Cold ion chemistry within a Rydberg-electron orbit: test of the spectator role of the Rydberg electron in the He(n) + CO → C(n′) + O + He reaction

Recently, a new method has been introduced to study ion-molecule reactions at very low collision energies, down to below k B ⋅ 1 K (Allmendinger et al 2016 ChemPhysChem 17 3596). To eliminate the acceleration of the ions by stray electric fields in the reaction volume, the reactions are observed within the orbit of a Rydberg electron with large principal quantum number n > 20. This electron is assumed not to influence the reaction taking place between the ion core and the neutral molecules. This assumption is tested here with the example of the He(n) + CO → C(n′) + O + He reaction, which is expected to be equivalent to the He+ + CO → C+ + O + He reaction, using a merged-beam approach enabling measurements of relative reaction rates for collision energies E coll in the range from 0 to about k B ⋅ 25 K with a collision-energy resolution of ∼k B ⋅ 200 mK at E coll = 0. In contrast to the other ion-molecule reactions studied so far with this method, the atomic ion product (C+) is in its electronic ground state and does not have rotational and vibrational degrees of freedom so that the corresponding Rydberg product [C(n′)] cannot decay by autoionization. Consequently, one can investigate whether the principal quantum number is effectively conserved, as would be expected in the spectator Rydberg-electron model. We measure the distribution of principal quantum numbers of the reactant He(n) and product C(n′) Rydberg atoms by pulsed-field ionization following initial preparation of He(n) in states with n values between 30 and 45 and observe that the principal quantum number of the Rydberg electron is conserved during the reaction. This observation indicates that the Rydberg electron is not affected by the reaction, from which we can conclude that it does not affect the reaction either. This conclusion is strengthened by measurements of the collision-energy-dependent reaction yields at n = 30, 35 and 40, which exhibit the same behavior, i.e. a marked decrease below E coll ≈ k B ⋅ 5 K.


Introduction
Experimental studies of ion-molecule reactions at low temperatures or low collision energies are notoriously difficult because stray electric fields in the reaction volume accelerate the ions. Data on several ion-molecule reactions have been obtained down to temperatures of ∼ 10 K using uniform supersonic flows [1][2][3][4] and buffer-gas-cooled samples in multipole radio-frequency ion traps [5][6][7][8][9]. New methods are currently being developed to reach lower temperatures [10,12]. An attractive strategy relies on the preparation of cold-ion samples in ion crystals [11][12][13][14] and promising results have recently been obtained on the reactions between electronically excited ultracold neutral atoms and cold molecular ions in ion-neutral hybrid traps [15]. Nevertheless, ion-molecule reactions in the range of temperatures and collision energies (E coll /k B ) below about 10 K remain essentially unexplored experimentally. This situation is unfortunate because it is precisely in this range that theoretical investigations predict that the rates of fast ion-molecule reactions should strongly depend on the collision energy or the temperature, particularly for reactions involving neutral molecules having permanent electric dipole and quadrupole moments [16][17][18][19][20][21][22][23][24][25][26]. In these cases, the rate coefficients of state-selected ion-molecule reactions are predicted to strongly depend on the rotational state of the neutral molecules through the orientation of the molecular axes and the locking of the rotational-angular-momentum vector to the collision axis by the electric field of the colliding ion.
In the past years, we have developed an alternative method to study ion-molecule reactions at collision energies down to below k B · 1 K and studied the reactions of H + 2 with H 2 [27][28][29], HD [30], and D 2 [29] and those of He + with CH 3 F [31], NH 3 [32], and CH 4 [33]. This method consists of observing the ion-molecule reactions within the orbit of a Rydberg electron in a state of high principal quantum number n. In such a state, the Rydberg electron is expected not to influence the reaction taking place between the ion core and neutral molecules located within its orbit but to shield the ion-core-molecule reaction from the undesirable heating effects of stray fields, enabling studies at low collision energies.
The similarity of the ion-molecule reaction to the corresponding reaction involving the ion core of a Rydberg state A(n) + B → C(n ) + D ( 2 ) has been discussed in earlier work [34][35][36][37] and can be justified within the independent-particle model of collisions involving Rydberg states (see references [38,39] and also the chapters by Hickman, Olson and Pascale, by Gounand and Berlande, by Matsuzawa and by Dunning and Stebbings in reference [40]). It is only recently that this similarity was exploited in cold-ion-molecule-chemistry experiments. In the present article, we report on an investigation of the reaction through measurements of the He(n) + CO → C(n ) + O + He (4) reaction. The C + products of reaction (3) are formed in the electronic ground state. Consequently, the C(n ) products of reaction (4) cannot autoionize for energetic reasons. One can therefore investigate experimentally by pulsed-field ionization (PFI) whether the n value of the initially prepared Rydberg state changes or remains conserved during reaction (3), as would be expected if the Rydberg electron were indeed a spectator. In this article, we present the results of such an investigation using the merged-beam technique we have employed in our recent studies of the reactions of He + and H + 2 mentioned above [27][28][29][30][31][32][33].

Experiment
The He + + CO reaction is studied in the merged-beam apparatus described in reference [32] and depicted schematically in figure 1. Briefly, a supersonic beam of helium atoms is produced by a home-built pulsed valve (20 μs pulse duration) operated at a repetition rate of 25 Hz. At the valve opening, an electric discharge populates the (1s) 1 (2s) 1 3 S 1 metastable state, referred to as He * henceforth. The He * beam is skimmed twice before it intersects at right angles a laser beam (λ ∼ 260 nm) which excites the atoms to a selected Rydberg state with principal quantum number n in the 30-45 range. A curved surface-electrode deflector [31,41,42] is used to deflect, and set the velocity of the He(n) Rydberg atoms, which are subsequently merged with a supersonic beam of ground-state CO molecules also generated with a home-built short-pulse valve. The C(n ) products formed in the He(n) + CO → C(n ) + O + He reaction are ionized by a pulsed electric field and the C + ions are monitored using a micro-channel-plate (MCP) detector in a time-of-flight mass spectrometer (TOFMS). The He and CO beams are generated via supersonic expansions of the respective pure gases from stagnation pressures of P He = 2.5 bar and P CO = 6.5 bar. The CO valve is temperature-stabilized to T CO-valve = 340 ± 1 K to produce a beam with an initial mean velocity v CO ≈ 870 m s −1 . To carry out experiments under different sets of conditions and verify that they give the same result, the He valve was stabilized to either T He-valve = 100.0 ± 0.1 K or 66.0 ± 0.1 K, resulting in mean initial helium velocities of 1040 m s −1 or 860 m s −1 , respectively. Both beams pass through two skimmers which select their central, coldest parts. The CO-beam valve trigger is set so that the molecules belonging to a selected velocity class and the He(n) atoms arrive at the center of the TOFMS at the same time. The Rydberg-excitation laser beam (λ ∼ 260 nm, pulse duration ∼ 10 ns, repetition rate 25 Hz, pulse energy ∼ 700 μJ) is produced by frequency tripling the output of a pulsed Nd:YAG-pumped (Spectra Physics, Quanta Ray Lab 170) commercial dye laser (Radiant Dyes, NarrowScan with a double grating, operated with the dye Styryl 11). The magnitude of the dc electric field in the photoexcitation volume and the laser frequency are chosen such that a low-field-seeking (lfs) Rydberg-Stark state of He is populated at fields just below the Inglis-Teller field, where the n and n + 1 Stark manifolds start overlapping spectrally. The polarization of the laser beam is set parallel to the dc electric field so that Rydberg-Stark states with magnetic quantum number m = 0 are produced.
The principle of the Rydberg-Stark deflector used in the experiments is described in references [41][42][43]. The deflector consists of 50 parallel electrodes located at the surface of a curved printed circuit board. The force exerted on a Rydberg-Stark state with potential energy E = − μ el · F and electric dipole moment | μ el | = 3 2 nkea 0 (k = n 1 − n 2 , and n 1 and n 2 are the parabolic numbers with n = n 1 + n 2 + |m| + 1 [39]) in an inhomogeneous electric field F is f trap = −∇E. We excite the fifth outermost lfs Stark state (i.e. the |n, k = n − 9, m = 0 state) to ensure simultaneously a large-enough dipole moment for deflection and acceleration and a good excitation probability. Upon application of oscillatory time-dependent potentials to the surface-deflector electrodes [41][42][43], the atoms are loaded and guided in moving electric traps above the surface-electrode deflector and can be accelerated or decelerated to a desired final velocity, v He(n) , during the deflection. By adjusting v He(n) , the collision energies E coll between the He(n) atoms and the CO molecules can be adjusted in the range between 0 and ∼ k B · 25 K with a collision-energy resolution of about k B · 200 mK at E coll = 0. The deflected He(n) atoms are merged with the CO beam at the entrance of the TOFMS (see figure 1).
The TOFMS consists of three cylindrical plates (E 1 -E 3 ) to which appropriate potentials (V 1 -V 3 ) are applied. In experiments requiring a good mass resolution, such as those in which the reaction products are monitored, the potentials are chosen so as to fulfill the Wiley-McLaren conditions [44], i.e. V 1 , V 2 = 1 2 V 1 , and V 3 = 0. Because the maximal value of the pulsed potential we can apply is 5.5 kV, this choice limits the electric field to values below 605 V cm −1 , with which only Rydberg states with n 34 can be efficiently field ionized. In experiments that do not require a high mass resolution, such as those in which we study the n-changing processes affecting the He(n) Rydberg atoms as they travel from the photoexcitation spot to the reaction region, we set both V 2 and V 3 to zero. The maximal electric field we can apply is then 1210 V cm −1 , which enables us to efficiently ionize Rydberg states with n 29.
Two main types of measurements are carried out: (i) measurements of the field ionization of the He(n) reactants and C(n ) products as a function of the strength of the applied electric-field pulse. These measurements enable us to derive the n distributions of He-reactant and C-product Rydberg states and to quantify the possible changes in n resulting from the reaction. (ii) Measurements of the C(n ) product yield as a function of the collision energy. These measurements are performed at field strengths and n values which guarantee a close-to-100% field-ionization yield and enable us to detect possible deviations of the capture rates from the Langevin capture rate at low collision energies. Comparing the product-ion-yield measurements carried out at different n values enables us to see whether the reaction rate is n-dependent or not.
The experiments are carried out under conditions where typically less than 1% of the initially prepared He(n) Rydberg atoms react to form C(n ) atoms. Moreover, the density of the CO reactants is much larger than that of the He(n) reactants. Consequently, the reaction rate follows pseudo-first-order kinetics and is constant over the time window of ∼ 15 μs during which we monitor the reaction at each experimental cycle. Figure 2 displays TOF mass spectra of the product ions resulting from the reaction between He atoms excited to the |n = 40, k = 31, m = 0 state and CO molecules recorded with extraction fields of 110 V cm −1 (a) and 550 V cm −1 (b). In the mass spectrum shown in figure 2(a), the first peak, at a TOF of 1.7 μs, corresponds to field-ionized He(n) atoms. The product ion C + appears as a small peak near 2.8 μs, highlighted by the blue-shaded area, and is followed by the ions OH + , H 2 O + , CO + , N + 2 and O + 2 that originate from Penning-ionization reactions of He * with water, CO, N 2 , and O 2 molecules in the vacuum chamber (P background ≈ 10 −6 mbar). The capacitive coupling between the MCP detector and the extraction plates leads to an oscillatory perturbation in the TOF spectra between 0 and 1.5 μs when the pulsed potentials are applied. The amplitude of this perturbation increases with increasing applied potential.

Time-of-flight mass spectra
To distinguish Penning-ionization products formed in reactions of He * with background-gas molecules present in the vacuum chamber from product ions originating from the He(n)+ CO reaction, we record TOF mass spectra with the Rydberg-excitation laser turned off (red traces in figure 2). These TOF mass spectra only display the Penning-ionization products, allowing us to identify C + as the only reaction product in the TOF mass spectra recorded with the excitation laser turned on (black traces in figure 2).
The mass spectra presented in figure 2(b) were recorded with a pulsed extraction field of 550 V cm −1 . The main differences between these mass spectra and those displayed in figure 2(a) are that all product ions have earlier arrival times and larger intensities. These differences arise because increasing the electric field imparts more kinetic energy to the product ions, which increases their velocity and leads to an increase of the H 2 O + , CO + , N + 2 , and O + 2 signal by a factor of ∼ 2. In contrast, the C + signal increases by a factor of about 6 when the strength of the pulsed field increases from 110 to 550 V cm −1 . The increase of the C + signal thus cannot be explained solely by a more efficient detection, but indicates instead that the C + ions are generated by PFI of the C(n ) reaction products. Because fields of 110 and 550 V cm −1 only efficiently ionize Rydberg states with n 50 and n 35, respectively, one can further conclude that the C(n ) products are formed in Rydberg states with 35 n 50. The Penning-ionization products in figure 2(b) have a lower signal in the mass spectrum recorded with the Rydberg-excitation laser turned on. This signal reduction is a result of the saturation of the MCP-detector caused by the strong He + signal from the field ionization of He(n). When determining the reaction yield, we correct for this effect by adapting the intensity scale so that the CO + Penning-ionization signal has the same integrated intensity in the spectra recorded with the excitation laser turned on and off. We obtain the same results within the experimental uncertainty when this correction is carried out using the H 2 O + and O + 2 peaks as reference. These ions, like CO + , are only generated by Penning-ionization reactions with He * . To obtain more precise information on the range of n values of the C(n ) Rydberg atoms formed in the reaction and on its dependence on the n value of the initially prepared He Rydberg atoms, we recorded series of TOF mass spectra for pulsed electric fields ranging from 55 to 550 V cm −1 in steps of 55 V cm −1 , and for n values of 30, 35, 40, and 45. The results obtained for n = 30 and 40 are displayed in figure 3. The intensities of each mass spectrum were scaled to account for the saturation of the MCP detector, as explained above. In both cases, the intensity of the C + signal increases with increasing ionization field, and intense field-ionization signals are observed at lower field strengths for n = 40 than for n = 30.
Three distinct processes determine the distribution of n values of the C Rydberg products observed following the reaction of CO with the He Rydberg atoms initially prepared in a well-defined n state: (i) transitions n → n caused by the reaction itself. (ii) Transitions n → n occurring in the He Rydberg atoms prior to the reaction, during their ∼ 85 μs-long trajectories from the photoexcitation spot to the center of the reaction zone. In the collision-free, low-density conditions of our experiments, such transitions are primarily stimulated by the ∼ 300 K blackbody-radiation (BBR) field in the vacuum chamber [45]. (iii) Transitions n → n occurring in the C Rydberg atoms after the reaction but before the field-ionization pulse. Because the reaction is observed during a temporal window of ∼ 15 μs, process (iii) is expected to be much less significant than process (ii). In the following, we present the results of experiments and analyses which helped to quantify the role of these processes.

Field-ionization experiments
To determine the n and n distributions of the He(n) and C(n ) Rydberg-atom populations at the time of PFI, we measure the He + and C + PFI yields as a function of the pulsed-electric-field strength following initial excitation to selected He |n, k, m = 0 Rydberg-Stark states. The full widths at half-maximum of the He + and C + peaks in the TOF mass spectra are about 100 ns so that the ionization rates of the corresponding He(n) and C(n ) atoms must be at least 10 7 s −1 for them to be efficiently detected.
Examples of such measurements for C(n ) are presented in figures 3(a) and (b). These measurements are limited to field strengths 605 V cm −1 because of the necessity to clearly separate C + and OH + ions in the TOF mass spectra, as explained in section 2. Similar measurements were also carried out for He(n) without turning the CO beam on to detect n → n transitions in the He(n) Rydberg atoms (process (ii) above). In this case, fields up to 1210 V cm −1 could be applied because it was not necessary to operate the mass spectrometer under Wiley-McLaren conditions. The He + PFI signals obtained following initial preparation of the He atoms in the |nkm = |45, 36  The slow, almost linear signal growth at the highest fields in the measurements carried out at n 35 (i.e. beyond 300, 420, and 900 V cm −1 at n = 45, 40, and 35, respectively) is entirely caused by the increase of the ion-detection efficiency resulting from the increasing kinetic energy imparted to the ions by the field-ionization pulse. We correct for this effect by dividing all ion signals by the same linear function. The corrected PFI signals are presented in figure 4 as open circles for He + and full black circles for C + . For direct comparison, the C + PFI signal had to be scaled up by the same factor of about 100, corresponding to a reaction probability of less than 1% for a He(n) atom to form a C(n ) product in the reaction zone.
At n = 40 and 45, the corrected relative field-ionization yields of He(n) and C(n ) are identical within the error bars, which indicates that no significant changes of the principal quantum number result from the reaction at these n values. In turn, this observation implies that the Rydberg electron is decoupled from the reaction He + + CO → C + + O + He taking place within its orbit, as expected for a 'spectator' Rydberg electron. At lower n values, the C + field-ionization signal grows faster than the He + signal with increasing field strength.

Field-ionization yields and mechanism
The slew rate dF/dt of the ionization field ranges from ∼ 1.8 × 10 9 V cm −1 s −1 for the lowest applied fields (55 V cm −1 ) to ∼ 2.0 × 10 10 V cm −1 s −1 for the highest ones (1210 V cm −1 ). Of the S = 1 n Rydberg series of He, only the s series has a quantum defect significantly different from zero (δ s = 0.2967 [46]). We estimate the typical size 2V ij of the avoided crossings between the Rydberg-Stark states i and j of adjacent n manifolds in the Stark map of He using the approximate formula [47] | nn 1 n 2 m|V ij |n n 1 n 2 m | ≈ (nn ) − 3 2 min(n,n )−1 In equation (5), δ are the -dependent quantum defects, K = 1 2 (n − 1), and the terms in brackets are Clebsch-Gordan coefficients. This expression gives values of V ij of 0.029 cm −1 and 0.006 cm −1 for the outer Stark states of the n = 30 and 45 manifolds, respectively. The probability of a diabatic traversal of the avoided crossings is thus 41% and 97% at n = 30 and 45, respectively, if dE/dF is approximated by 3 2 nka 0 e. To obtain these probabilities we use, for n = 30, the slew rate corresponding to the highest applied fields (2 × 10 10 V cm −1 s −1 ) and for n = 45, the slew rate of the fields leading to full ionization of the sample (10 10 V cm −1 s −1 ). These considerations indicate that the field ionization of He(n > 35) Rydberg atoms follows a diabatic (or hydrogenic) mechanism [39,40] over the range of slew rates used in our experiments, but that a gradual transition to an adiabatic ionization mechanism takes place as n decreases below 35.
The quantum defects of C Rydberg states are larger than those of He. Consequently, the transition from diabatic to adiabatic field ionization takes place at higher n values in C than in He, i.e. between 35 and 40, as indicated by the measurements presented in figure 4. In this figure, one clearly sees that the C + PFI signal starts increasing at lower field strengths than the He + PFI signal, as expected for a larger contribution arising from adiabatic field ionization.
To calculate the diabatic-field-ionization yields, we use the expression for the field-dependent hydrogenic ionization rates derived by Damburg and Kolosov [48] where R = (−2E) 3/2 /F, and E and F are the binding energies of the Rydberg states and the field strength, respectively. We consider the ionization probability to be 1 if Γ > 10 7 s −1 and zero otherwise. Previous work [49] has shown that this procedure provides adequate diabatic ionization rates if E is calculated up to the fourth order of perturbation theory.
In panels (a)-(c) of figure 5, results of the model calculations of the field-ionization yields are compared to the experimental data obtained for He. The red step functions in figure 5 indicate the behavior expected for the diabatic field ionization of the initially prepared Rydberg states |n, k = n − 9, m = 0 of He. Because the He(n) Rydberg atoms traverse regions of low fields with varying direction of the field vector on their way to the field-ionization region, the value of k is likely to be randomized when the field-ionization pulse is applied. In this case, the calculations based on equation (7) predict a less sharp rise of the field-ionization yield with the pulsed fields, as depicted by the green lines in figure 5.
The calculated yields assuming randomization of k agree well with the experimental results at high fields but do not describe well the slow increase of the observed yields at the lowest fields. Instead, they predict a sharp low-field onset of the field-ionization signal and a zero field-ionization signal in regions where the experimental field-ionization yield is already substantial. This observation suggests that some of the He(n) Rydberg states undergo transitions to Rydberg states of higher n values before they reach the field-ionization region. As explained above, these transitions can only be radiative under our experimental conditions.

Modeling radiative transitions of the He(n) Rydberg atoms
The overall decay rate K tot nkm of a |nkm state is given by the sum of the fluorescence rates, the BBR-induced transition rates to bound states and BBR-induced ionization rates: The fluorescence decay rate of an |nkm state is given by the sum of the Einstein A coefficients: where n , k , m represent all accessible lower-lying levels. The rate of BBR-induced transitions to bound states at a temperature T BB is where ω nkm,n k m is the angular frequency corresponding to the energy difference between the |nkm and |n k m states, and the average photon numbern(ω nkm,n k m ) at the transition frequency is The BBR-induced ionization rate is where R ion (n = 23-65, T = 300 K) ≈ 0.1 under our experimental conditions (see discussion in reference [45]). The Einstein A nkm,n k m coefficients for spontaneous emission are given by [45]: whereμ α = eα (α =x,ŷ,ẑ) is the electric-dipole operator. The transition moments n m |μ α |n m can be separated into an angular and a radial integral, the latter being evaluated using the Numerov method [50].
To model the sequence of radiative events that leads to the final distribution of Rydberg-Stark states in the reaction zone, we adapt the Monte Carlo (MC) simulation developed by Seiler et al [45]. At each time step of the simulation, an algorithm is used to determine (i) if a transition occurs, (ii) which type of radiative process takes place, and (iii) the state of the particle after the transition. In addition, we determine whether each He atom is in a state that can be trapped over the surface decelerator, i.e. whether its dipole moment is large enough (see reference [45] for details).
The MC simulation indicates that significant losses from the trap occur during the 85 μs time between excitation and detection, particularly in the experiments carried out at the lower n values. About 35% of the atoms initially prepared in the |30, 21, 0 state are lost during deflection. For the other states, the losses are 28% for the |35, 26, 0 state, 21% for the |40, 31, 0 state, and 17% for the |45, 36, 0 state.
The calculated final-state distributions of the particles reaching the reaction zone after 85 μs are displayed in figure 6 where panels (a)-(d) present the results corresponding to initial excitation to the |45, 36, 0 , |40, 31, 0 , |35, 26, 0 , and |30, 21, 0 states, respectively. In all cases, the initially prepared state remains the most populated one, but its contribution to the total population in the reaction zone decreases from nearly 50% for |45, 36, 0 to about 20% for |30, 21, 0 . In each case, about half of the remaining population is in states of slightly higher n value, which explains the significant field-ionization signals at low fields in figure 4. The orange lines in figure 5 represent the field-ionization signals calculated for the final-state distributions, which are in excellent agreement with the experimental results.

n-dependence of the He(n) + CO → C(n ) + O + He reaction yield
The results of the PFI measurements presented in section 3.2.1 demonstrate the spectator role of the Rydberg electron at n 40. Below n = 40, no clear conclusion can be drawn from the PFI profiles because of the different contribution of adiabatic field ionization in C(n ) and He(n). In this range of n values, we tested the spectator role of the Rydberg electron by measuring the collision-energy-dependent reaction yield after preparing the atoms in n = 40, 35, and 30 Rydberg-Stark states. The results of these experiments are presented in figure 7. Panels (a)-(c) of this figure display the C(n ) field-ionization yield as a function of the collision energy E coll . The full and empty circles correspond to measurements for which v He(n) was set to be greater and smaller than v CO , respectively. The C + signal strength was divided by the He + signal for normalization. The relative intensity scale was chosen so that the signal is unity at the high-collision-energy side. The vertical error bars in figure 7 represent one standard deviation. The horizontal bars represent the ranges of collision energies contributing to the observed reaction and correspond to the energy resolution of our measurements, which increases from 200 mK at the lowest collision energies to about 2 K at collision energies of k B · 20 K (see equation (1) of reference [31]).
The experimental data exhibit a gradual drop in the reaction product yield below k B · 15 K. At the lowest collision energies, the C + signal is weaker than the signal at E coll = k B · 20 K by about 30%. All three data sets follow the same behavior, which enables us to exclude a significant effect of the Rydberg electron on the reaction in the range of n between 30 and 40. Together with the PFI measurements described in section 3.2.1, this result demonstrates the equivalence of reactions (3) and (4) and proves that the Rydberg electron merely acts as a spectator. We attribute the 30%-decrease of the rate of the reaction He + + CO → C + + O + He at the lowest collision energies to the fact that CO has a negative quadrupole moment (−9.47 × 10 −40 cm 2 [51]), which leads to a less attractive long-range interaction potential, as will be demonstrated rigorously in a separate publication [52].

A simple model to estimate n → n changes upon reaction
A mechanism by which the n-value would be expected to change during the reaction is illustrated schematically in figure 8 and is a consequence of the displacement of the positive charge center upon the charge transfer to CO + that precedes the formation of C + by (pre)dissociation. Assuming that the transfer takes place instantaneously when He + and CO are separated by the Langevin radius R L = k L /(πv rel ) (k L is the Langevin rate), the radius R n of the Rydberg electron orbit abruptly changes. The two extreme situations are depicted in panels (a) and (b) of figure 8. In the former case, R n decreases from ∼ a 0 n 2 to R n − R L = a 0 n 2 whereas in the latter, it increases to R n + R L = a 0 n 2 . The new radii would imply that at E coll = k B · 1 K (R L = 3 nm) and n = 45 (a 0 n 2 = 107 nm) a transition to Rydberg states with n = 44.4 and 45.6 takes place, respectively. The same calculations for n = 30 give n values in the range between 29.1 and 30.9. This simple model, which was previously used to explain the slight broadening of the shape resonances of H + 2 and D + 2 [53], therefore predicts changes in n of less than 1, in support of the observation of almost identical PFI behavior for He(n) and C(n ) at n = 40 and n = 45 (see figure 4).

Conclusions
In previous studies of ion-molecule reactions within the orbit of a Rydberg electron [27,28,30,31,[34][35][36], the reaction products were Rydberg states with molecular ion cores in excited electronic, vibrational, or rotational levels. These Rydberg states autoionize after the reaction so that it was not possible so far to assess to what extent the n value of the Rydberg electron is conserved in the reactions.
In the reaction He + + CO → C + + O + He, the C + ion product is formed in its electronic 2 P J ground state (J = 1/2, 3/2). Whereas Rydberg states with a 2 P 1/2 ground-state C + core cannot autoionize, Rydberg states with a C + 2 P 3/2 core can autoionize if n 41.5 [54]. Consequently, our measurements for n 40 all lead to long-lived Rydberg states of C given that n is conserved. The reactions of He(n = 45) could in principle produce autoionizing Rydberg states of the C atom with a 2 P 3/2 core. Our experiments, however, indicate that the detected C + ions are generated by PFI and not by autoionization. We therefore conclude that either the C + ions are generated preferentially in the 2 P 1/2 ground state or that the n = 45 Rydberg states produced in the reaction do not autoionize on the timescale of the reaction.
In this article, we have investigated the reaction between He(n) Rydberg states and CO forming C(n ), O and He and demonstrated its equivalence to the ion-molecule reaction He + + CO → C + + O + He for n values in the 30-45 range. This conclusion was drawn from (i) the observation, in PFI measurements at n = 40 and 45, that the n-value of the Rydberg electron does not change during the reaction, and (ii) the identical collision-energy dependence of the reaction rate observed for n = 30, 35 and 40 below E coll = k B · 25 K. This observation can be intuitively rationalized by the fact that the average distances of the Rydberg electron from the ion (48 nm at n = 30 and 107 nm at n = 45) are more than 15 and 35 times larger than the radius of ∼ 3 nm corresponding to the Langevin cross section at 1 K, respectively. The results presented in this article thus legitimate the approach to cold ion-molecule chemistry consisting of substituting the atomic or molecular ion by a Rydberg atom or a Rydberg molecule.