	−1.32(−16)	+1.73(−16)
1.86(−1)	7.19(−3)	1.36(−15)	−6.86(−17)	+7.40(−17)	−1.87(−16)	+1.34(−16)
1.93(−1)	7.33(−3)	1.62(−15)	−9.83(−17)	+8.85(−17)	−1.57(−16)	+2.00(−16)
2.00(−1)	7.47(−3)	1.48(−15)	−6.17(−17)	+7.17(−17)	−1.74(−16)	+1.43(−16)
2.08(−1)	7.61(−3)	1.53(−15)	−4.42(−17)	+4.28(−17)	−1.48(−16)	+1.86(−16)
2.15(−1)	7.74(−3)	1.30(−15)	−4.92(−17)	+5.15(−17)	−1.46(−16)	+1.27(−16)
2.23(−1)	7.88(−3)	1.37(−15)	−5.99(−17)	+6.45(−17)	−1.47(−16)	+1.32(−16)
2.31(−1)	8.02(−3)	1.53(−15)	−5.01(−17)	+4.76(−17)	−1.44(−16)	+1.55(−16)
2.39(−1)	8.16(−3)	1.72(−15)	−5.16(−17)	+4.74(−17)	−1.64(−16)	+1.59(−16)
2.47(−1)	8.29(−3)	1.80(−15)	−5.25(−17)	+6.46(−17)	−1.65(−16)	+1.86(−16)
2.56(−1)	8.43(−3)	1.64(−15)	−5.00(−17)	+4.78(−17)	−1.53(−16)	+1.53(−16)
2.64(−1)	8.57(−3)	1.50(−15)	−5.37(−17)	+6.41(−17)	−1.43(−16)	+1.41(−16)
2.73(−1)	8.71(−3)	1.40(−15)	−4.23(−17)	+4.74(−17)	−1.40(−16)	+1.32(−16)
2.82(−1)	8.84(−3)	1.62(−15)	−7.37(−17)	+6.95(−17)	−1.51(−16)	+1.73(−16)
2.91(−1)	8.98(−3)	1.46(−15)	−3.97(−17)	+4.09(−17)	−2.29(−16)	+1.36(−16)
3.00(−1)	9.12(−3)	1.89(−15)	−4.32(−17)	+4.50(−17)	−1.71(−16)	+2.16(−16)
3.11(−1)	1.44(−2)	1.86(−15)	−5.21(−17)	+5.21(−17)	−1.69(−16)	+1.71(−16)
3.22(−1)	7.25(−3)	1.57(−15)	−5.91(−17)	+6.68(−17)	−1.64(−16)	+1.47(−16)
3.30(−1)	7.47(−3)	1.58(−15)	−6.43(−17)	+5.95(−17)	−1.51(−16)	+1.99(−16)
3.37(−1)	7.70(−3)	1.26(−15)	−5.21(−17)	+5.77(−17)	−1.59(−16)	+1.23(−16)
3.47(−1)	1.21(−2)	1.12(−15)	−3.15(−17)	+2.61(−17)	−1.10(−16)	+1.12(−16)
3.59(−1)	1.25(−2)	1.03(−15)	−3.69(−17)	+4.18(−17)	−1.25(−16)	+1.02(−16)
3.70(−1)	8.71(−3)	1.01(−15)	−3.98(−17)	+3.71(−17)	−1.02(−16)	+2.05(−16)
3.79(−1)	9.00(−3)	7.46(−16)	−3.44(−17)	+3.23(−17)	−1.67(−16)	+8.03(−17)
3.88(−1)	9.29(−3)	6.29(−16)	−3.33(−17)	+3.55(−17)	−7.22(−17)	+1.04(−16)
3.97(−1)	9.60(−3)	5.31(−16)	−2.94(−17)	+2.98(−17)	−9.56(−17)	+6.39(−17)
4.07(−1)	9.92(−3)	4.92(−16)	−3.00(−17)	+3.05(−17)	−6.35(−17)	+9.55(−17)
4.17(−1)	1.03(−2)	3.75(−16)	−2.69(−17)	+2.84(−17)	−8.89(−17)	+5.08(−17)
4.28(−1)	1.06(−2)	3.98(−16)	−2.80(−17)	+2.77(−17)	−5.19(−17)	+5.81(−17)
4.39(−1)	1.10(−2)	4.14(−16)	−2.61(−17)	+2.50(−17)	−5.63(−17)	+5.32(−17)
4.50(−1)	1.14(−2)	4.96(−16)	−2.49(−17)	+2.29(−17)	−6.13(−17)	+5.87(−17)
4.61(−1)	1.18(−2)	5.75(−16)	−2.43(−17)	+2.40(−17)	−6.45(−17)	+8.27(−17)
4.73(−1)	1.22(−2)	5.80(−16)	−1.96(−17)	+1.96(−17)	−8.99(−17)	+6.52(−17)
4.86(−1)	1.27(−2)	6.68(−16)	−2.21(−17)	+2.14(−17)	−7.03(−17)	+9.85(−17)
4.99(−1)	1.32(−2)	6.39(−16)	−2.36(−17)	+2.31(−17)	−1.01(−16)	+6.57(−17)
5.12(−1)	1.37(−2)	8.15(−16)	−2.14(−17)	+2.25(−17)	−8.12(−17)	+8.48(−17)
5.26(−1)	1.42(−2)	8.81(−16)	−2.38(−17)	+2.32(−17)	−8.77(−17)	+9.41(−17)
5.41(−1)	1.48(−2)	7.26(−16)	−1.56(−17)	+1.55(−17)	−7.58(−17)	+7.62(−17)
5.56(−1)	1.54(−2)	6.03(−16)	−1.58(−17)	+1.38(−17)	−7.16(−17)	+6.46(−17)
5.71(−1)	1.60(−2)	5.49(−16)	−1.68(−17)	+1.82(−17)	−6.24(−17)	+7.36(−17)
5.88(−1)	1.67(−2)	3.74(−16)	−1.04(−17)	+9.33(−18)	−5.15(−17)	+4.90(−17)
6.05(−1)	1.74(−2)	3.05(−16)	−1.13(−17)	+1.18(−17)	−4.77(−17)	+4.43(−17)
6.22(−1)	1.81(−2)	3.55(−16)	−9.79(−18)	+8.36(−18)	−4.62(−17)	+4.62(−17)
6.41(−1)	1.89(−2)	4.26(−16)	−9.19(−18)	+1.00(−17)	−5.10(−17)	+4.96(−17)
6.60(−1)	1.98(−2)	5.28(−16)	−1.38(−17)	+1.18(−17)	−5.71(−17)	+5.79(−17)
6.81(−1)	2.07(−2)	5.38(−16)	−9.75(−18)	+9.36(−18)	−5.88(−17)	+5.92(−17)
7.02(−1)	2.16(−2)	4.65(−16)	−9.49(−18)	+8.22(−18)	−5.33(−17)	+5.58(−17)
7.24(−1)	2.27(−2)	3.32(−16)	−1.03(−17)	+1.04(−17)	−4.79(−17)	+4.35(−17)
7.47(−1)	2.38(−2)	3.59(−16)	−7.03(−18)	+7.90(−18)	−4.58(−17)	+4.58(−17)
7.71(−1)	2.50(−2)	3.85(−16)	−7.09(−18)	+7.62(−18)	−4.69(−17)	+4.72(−17)
7.97(−1)	2.63(−2)	3.63(−16)	−8.34(−18)	+8.15(−18)	−4.63(−17)	+4.58(−17)
8.24(−1)	2.76(−2)	4.01(−16)	−7.89(−18)	+8.58(−18)	−4.63(−17)	+4.63(−17)
8.52(−1)	2.91(−2)	4.10(−16)	−5.70(−18)	+6.40(−18)	−4.81(−17)	+4.81(−17)
8.82(−1)	3.07(−2)	4.03(−16)	−5.69(−18)	+5.82(−18)	−4.79(−17)	+4.82(−17)
9.14(−1)	3.24(−2)	3.45(−16)	−5.53(−18)	+5.69(−18)	−4.31(−17)	+4.32(−17)
9.47(−1)	3.43(−2)	2.77(−16)	−5.18(−18)	+5.31(−18)	−3.95(−17)	+3.95(−17)
9.83(−1)	3.63(−2)	2.29(−16)	−6.65(−18)	+6.83(−18)	−3.72(−17)	+3.70(−17)
1.02(+0)	3.85(−2)	2.26(−16)	−1.15(−17)	+1.33(−17)	−2.16(−17)	+2.23(−17)
1.06(+0)	4.09(−2)	1.77(−16)	−9.88(−18)	+1.01(−17)	−1.74(−17)	+1.74(−17)
1.10(+0)	4.36(−2)	1.64(−16)	−1.06(−17)	+9.14(−18)	−1.62(−17)	+1.62(−17)
1.15(+0)	4.64(−2)	1.56(−16)	−1.09(−17)	+1.03(−17)	−1.56(−17)	+1.57(−17)
1.19(+0)	4.96(−2)	1.09(−16)	−1.02(−17)	+9.20(−18)	−1.15(−17)	+1.15(−17)
1.25(+0)	5.31(−2)	1.03(−16)	−9.35(−18)	+8.48(−18)	−1.09(−17)	+1.09(−17)
1.30(+0)	5.70(−2)	1.06(−16)	−6.24(−18)	+6.42(−18)	−1.13(−17)	+1.15(−17)
1.36(+0)	6.13(−2)	7.27(−17)	−7.63(−18)	+6.92(−18)	−8.43(−18)	+8.40(−18)
1.42(+0)	6.61(−2)	8.52(−17)	−5.89(−18)	+5.11(−18)	−9.50(−18)	+9.45(−18)
1.49(+0)	7.12(−2)	5.52(−17)	−7.17(−18)	+7.35(−18)	−6.92(−18)	+6.93(−18)
1.57(+0)	7.59(−2)	6.39(−17)	−4.96(−18)	+5.08(−18)	−7.61(−18)	+7.62(−18)
1.64(+0)	7.99(−2)	5.35(−17)	−6.73(−18)	+6.77(−18)	−6.75(−18)	+6.78(−18)
1.73(+0)	8.36(−2)	4.50(−17)	−4.13(−18)	+4.14(−18)	−6.05(−18)	+6.06(−18)
1.81(+0)	8.75(−2)	3.97(−17)	−4.34(−18)	+4.14(−18)	−5.68(−18)	+5.66(−18)
1.90(+0)	9.16(−2)	3.66(−17)	−3.80(−18)	+4.03(−18)	−5.24(−18)	+5.25(−18)
2.00(+0)	9.58(−2)	4.98(−17)	−5.83(−18)	+5.97(−18)	−6.40(−18)	+6.43(−18)
2.09(+0)	1.00(−1)	3.36(−17)	−3.95(−18)	+3.63(−18)	−4.96(−18)	+4.96(−18)
2.20(+0)	1.05(−1)	3.45(−17)	−3.79(−18)	+4.12(−18)	−4.98(−18)	+4.98(−18)
2.30(+0)	1.09(−1)	3.32(−17)	−4.13(−18)	+3.58(−18)	−4.86(−18)	+4.85(−18)
2.41(+0)	1.14(−1)	2.87(−17)	−3.42(−18)	+3.34(−18)	−4.45(−18)	+4.45(−18)
2.53(+0)	1.19(−1)	3.93(−17)	−3.74(−18)	+3.71(−18)	−5.23(−18)	+5.23(−18)
2.65(+0)	1.24(−1)	3.66(−17)	−3.91(−18)	+4.07(−18)	−5.01(−18)	+5.02(−18)
2.78(+0)	1.30(−1)	3.06(−17)	−4.08(−18)	+3.55(−18)	−4.60(−18)	+4.59(−18)
2.91(+0)	1.35(−1)	1.68(−17)	−2.59(−18)	+2.26(−18)	−3.62(−18)	+3.61(−18)
3.05(+0)	1.41(−1)	1.09(−17)	−3.02(−18)	+3.28(−18)	−3.42(−18)	+3.44(−18)
3.19(+0)	1.47(−1)	4.94(−18)	−2.52(−18)	+2.99(−18)	−2.75(−18)	+2.81(−18)
3.34(+0)	1.53(−1)	4.00(−18)	−2.58(−18)	+3.09(−18)	−2.49(−18)	+2.49(−18)
3.50(+0)	1.59(−1)	4.18(−18)	−2.06(−18)	+2.37(−18)	−2.36(−18)	+2.37(−18)
3.66(+0)	1.65(−1)	9.06(−18)	−2.80(−18)	+2.95(−18)	−3.04(−18)	+3.05(−18)
3.83(+0)	1.72(−1)	3.31(−18)	−1.81(−18)	+2.36(−18)	−2.03(−18)	+2.10(−18)
4.01(+0)	1.79(−1)	5.15(−18)	−2.49(−18)	+2.87(−18)	−2.30(−18)	+2.35(−18)
4.19(+0)	1.85(−1)	8.29(−18)	−2.32(−18)	+2.01(−18)	−2.59(−18)	+2.59(−18)
4.38(+0)	1.92(−1)	8.17(−18)	−2.42(−18)	+2.59(−18)	−2.49(−18)	+2.49(−18)
4.57(+0)	1.99(−1)	9.22(−18)	−2.15(−18)	+2.14(−18)	−2.50(−18)	+2.51(−18)
4.78(+0)	2.07(−1)	1.57(−17)	−2.37(−18)	+2.65(−18)	−3.04(−18)	+3.09(−18)
4.99(+0)	2.14(−1)	1.13(−17)	−1.88(−18)	+2.11(−18)	−2.59(−18)	+2.62(−18)
5.20(+0)	2.21(−1)	1.32(−17)	−2.15(−18)	+1.97(−18)	−2.77(−18)	+2.73(−18)
5.43(+0)	2.29(−1)	1.64(−17)	−1.49(−18)	+1.52(−18)	−2.90(−18)	+2.90(−18)
5.66(+0)	2.36(−1)	1.56(−17)	−1.90(−18)	+1.96(−18)	−2.77(−18)	+2.77(−18)
5.90(+0)	2.44(−1)	1.95(−17)	−1.43(−18)	+1.68(−18)	−3.05(−18)	+3.07(−18)
6.15(+0)	2.52(−1)	1.85(−17)	−1.49(−18)	+1.43(−18)	−2.93(−18)	+2.93(−18)
6.40(+0)	2.59(−1)	2.50(−17)	−1.53(−18)	+1.69(−18)	−3.41(−18)	+3.42(−18)
6.67(+0)	2.67(−1)	2.47(−17)	−2.38(−18)	+2.33(−18)	−3.38(−18)	+3.39(−18)
6.94(+0)	2.75(−1)	2.59(−17)	−2.72(−18)	+2.48(−18)	−3.42(−18)	+3.41(−18)
7.22(+0)	2.85(−1)	2.76(−17)	−2.66(−18)	+2.34(−18)	−3.54(−18)	+3.53(−18)
7.51(+0)	2.97(−1)	2.39(−17)	−2.32(−18)	+2.85(−18)	−3.19(−18)	+3.23(−18)
7.81(+0)	3.11(−1)	2.45(−17)	−2.06(−18)	+2.18(−18)	−3.20(−18)	+3.21(−18)
8.13(+0)	3.26(−1)	3.27(−17)	−2.54(−18)	+2.38(−18)	−3.86(−18)	+3.84(−18)
8.47(+0)	3.42(−1)	2.96(−17)	−2.36(−18)	+2.66(−18)	−3.55(−18)	+3.56(−18)
8.82(+0)	3.59(−1)	3.70(−17)	−2.27(−18)	+2.55(−18)	−4.15(−18)	+4.18(−18)
9.18(+0)	3.76(−1)	4.29(−17)	−2.34(−18)	+2.20(−18)	−4.63(−18)	+4.63(−18)
9.57(+0)	3.95(−1)	3.75(−17)	−2.88(−18)	+2.49(−18)	−4.22(−18)	+4.18(−18)
9.97(+0)	4.16(−1)	4.41(−17)	−2.36(−18)	+2.38(−18)	−4.72(−18)	+4.72(−18)
1.04(+1)	4.37(−1)	3.71(−17)	−2.04(−18)	+2.33(−18)	−4.13(−18)	+4.14(−18)
1.08(+1)	4.60(−1)	3.76(−17)	−2.03(−18)	+1.80(−18)	−4.17(−18)	+4.17(−18)
1.13(+1)	4.85(−1)	3.50(−17)	−2.27(−18)	+2.12(−18)	−3.96(−18)	+3.96(−18)
1.18(+1)	5.11(−1)	3.18(−17)	−1.80(−18)	+1.77(−18)	−3.71(−18)	+3.71(−18)
1.25(+1)	8.11(−1)	3.21(−17)	−1.59(−18)	+1.94(−18)	−3.75(−18)	+3.75(−18)

Notes. The binned cross section is given as a function of bin energy center, E_center. Also listed is the energy width, E_width, of each bin. The bin start and end energies can be obtained as E_center∓0.5E_width. The asymmetric statistical and systematic uncertainties are given by U_stat and U_syst, respectively. The superscripts "lo" and "hi" give the lower and upper limits, respectively, for the corresponding uncertainties. The total systematic error in the table includes the 8.4% absolute scaling error and the uncertainties from background correction, detector geometrical efficiency correction, and $k_{\rm B}T_{\hspace{-1.49994pt}{\perp }}^{\rm T}$ and $k_{\rm B}T_{\parallel }^{\rm T}$ (see the text). The format x(y) signifies x × 10^y.

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For the conversion of α_mb to σ, we followed the procedure developed by Novotný et al. (2013). The method involves fitting α_mb with a model rate coefficient. The fitting yielded a minimum chi-squared of χ²/N_DF = 1.49, where N_DF = 46 is the number of degrees of freedom in the fit. The conversion procedure allows for propagating the uncertainties of α_mb to the cross section. The systematic errors from the absolute scaling, the background subtraction, and the correction on the geometrical detector efficiency propagate all nearly directly, i.e., relative errors in σ at E are close to those in α_mb at E_d = E. The statistical errors also propagate similarly, except for energies ${\rm E}_{\rm d}\lesssim k_{\rm B}T_{\parallel }^{\rm T}$, where the statistical uncertainty increases up to 30%.

The uncertainties in the electron beam parameters, primarily in $k_{\rm B}T_{\parallel }^{\rm T}$ and $k_{\rm B}T_{\hspace{-1.49994pt}{\perp }}^{\rm T}$, also affect the cross-section error. We calculate this error by modeling the experimental electron-ion collision energy distribution. The corresponding uncertainties in σ are displayed as gray bars in Figure 3. The largest sensitivity can be seen at collision energies ${E}_{\rm d}\lesssim k_{\rm B}T_{\parallel }^{\rm T}$, where the collision energy spread is comparable to the mean collision energy. Some enhanced uncertainties appear also at E ≈ 0.1 eV. This is due to the cross-section bins being comparable in width to the energy spread at these energies.

We have converted σ to a plasma rate coefficient using the procedures described in Section 3.4. The resulting α_pl(T_pl) is plotted in Figure 4 for a plasma temperature range of T_pl = 10–18,000 K. Note that T_pl represents only the spread in the collision energies between the electrons and ions. As discussed in Section 3.2, the internal excitation of the studied ions is expected to be ∼300 K.

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The statistical uncertainties propagate to α_pl at very low levels, amounting to less than 1% at all temperatures. This is due to the integrative nature of the transformation from σ to α_pl. Three systematic errors are relevant in the given temperature range for the plasma rate coefficient. First, the absolute scaling error of α_mb propagates directly to α_pl as an 8.4% relative error, which describes a single scaling of the complete α_pl(T_pl) curve. Second, the background subtraction uncertainty generates an absolute error in α_pl of ±7 × 10⁻¹⁰ cm³ s⁻¹, independent of T_pl. Lastly, the uncertainties of the electron beam parameters propagate to α_pl as an absolute error, which can be well approximated by ±6.1 × 10⁻⁶ (T_pl/K)^−1.3 cm³ s⁻¹. The behavior of the various systematic errors needs to be taken into account when propagating the resulting rate coefficient uncertainties. For chemical models involving a range of temperatures, the three systematic errors must be applied to all α_pl(T_pl) points in a correlated way according to the description given. For models at a single fixed temperature, their appropriate absolute values can be added in quadrature. This results in a systematic error of ∼16% at T_pl = 10 K, ∼10% at 100 K, ∼8% at 1000 K, ∼9% at 10,000 K, and ∼9% at 18,000 K.

To parameterize the results for use in astrochemical modeling, we have fit the data with an analytical formula. We tried to fit the data with both the two- and three-parameter functions commonly used to describe DR plasma rate coefficients in astrochemical models and databases (e.g., Florescu-Mitchell & Mitchell 2006; Wakelam 2010), but were unable to fit our measured plasma rate coefficient over the entire temperature range with a precision of any better than 40%. Therefore, we used the form proposed by Novotný et al. (2013), namely

$$\begin{equation} \alpha _{\rm pl}^{\rm fit}(T_{\rm pl}) = A\,\left(\protect \frac{300 \ \rm K}{T_{\rm pl}}\protect \protect \protect \right)^n + B, \end{equation} \tag{ 6 }$$

where

$$\begin{equation} B = T_{\rm pl}^{-3/2}\sum _{i=1}^4 c_i \exp (-T_i/T_{\rm pl}). \end{equation} \tag{ 7 }$$

We fit Equation (6) to our data over the full temperature range. The resulting parameters are given in Table 4. The deviations of $\alpha _{\rm pl}^{\rm fit}$ from the data are less than 1% over the reported temperature range.

The evolution of the NH⁺ DR rate coefficient with collision energy displays diverse features, which can be used to probe the underlying quantum nature of the process. For clarity, we use Roman numerals to label the features in Figures 1, 2, and 3, which we discuss below. We also plot the thresholds for the opening of various DR product excitation channels. Additionally, we include in the figures the energies of various NH⁺ states, which are upper limits for Rydberg series of NH states. As we have discussed in Section 2, these neutral states are potentially involved in both direct and indirect DR processes, and their energies may be reflected in the DR energy spectrum.

The overall shapes of α_mb and σ are dominated by a decreasing magnitude with increasing energy, roughly following the σ∝E⁻¹ expected for direct DR process (Florescu-Mitchell & Mitchell 2006; Larsson & Orel 2008). Numerous structures appear on top of this global shape. Three broad features (labeled I, II, and III) are visible at energies below ∼0.05 eV. The features at these low collision energies can be caused by electron capture to rotationally excited NH Rydberg states converging to the NH⁺ X ²Π_1/2, X ²Π_3/2, and a ⁴Σ⁻ ionic cores. The decreasing strength of these features with increasing collision energy can be attributed to the opening up of additional autoionization channels, though individual resonances cannot be distinguished due to the experimental energy resolution. Similar features, which are associated with an even stronger cross-section decrease for increasing energy, were seen for DR of HCl⁺ (Novotný et al. 2013) where a detailed discussion of this effect was also given.

We have excluded the possibility that these three low-energy structures are an experimental artifact due to ion beam dragging. The concern is that if the electron beam is detuned slightly from the cooling energy, such as for measurements at low collision energies, then Coulomb forces between the beams can drag the ion beam to match the velocity of the electrons. As a consequence, the real collision energy would differ from that calculated by Equation (5). As discussed in Novotný et al. (2013), this distorts the curve of α_mb at low collision energies and may appear as a low energy peak. However, our experimental configuration with two electron beams greatly minimizes this effect by enabling us to simultaneously cool the stored ions with the Cooler while measuring DR data using the Target. Additionally, we have performed a set of tests similar to Novotný et al. (2013) that further excluded ion beam dragging as the origin for these features.

In the collision energy range between ∼0.05 eV and ∼3 eV, a significant enhancement is observed of the DR merged-beams rate coefficient compared to the E⁻¹ dependence for direct DR, as can be seen in Figure 3. The rather narrow substructures in this energy range (IV to XII, best seen in Figure 2) suggest that indirect DR is contributing in this energy range. Possible origins for the structure seen include DR pathways via NH states with electronically excited ion cores, DR pathways via NH states with vibrationally excited ion cores, and the opening of new final channels as we now describe.

At these energies, similarly strong enhancements were seen for OH⁺ (Amitay et al. 1996b). There the comparison with calculated data indicated that the enhancements stemmed from indirect DR through neutral Rydberg resonances associated with bound, electronically excited ion-core molecular states. Comparable DR enhancements, possibly of the same origin, have also been observed for CD⁺ (Forck et al. 1994), N$_2^+$ (Peterson et al. 1998), and several other systems (Amitay et al. 1996a; Tanabe et al. 1998; Padellec et al. 1999; Novotný et al. 2009). For NH⁺ neutral resonances of this type are expected to occur below the three bound excited states A ²Σ⁻, B ²Δ, and C ²Σ⁺, i.e., in the energy range of where the observed structure indeed occurs in the measured DR rate coefficient. However, we are unaware of any published potential energy curves for doubly excited bound neutral NH. Lacking such calculations, the observed structures cannot be uniquely assigned to specific DR pathways via the neutral Rydberg series converging to the ionic A, B, or C states. Nevertheless, as explained in Section 2, a noticeable change in the DR rate is expected when scanning over a Rydberg series limit converging to an ionic state. In the NH⁺ DR spectrum, such a threshold feature can be identified for the v = 0 level of the A and B ionic states at ∼2.7 eV as a drop in the DR rate coefficient (structure XII). Interestingly, no clear feature in α_mb can be found at the excitation energy of the C ²Σ⁺ state of NH⁺.

In addition to the above DR via neutral Rydberg states converging to excited electronic ionic states, some of the sub-structures in α_mb above ∼0.05 eV may also be due to electron capture into neutral Rydberg series converging to the vibrationally excited X ²Π(v ⩾ 1) and a ⁴Σ⁻(v ⩾ 1) NH⁺ states. The most clear feature suggesting an influence of these excitation channels on the measured DR rate coefficient is the sharp drop in α_mb at E_d ≈ 0.35 eV (labeled by VIII). This edge matches well to the v = 1 levels of the X ²Π and a ⁴Σ⁻ NH⁺ states. At higher energies, the upper edges of peaks X and XI may be related to v = 2 and v = 3 levels of the X ²Π_3/2 and a ⁴Σ⁻ states of NH⁺. However, between features VIII and X lies peak IX, the upper edge of which cannot be assigned to any NH⁺ vibrational level. This feature may be due to DR resonances via doubly excited bound neutral states with electronically excited NH⁺ cores, as is discussed in the previous paragraph. Feature VII may also have a similar origin.

Some of the structures seen in the ∼0.05 to ∼3 eV energy range also seem to be related to the opening of new final channels associated with higher excitation of the products. For example, peak IV at E_d ≈ 0.12 eV matches very well with the threshold for product excitation channel 4 of N and H from the NH⁺ ground state (see Table 1). According to Goldfield & Kirby (1987) and Owono Owono et al. (2007), at least six NH states can predissociate to product excitation channel 4. Taking all possible switching between these states into account, a large number of predissociation pathways to channel 4 are available. This is to be contrasted with the more endothermic product excitation channels (5, 6, etc.), which do not show as good of a match with peaks in our experimental DR spectrum. Moreover, the existence of additional peaks between the predicted energy thresholds, such as feature IX, again suggests the existence of more complex DR pathways as discussed above.

A more general phenomenon of molecular DR, known for most species, is the increase of the DR rate above ∼4 eV with two broad peaks, XIII and XIV at E_d ≈ 7 eV and 10 eV, respectively (see Figure 1). These reflect direct electron capture to NH doubly excited unbound states with 2 ²Π and 2 ⁴Σ⁻ NH⁺ ionic cores. In Figures 1 and 3, we label the respective vertical excitation energies for these two NH⁺ states by D and E. We have investigated this phenomenon in more detail independently by the fragment imaging technique (Yang et al. 2014).

Our experimentally derived DR plasma rate coefficient for NH⁺ differs significantly from the currently recommended DR data. The only previous experimental investigation for DR of NH⁺ is by McGowan et al. (1979). The results published in their original paper were later corrected for an erroneous form factor (Mitchell 1990; J. B. A. Mitchell 2012, private communication) yielding a plasma rate coefficient of $\alpha _{\rm pl}^{\rm MG} = 4.3\times 10^{-8}(300/T_{\rm pl})^{0.5}$ cm³ s⁻¹ with an uncertainty of ∼15%. Based on the range of collision energies covered in the experiment of McGowan et al., $\alpha _{\rm pl}^{\rm MG}$ is valid for collisional plasma temperatures between approximately 100 K and 1000 K. However, astrochemical models commonly extrapolate $\alpha _{\rm pl}^{\rm MG}$ outside this temperature range by simply following the functional expression given above. Comparing to our new results for DR of NH⁺, we find that the magnitude of our rate coefficient is significantly larger than $\alpha _{\rm pl}^{\rm MG}$ for all values of T_pl. Additionally, we see that for T_pl ≲ 1000 K our α_pl decreases with increasing T_pl about 1.5 times faster than does $\alpha _{\rm pl}^{\rm MG}$. The unusual bump in our thermal rate coefficient starting at ∼1000 K and reaching a maximum at ∼4000 K originates from the cross-section enhancement at E ≈ 0.05–3 eV. As discussed above, this can be attributed to electron capture to doubly excited states attached to electronically excited bound states of the NH⁺ ion. Similar cross-section enhancements were observed for other systems, such as CH⁺ and OH⁺ (Amitay et al. 1996a, 1996b). The corresponding high temperature increase in α_pl should thus be considered as a general DR feature, which cannot be correctly described by the hyperbolic fit functions used by the astrochemical databases. Instead a more general formula, such as Equation (6), is needed to describe α_pl for all T_pl relevant for molecular ions.

Taking the ratio of $\alpha _{\rm pl}/\alpha _{\rm pl}^{\rm MG}$ yields factors of 9.0, 5.8, 4.0, 2.8, and 2.3 at T = 10, 30, 100, 300, and 1000 K, respectively. These differences greatly exceed the combined experimental error bars of McGowan et al. and our present results. We attribute the differences between α_pl and $\alpha _{\rm pl}^{\rm MG}$ to the substantially different internal excitation of the NH⁺ ions in the two experiments. As discussed in Section 3.2, NH⁺ is expected to relax while stored in TSR and reach thermal equilibrium with the 300 K temperatures of the TSR chamber. Only rotational and fine-structure levels in the lowest two electronic states are expected to remain populated. On the other hand, in the single-pass merged-beams experiment of McGowan et al. the flight time from the ion source to the interaction region was ∼1 μs. Thus, the NH⁺ ions are expected to have been highly excited vibrationally, rotationally, and electronically. Other experimental studies show that internal excitation of the ions may significantly affect the DR rate coefficient (e.g., Amitay et al. 1998; McCall et al. 2004).

Where no reliable DR data exist for diatomic molecules, astrochemical models commonly assume a "typical" rate coefficient of $\alpha _{\rm pl}^{\rm di}\approx 2.0\times 10^{-7}\times (300/T)^{0.5}$ cm³ s⁻¹ (Florescu-Mitchell & Mitchell 2006). As has been shown for CF⁺ (Novotný et al. 2005) and HCl⁺ (Novotný et al. 2013), $\alpha _{\rm pl}^{\rm di}$ does a poor job of matching the experimentally derived rate coefficient, α_pl, both in magnitude and temperature dependence. Taking the ratio of our new DR results to that commonly assumed, we find $\alpha _{\rm pl}/\alpha _{\rm pl}^{\rm di}=1.9$, 1.2, 0.9, 0.6, and 0.5 at T = 10, 30, 100, 300, and 1000 K, respectively.

Although many attempts have been made to detect NH⁺ in the ISM, none have been successful (Snow 1979; Polehampton et al. 2007; Hily-Blant et al. 2010; Persson et al. 2010, 2012; Benz et al. 2013). The nondetection of NH⁺ at the sensitivity limits of the various observational techniques is in agreement with existing astrochemical models (e.g., Persson et al. 2010). Our new data predict that the NH⁺ destruction by DR at T_pl ≲ 50 K is significantly faster than previously assumed. For cold ISM environments at T_pl = 10 K this enhancement reaches a factor of between 1.9 and 9.0 depending on the NH⁺ DR data used in the model (see Figure 4).

To estimate the relative effect of DR on the NH⁺ abundance, we compare the two most important NH⁺ destruction channels: DR of NH⁺, reaction (4), and NH⁺ reacting with H₂, reaction (1). Using the NH⁺ + H₂ reaction rates from Zymak et al. (2013) and our new NH⁺ DR data, we calculate that DR is a competitive destruction channel at electron-to-H₂ density ratios of $n_{\rm e}/n_{\rm H_2} \gtrsim 1.5\times 10^{-5}$ and ≳ 1.3 × 10⁻³ at T_pl = 10 and 100 K, respectively. Such electron densities are predicted for diffuse and translucent interstellar clouds (Snow & McCall 2006). Our new DR data will thus result in NH⁺ abundances significantly lower than currently predicted. As a consequence, NH⁺ detection in the ISM is unlikely unless the current detection limits can be significantly lowered. A reduced NH⁺ abundance will also result in lower abundances for other nitrogen hydrides produced from NH⁺ by reactions (2) and (3). More precise quantitative predictions will require that our new NH⁺ DR data be implemented into current gas-phase and gas–grain nitrogen chemical models of the interstellar clouds. That is, however, beyond the scope of our work.

Lastly, we note that even in our present storage ring experiment, the NH⁺ ions are still internally excited to T_exc ∼ 300 K. In the cold ISM, however, the internal excitation is expected to be significantly lower. This is because in very low density ISM environments the collision rate is much lower than the typical radiative decay time (Spitzer 1978). Thus, T_exc is generally even lower than the kinetic temperature, T_pl, and most of the molecules are expected to be in their rotational ground state. The response of the DR rate coefficients to T_exc have been investigated only for light ions (e.g., Amitay et al. 1996a; Zhaunerchyk et al. 2007, Petrignani et al. 2011; Schwalm et al. 2011). From these few studies, we are unable to draw predictions for NH⁺ DR data with T_exc < 300 K. Future studies at MPIK using the currently under-construction Cryogenic Storage Ring, which will have an internal ambient temperature of ∼10 K, will be able to address this issue (Fadil et al. 2006; Wolf et al. 2006; Krantz et al. 2011; von Hahn et al. 2011).