State selected reactions of krypton ions with methane

Chemical Physics 258 (2000) 47±54

www.elsevier.nl/locate/chemphys

State selected reactions of krypton ions with methane A. Kok, P.A. Zeijlmans van Emmichoven, A. Niehaus * Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands Received 25 April 2000

Abstract Using a photo-electron product-ion coincidence method, the reactions of Kr‡ (2 P1=2;3=2 ) ions with methane molecules are studied in the relative kinetic energy range between 0.1 and 1 eV. The relative total cross-sections and the branching ‡ ratios for production of CH‡ 4 and CH3 are determined selectively for the two krypton ions. Using available absolute reaction rates for unselected krypton ions, absolute selective rates are obtained. In addition, a simple model is presented that describes the reactions quantitatively in terms of two distinct mechanisms: (1) reactions via ``close collisions'', and (2) reactions via charge exchange in ``distant collisions''. Based on this model, evidence for breakdown of the ``orbiting transition state theory'' for the description of the close collision complex at collision energies above about 0.4 eV, is obtained. Ó 2000 Elsevier Science B.V. All rights reserved.

1. Introduction

2

In the relative collision energy range between thermal energies and 1 eV, several reactions can occur between krypton ions and CH4 molecules. We have to consider the following possible reaction paths for the ground state ion Kr‡ (2 P3=2 ): Kr‡ …2 P3=2 † ‡ CH4 ! Kr ‡ CH‡ 4 …DQ ˆ 1:39 eV†

…1a†

…1b†

…DQ ˆ ÿ0:23 eV†

Kr‡ …2 P1=2 † ‡ CH4 ! Kr ‡ CH‡ 4 …DQ ˆ 2:06 eV†

…2a†

2

Kr‡ … P1=2 † ‡ CH4 ! KrH‡ ‡ CH3 …2b†

Kr‡ …2 P1=2 † ‡ CH4 ! Kr ‡ CH‡ 3 ‡H …DQ ˆ 0:44 eV†

Kr‡ …2 P3=2 † ‡ CH4 ! Kr ‡ CH‡ 3 ‡H …1c†

2

…2c† 2

Kr‡ … P1=2 † ‡ CH4 ! Kr‡ … P3=2 † ‡ CH4 …DQ ˆ 0:67 eV†

* Corresponding author. Tel.: +31-30-253-2923; fax: +31-30253-7468. E-mail address: [email protected] (A. Niehaus).

…1d†

and the corresponding paths for the Kr‡ (2 P1=2 ) ion, which is excited by 0.67 eV:

…DQ ˆ 1:15 eV†

2

Kr‡ … P3=2 † ‡ CH4 ! KrH‡ ‡ CH3 …DQ ˆ 0:48 eV†

2

Kr‡ … P3=2 † ‡ CH4 ! Kr‡ … P1=2 † ‡ CH4 …DQ ˆ ÿ0:67 eV†

…2d†

Kr‡ …2 P1=2 † ‡ CH4 ! Kr ‡ CH‡ 2 ‡ H2 …DQ ˆ ÿ0:4 eV†

0301-0104/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 0 ) 0 0 1 6 9 - 5

…2e†

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A. Kok et al. / Chemical Physics 258 (2000) 47±54

The DQ values give the exothermicity (plus sign), or the endothermicity (minus sign) of the reactions, respectively. The values follow from known thermo-chemical data. In case of reactions (1b,2b), we used a recently determined (higher) value for the KrH‡ -binding energy of 4.8 eV [1] to calculate the exothermicities. Previous experimental studies of the Kr‡ /CH4 collision systems have shown [2±5] that the main reactions occurring in the collision energy range below 1 eV are the charge exchange reactions (1a,2a), and the dissociative charge exchange reactions (1c,2c) that yield CH‡ 3 ions. The endothermic process (2e) was found to be less ecient by two orders of magnitude at 2 eV collision energy [5], and the formation of KrH‡ by the exothermic reactions (1b,2b) has not been observed at all to our knowledge. Also, no experimental information on the reactions (1d,2d), in which the ®ne structure state of the ion changes, seems to be available. We already mention at this point that our present calculations, based on the orbital transition state (OTS) theory [6,7] are consistent with very low probabilities for the reactions (b,d, and 2e). In this work, we therefore only consider the charge exchange reactions leading to formation of CH‡ 4 , and the dissociative charge exchange reactions leading to formation of CH‡ 3 . To characterize this branching, we de®ne the branching ratio ‡ ‡ Dissociative R ˆ I…CH‡ 3 †=fI…CH3 † ‡ I…CH4 †g. charge exchange is exothermic by 0.44 eV for the …j ˆ 1=2† ion (reaction 2c), and endothermic by 0.23 eV for the …j ˆ 3=2† ion (reaction 1c). At low collision energies, reaction (1c) is therefore impossible, leading to R ˆ 0 for the …j ˆ 1=2† ion. For the …j ˆ 1=2† ion, on the other hand, (R) should be close to unity. This follows from the break-down diagram of CH‡# 4 , which shows ‡ H for the case of complete decay into CH‡ 3 vibrational excitation by 2.06 eV, [8]. Actually, from selected-ion drift tube (SIFT) experiments [2,3], a branching ratio of R ˆ 0:9 was derived, suggesting that, to some extent, the decomposition is in¯uenced by of the vibrationally excited CH‡# 4 the presence of the Kr atom. When the collision energy is increased, formation of CH‡ 3 via charge exchange with the …j ˆ 3=2† ion becomes energetically possible (reaction 1c). Qualitatively, this has

been con®rmed in crossed beam experiments using a mixed …j ˆ 1=2; j ˆ 3=2† krypton ion beam [4]. It is estimated from these experiments that the branching ratio at 1.18 eV collision energy is approximately R ˆ 0:15 for the …j ˆ 3=2† ion. In SIFT experiments at thermal energies [2,3], the total absolute charge exchange rate is found to be equal (1.0(±9) cm3 /s) for both ions, while for higher energies, no direct state selective information on the rates is available. Herman and Friedrich [4] estimated from their crossed beam data that the integral …j ˆ 3=2†=…j ˆ 1=2† cross-section ratio has a value of approximately 3. This, however, is to some extent in disagreement with measurements of Tosi et al. [5], who determined the energy dependence of the absolute total charge exchange cross-section and of the branching ratio for a mixed …j ˆ 1=2; 3=2† ion beam, in the range from 0.02 to 10 eV. The nearly constant branching ratio observed in these measurements suggests a nearly constant cross-section ratio in the whole energy range. In this paper, we present the ®rst direct and state selective measurements of the …j ˆ 3=2†= …j ˆ 1=2† cross-section ratio, and of the branching ratios (R), in the collision energy range between 0.1 and 1 eV. This energy range is especially interesting because, as has been discussed earlier [4], at the lower energies the reactions probably occur # via an intermediate …Kr±CH‡ 4 † complex, while at the higher energies reactions probably are better described as a decomposition of the isolated exion formed by charge exchange. The cited CH‡# 4 variation of the branching ratios in this region is expected to re¯ect this change of mechanisms. 2. Experiment and results To achieve state selection of the primary Kr‡ (2 P1=2;3=2 ) ions, we apply the photo-electron product-ion coincidence (PEPICO) method. The experimental setup and the method have been described earlier [9]. Brie¯y, Kr atoms contained in a supersonic beam are photoionized by photons from a He-discharge lamp. The photoelectrons are energy analyzed and detected using a hemispherical electrostatic analyzer with a large solid angle of

A. Kok et al. / Chemical Physics 258 (2000) 47±54

acceptance (ca. 1%). The ions are accelerated to the desired energy by a short electric pulse (pulse 1), and focussed into a chamber containing the CH4 molecules at a density suciently low to guarantee single collision conditions. Product ions, formed in the chamber due to collisions with the Kr‡ ions, are also extracted by a short electric pulse (pulse 2), and their mass is analyzed by the time of ¯ight method using a re¯ectron con®guration [10]. Both ions and electrons are detected as single counts at the anode of multichannel plates. By measuring the mass selected product ion counts in delayed coincidence with counts due to energy selected photoelectrons, one is able to correlate product ions with primary Kr‡ ions having a speci®c ionization energy. In order to obtain true coincidence counts, free from accidental coincidences, we proceed in the following way: for every electron detected, alternately a correlated and an uncorrelated measurement is performed, by triggering pulse 1 by the detected electron at di€erent delay times. In case of the correlated measurement, the delay time is set in such a way that a detected product ion could have been formed by the krypton ion labeled by detection of the corresponding photoelectron. And in case of the uncorreleated measurement, the delay time is set suciently long to guarantee that a detected product ion can only be due to a krypton ion not belonging to the detected electron. The uncorrelated measurement therefore yields purely accidental electron±ion coincidences, while the correlated measurement yields accidental plus true coincidences. The true coincidences are thus obtained as the di€erence between the counts of the two measurements. They can be obtained simultaneously for several mass channels. As an example, we show the result of a measurement in Fig. 1. Plotted are the accumulated true coincidence counts as a function of the ionization energy of the primary ion, which is obtained from the energy of the detected photoelectrons. For such a measurement, single electron counts on the peaks are of the order of a few hundred per second, and the ratio of true to accidental coincidences is about 5. Due to this large ratio, the error of the true coincident count rate is purely statistical. The upper trace corresponds

49

Fig. 1. True electron±ion coincident counts as a function of the ionization energy for di€erent ion masses. Uppermost trace: krypton mass; middle trace: mass 16 …CH‡ 4 †; lower trace: mass 15 …CH‡ 3 †. The experimental points are ®tted by Gaussians.

to Kr‡ , the middle trace to CH‡ 4 , and the lower ‡ 2 trace to CH‡ 3 . We see that, when the Kr ( P3=2 ) ion with its ionization energy of 14 eV is formed, predominantly CH‡ 4 product ions are measured, corresponding to a branching ratio close to zero, and when Kr‡ (2 P1=2 ) with its ionization energy of 14.67 eV is formed, almost exclusively CH‡ 3 ions are measured leading to a branching ratio close to unity. The …j ˆ 3=2†=…j ˆ 1=2† total charge exchange cross-section ratio is directly obtained from the intensities of the product ions and the intensity of the primary ion. Measurements of the type shown in Fig. 1 have been performed for several primary energies of the krypton ions. The results are given in Table 1. The cross-section ratios and the selective branching ratios with their respective statistical possible error are given for several average relative collision energies. These average relative energies are calculated for the situation that the krypton beam of an accurately de®ned laboratory energy crosses a volume containing the CH4 molecules, which have a thermal velocity distribution. 3. Discussion For the further discussion, we make use of our result that the …j ˆ 3=2†=…j ˆ 1=2† total charge

50

A. Kok et al. / Chemical Physics 258 (2000) 47±54

Table 1 ‡ ‡ ‡ 2 ‡ 2 Experimentally determined branching ratios R ˆ r…CH‡ 3 †=fr…CH4 † ‡ r…CH3 †g for the two krypton ions Kr … P3=2 † and Kr … P1=2 †, in the second and third column, and the total charge exchange cross-section ratios for the two ions in the last columna

a

Energy (eV)

R …j ˆ 3=2†

R …j ˆ 1=2†

r …j ˆ 1=2†=r …j ˆ 3=2†

0.127 0.248 0.380 0.560 0.721 0.825 0.993 1.002

0.010 ÿ0.015 0.067 0.109 0.077 0.043 0.056 0.032

0.86 0.88 1.00 0.96 0.98

1.20 1.12 1.06 1.15 1.20

(0.011) (0.020) (0.014) (0.016) (0.018) (0.018) (0.018) (0.020)

(0.04) (0.04) (0.04) (0.04) (0.04)

0.88 (0.04)

(0.2) (0.2) (0.2) (0.2) (0.2)

1.05 (0.2)

The errors in brackets are statistical errors. The energy values in the ®rst column are the average relative collision energies.

exchange cross-section ratio is very close to unity in the whole energy region. Within the limits of error, there is no energy dependence. The ratio averaged over the points at di€erent energies is 1:13  0:1. This result allows us to conclude that the total cross-section curve obtained by Tosi et al. [5] for a mixed …j ˆ 3=2; 1=2† ion beam represents the total cross-section curve for both ions to a very good approximation. We thus obtain, using our ‡ selective branching ratios, absolute CH‡ 3 and CH4 formation cross-section curves for both ions. These curves are shown in Fig. 2(a) and (b). In Fig. 3, we demonstrate that the cross-section curve of Tosi et al. [5] can very well be reproduced by a theoretical model we developed. Shown are the original experimental data, and the same data multiplied by a factor of 1.15. As can be seen, these slightly corrected data are quantitatively reproduced by the model calculations. Based on the model, the reaction mechanisms can be discussed in some detail. We ®rst give a brief outline of the theoretical model. As is well known, at suciently low collision energies, the so called close collision cross-section accurately describes the cross-section for close contact of the collision partners [11]. In the present case of a collision between a neutral molecule having no permanent dipole moment and a singly 1=2 charged ion, it is given by rcc ˆ p‰2a=Ecm Š , with …a† the electric dipole polarizability of the molecule. The dashed straight line in Fig. 3 represents rcc calculated with the average polarizability of CH4 …a ˆ 17:41 a:u:† [12]. It should be noted that rcc calculated in this way is a good approximation

of the real close collision cross-section only up to energies, where it becomes comparable to the geometrical cross-section, indicated by the constant value labeled size of molecule in Fig. 3. We notice that the absolute experimental total crosssection curve of Tosi et al. [5] agrees rather well with rcc in the low energy region, regarding both: absolute value and slope. This suggests that, in this region, (i) close collisions lead to charge exchange, and (ii) charge exchange in distant collisions ± with a distance of closest approach larger than the close 1=4 ± collision impact parameter bcc ˆ ‰2a=Ecm Š contributes little to the cross-section. This is of course expected, because charge exchange depends on the overlap of wave functions, which decreases exponentially with distance between the collision partners, so that charge exchange in these distant collisions will generally become insigni®cant at suciently low energies. As, with increasing collision energies, the close collision cross-section decreases and approaches the estimated size of the molecule (indicated by the dash-dotted line at 22 2 ), the situation changes, and charge exchange in A distant collisions can become signi®cant. We attribute the deviation of the experimental crosssection curve from the close collision cross-section to this e€ect. In our model, this general description is quanti®ed in a numerical program, which calculates the trajectories for impact parameters varying from zero to an appropriate maximum value, and determines the charge exchange probability for each trajectory. To calculate the probabilities for charge exchange, we make use of the fact that, acciden-

A. Kok et al. / Chemical Physics 258 (2000) 47±54

51

‡ Fig. 2. Absolute charge exchange cross-section, and partial cross-sections for CH‡ 4 and CH3 formation, as a function of the relative collision energy. (a) Kr‡ …2 P3=2 † ion; symbols with error bars: present experimental data; (): experimental total cross-section of Tosi et al. [5]; (b) Kr‡ …2 P1=2 † ion; symbols with error bars: present experimental data; (): experimental total cross-section of Tosi et al. [5].

situation for charge exchange. As an approximation, we use a formula for exact resonance derived for charge exchange between atoms [13]. In semiclassical approximation, this formula becomes (in atomic units) Z rtr ˆ 2p sin2 …d…b††b db; with Z …3† d…b† ˆ …H12 …R†=v…R†† dR:

Fig. 3. Comparison of the total experimental charge exchange cross-section data of Tosi et al. [5] (), with our present model calculations; (Ð): calculations with constant FC factor; (± ± ±): calculations with energy dependent FC factor. Also shown the close collision part of the cross-section …rcc †, and the distant collision part …rdc †. The open points are the experimental data of Tosi et al. multiplied by a factor of 1.15. Also indicated is the size of the molecule.

tally, the polarizabilities for CH4 and for Kr have very similar values, a ˆ 17:41 and a ˆ 16:68 a:u., respectively [12], so that the long range interaction potentials for the initial channel (Kr‡ ±CH4 ) and the charge exchange channels (Kr±CH‡# 4 ) run approximately parallel. Since the initial channel is embedded in a quasi-continuum of ro-vibrational states of the CH‡# 4 , this leads to a quasi-resonance

Here, H12 (R) is the electronic coupling matrix element between the two diabatic degenerate charge exchange channels, or equivalently, half the difference between the two adiabatic potentials that arise by diagonalization of the electronic Hamiltonian. The velocity v(R) in Eq. (3) is the impact parameter dependent radial velocity. In the present case, it is evaluated for the long range potential, ÿ…a=2†=R4 . Since the charge exchange implies the transition CH4 ! CH‡# 4 , i.e. an electronic transition with simultaneous vibrational excitation, the coupling matrix element contains the Franck± Condon factors for the relevant vibrational transitions. The distance dependence of H12 (R) will be dominated by the overlap of the relevant electron orbitals, as in the case of atoms. For charge exchange between atoms, Olson et al. have derived a semiempirical uniform expression for the coupling matrix element that is only dependent on the ionization energies of the two atoms [14]. In case of

52

A. Kok et al. / Chemical Physics 258 (2000) 47±54

exact resonance, where the ionization energies are identical, IP, the expression becomes …1=2†

H12 …R† ˆ ‰2Š

‰IPŠ

…3=2†

R expfÿ0:86‰2IPŠ

…1=2†

Rg: …4†

In order to adapt this expression to the present atom±molecule system, we introduce an extra preexponential factor (FC) to allow for the reduction of the matrix element due to the Franck±Condon factor for the relevant electronic±vibrational transition. To account for the ®nal size of the CH4 molecule, with a radius of approximately 5 a.u., we further replace (R) in expression (4) by (R ÿ 5), and set the exponential to unity for R < 5. With the value IP ˆ 14 eV, we thus obtain the matrix element H12 ˆ FC 0:396R exp fÿ0:872…R ÿ 5†g:

…5†

Using formula (3), it is now possible to calculate the charge exchange probability for a given impact parameter, and to obtain the cross-section for a given value of FC. In order to account for the fact that, for close collisions, the charge exchange probability is unity ± as evidenced by the equality between close collision cross-section and measured total cross-section at low collision energies (Fig. 3), we set for these collisions ± characterized by the condition that the distance between the collision partners gets smaller than 5 atomic units during the collision ± the phase d(b) to the value …p=2†. We emphasize that the cross-section corresponding to these close collisions approaches the analytical close collision cross-section rcc de®ned above at low velocities, and the geometrical crosssection (size of molecule in Fig. 3) at high velocities. The cross-section curve in Fig. 3 is obtained for FC ˆ 0:0015. The agreement with experiment is very gratifying and is, since only one free parameter is used, strong evidence that the physics of the process is well described by the model used. At the lower energies, the charge exchange cross-section approaches the close collision crosssection, and at higher energies, the increasing contribution of charge exchange without contact of the collision partners in distant collisions is evident. At the highest collision energies, the experimental curve is seen to fall below the calculated

curve. This is expected because the assumed resonance situation, implying a vibrational transition, is expected to change when the collision time …tcoll ˆ d=v† becomes equal to, or shorter than, the relevant vibration time …tvib ˆ 2p=xvib †, leading to a lower value of the Franck±Condon factor. To test this explanation, we tentatively replaced the constant (FC) by an energy dependent one, as FC…ECM † ˆ FC exp …ÿ ln 2 tvib =tcoll †:

…6†

We choose, as a typical relevant vibrational quantum of the CH‡ 4 ion, the value xvib ˆ 0:01 a.u. and leave the typical relevant distance (d) free as a parameter to adapt to the experimental data. We ®nd that the high energy behavior of the experimental data is very well described for d ˆ 1:2 a.u. The dashed line in Fig. 3, which is calculated using this value shows that the calculated crosssection curve agrees within the limits of relative errors of the experiment with the experimental curve in the whole energy range. Since the absolute normalization of the experiment is uncertain to at least 20% [5], we can therefore state excellent agreement. The successful decomposition of the crosssection curve into a contribution due to close collisions (given by rcc at low collision energies, and by the geometrical cross-section at high collision energies), and a contribution due to charge exchange in distant collisions (labeled rdc in Fig. 3), facilitates a further interpretation of the branching ratios (R). From the break-down curves for vib[8], it is known that, the rationally excited CH‡# 4 decomposition into CH‡ 3 ‡ H is complete if the molecular ion is formed by resonant charge ex2 change with Kr‡ … P1=2 † in distant collisions, while it cannot dissociate at all if it is formed by resonant 2 charge exchange with Kr‡ … P3=2 †. The observed deviation of R…j ˆ 1=2† from unity, and of R…j ˆ 3=2† from zero may therefore be ascribed to close collision. This makes it possible to derive from our data, the collision energy dependent decay probabilities of the close collision complex into CH‡ 3‡ H ‡ Kr, separately for formation of the complex at the di€erent internal energies corresponding to the two krypton ions. These decay probabilities are de®ned as

A. Kok et al. / Chemical Physics 258 (2000) 47±54

P ˆ R…rcc ‡ rdc †=rcc :

…7†

The result for the …j ˆ 3=2† ion, where our experimental data have a smaller statistical uncertainty, is shown in Fig. 4. We see that close to the thermodynamic threshold at 0.23 eV, CH‡ 3 formation starts. This proves that the relative kinetic energy is eciently transformed in the collision complex to internal energies, at least in the low energy region. In the low energy region, therefore, obviously a close collision complex is formed, which is suciently long-lived to be treated as a statistical complex, describable by the so-called orbital transition state theory (OTS) [6,7]. The fact that the species Kr±CH‡ 4 has actually been observed in ¯ow-tube studies [15] supports the existence of an intermediate complex. Also, angular distributions ‡ of CH‡ 4 and CH3 ions measured in crossed-beam studies of the reactions of unselected Kr ions with CH4 at di€erent relative kinetic energies [4,16] show that, at 0.45 eV, a fraction of the order of 50% of the charge exchange reactions occurs via a long-lived complex. If we use this result in connection with our decomposition of the total charge exchange crosssection into a close collision part and a distant collision part, with a ratio of approximately 40/20

Fig. 4. Probabilities for CH‡ and CH‡ formation in 4 3 Kr‡ (2 P3=2 )±CH4 close collisions as a function of relative collision energy. Symbols with error bars: present experimental data; lines: calculations assuming reactions via a statistical complex.

53

at 0.45 eV (Fig. 3), we have to conclude that about 3/4 of the close collisions (corresponding to a 2 ), still go through a complex cross-section of 30 A at 0.45 eV. The fact that the CH‡ 3 formation probability does not increase further with increasing collision energy, but rather decreases ®nally (Fig. 4), is an indication that, above a few tenths of an eV the kinetic energy becomes less ecient in promoting the endothermic reaction. In other words, it is an indication of the change from a collision complex mechanism to a direct mechanism in this energy range. It is interesting to get more quantitative information about this change. We get this information by carrying out calculations using the OTS theory for ion±molecule reactions going through a long lived complex [6,7], and by comparing the experimental probabilities with the calculated ones. This comparison is shown in Fig. 4. The theoretical results, shown as solid lines, are obtained by averaging the theoretical probabilities over the experimental relative energy distribution. We notice good agreement in the threshold region, and a starting disagreement above about 0.4 eV. Actually, it should be pointed out that the application of the OTS theory is not straight forward and contains some arbitrariness. This is especially true for the calculation of reaction paths that imply three free fragments asymptotically, like reaction (1c,2c). In such a case, one has to decide beforehand, whether the reaction occurs in two steps, or in one step. We have described it as a one-step process, using an orbiting transition state containing the fragments CH‡ 3 and Kr±H as a linear molecule. For the present purpose, it is not necessary to discuss the OTS calculations in any further detail. It is sucient to state that the requirement to reproduce the measured probabilities at low collision energies for both Kr ions makes it impossible to achieve agreement above 0.4 eV within the OTS theory. The calculated probability for CH‡ 3 always continues to increase towards unity, while the measured one goes through a maximum and ®nally decreases. It is also worth noticing that the calculations con®rm the dominance of the reaction paths 1a,c and 2a,c, as already mentioned in the introduction. Although all the other paths

54

A. Kok et al. / Chemical Physics 258 (2000) 47±54

considered in the introduction are included in the calculations, the sum of the probabilities for CH‡ 3 and CH‡ 4 formation is seen (Fig. 4) to add up to virtually unity. 4. Summary The cross-section ratio for charge transfer between the Kr‡ ions in the two ®ne structure states 2 2 … P3=2 † and … P1=2 † and CH4 , was measured in the collision energy range from 0.1 to 1 eV. The ratio was found to be independent of collison energy within an uncertainty of 10%, with a value of r…j ˆ 1=2†=r…j ˆ 3=2† ˆ 1:13. For each of these ions, selectively, also the branching ratio for CH‡ 3 to CH‡ 4 formation was measured. Using the mixed beam absolute cross-section curve for charge transfer of Tosi et al. [5], absolute formation cross‡ section curves for CH‡ 4 and CH3 formation by the two Kr ions were derived. The charge transfer cross-section curve of Tosi et al. was further analyzed using a model that describes the cross-section as consisting of two distinct contributions: one contribution from close collisions and one from distant collisions. By adapting one parameter in that model, quantiative agreement with the experiment was achieved. According to the model, the contribution from distant collisions amounts to a few percent at thermal energies, but becomes of increasing importance at increasing energies. At 1 eV, the contributions from distant and close collisions are about equal. At still higher energies, the contribution of distant collisions decreases again and the total crosssection approaches the geometrical size of the

molecule. Based on the model, a discussion of the ‡ 2 CH‡ 3 formation cross-section by Kr … P3=2 † in close collisions was carried out. It was found that these collisions proceed via a statistical complex in the low energy region up to approximately 0.4 eV, while at higher energies, the eciency of the kinetic energy to promote the endothermic reaction decreases.

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