Guided ion beam studies of electron and isotope transfer in N+N ...

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 16 22 APRIL 2000 

Guided ion beam studies of electron and isotope transfer 

in 14 N ¿ ¿ 15 N 2 collisions 

J. Glosik and A. Luca 

Department of Electronics and Vacuum Physics, Mathematics and Physics Faculty, Charles University, 

V Holesˇovičkách 2, Prague 8, Czech Republic 

S. Mark and D. Gerlich 

Institut für Physik, Technische Universität, 09107 Chemnitz, Germany 

�Received 27 October 1999; accepted 31 January 2000� 

Collisions of ground state N � ions with N 2 were investigated in a Guided Ion Beam �GIB� apparatus 

at center-of-mass �CM� collision energies up to 10 eV. Isotopic labeling of the target gas, 15 N 2, was 

used as one criterion to distinguish electron transfer, atom transfer, and isotope exchange channels. 

The absolute cross sections are in good agreement with previous measurements. By combining the 

GIB technique with time-of-flight analysis �acronym GIB-TOF� more detailed information on the 

reaction dynamics has been obtained. The product velocity distributions measured for 15 N 2 � and 

14 N 15 N � indicate that both, electron and atom transfer, have to be divided into at least two parts, a 

direct one and one which seems to be characteristic for a long lived complex. The branching ratios 

derived for these four channels show a strong energy dependence. The mean product kinetic energy 

indicates that the remaining nitrogen atom is most probably formed in the metastable N( 2 D) state. 

For the nearly thermoneutral 14 N � – 15 N � isotope exchange it was observed that a significant fraction 

of the translational energy is transferred into internal excitation of the neutral molecule. © 2000 

American Institute of Physics. �S0021-9606�00�00616-4� 

I. INTRODUCTION 

Despite its importance in modeling chemical processes 

in the earth ionosphere and planetary atmospheres, or for 

understanding details of nitrogen discharges and plasmas, 

etc., the reaction of N � with N 2 has been the subject of only 

a few rather contradicting experimental studies until 1991, as 

can be seen from the compilation by Phelps. 1 In order to use 

the 1.043 eV endothermic electron transfer reaction 

N � �N 2→N 2 � �N as a reliable chemical thermometer �e.g., 

in nonequilibrium ion/gas environments�, 2 it became necessary 

to measure reliable absolute cross sections, especially in 

the threshold region. In 1993, the first GIB results were reported 

from the Freiburg machine. 3 These data have clearly 

shown that, for ground state ions, the electron transfer cross 

section is extremely small in the threshold region �smaller 

than 0.005 Å 2 below 2 eV� and that it reaches its maximum 

of 2.5�0.5 Å 2 only at a collision energy of 8 eV. These 

results have been corroborated and extended using two other 

GIB machines, i.e., the Utah GIB mass spectrometer and the 

Trento GIB crossed beam experiment. 4 This publication 

which will be denoted paper I in the following gives a summary 

of the situation until 1994 including a complete list of 

references. More detailed results from the Freiburg/Chemnitz 

GIB apparatus have been reported in 1996. 5 In this publication, 

which will be denoted paper II in the following, among 

others the influence of doubly charged ions N 2 �� and excited 

metastable N � ions on the formation of products in the 

threshold region is discussed. 

One experimental way to distinguish between different 

reaction mechanisms, e.g., electron or atom transfer, is to use 

different isotopes. Maier and Murad 6 performed experiments 

with the two isotopic combinations 15 N � � 14 N2 and 

14 N � � 15 N2. They found that the cross sections for producing 

molecular ions in the two possible isotope combinations are 

roughly equal at energies below 10 eV. Similar observations 

have been reported in paper I from 15 N � � 14 N 2 studies: 

electron-transfer �production of 14 N 2 � � and atom-transfer 

�production of 15 N 14 N � � start at the same collision energy 

and have similar energy dependencies until about 6 eV. This 

experimental result can be explained with the statistical decay 

of a ( 15 N– 14 N– 14 N) � structure where full scrambling of 

the atoms is hindered. Isotopic labeling also allows to observe 

the nearly thermoneutral ion–atom interchange. The 

early results from a flowing afterglow experiment 7 that isotope 

scrambling occurs with (18�7)% of the Langevin rate 

coefficient, have been corroborated and extended in paper I. 

An experimental method to get deeper insight into reaction 

mechanisms is to measure differential cross sections. In 

the abovementioned paper II, Mark and Gerlich report axial 

velocity distributions of N 2 � products which have been obtained 

with the GIB-TOF method. The derived differential 

cross sections have shown that in the decay of the 

( 14 N– 14 N– 14 N) � collision complex, forward and backward 

scattering were almost equal and, at E T�5.94 eV, they obtained 

almost perfect symmetry relative to v CM the velocity 

of the center-of-mass. It was pointed out in paper II that 

velocity distributions with isotopically labeled reactants, the 

goals of this work, are required for deciding whether the 

measured symmetry is due to a complex lifetime which is 

longer than several rotational periods. 

Most experimental observations have been tentatively 

explained based on state correlation diagrams. 4,7,8 Only re- 

0021-9606/2000/112(16)/7011/11/$17.00 7011 

© 2000 American Institute of Physics

7012 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Glosik et al. 

cently more detailed theoretical support became available by 

the ab initio calculations of Bennett et al. who report 12 

potential curves for collinear structures of N 3 � . 8 For understanding 

the N � �N 2 reaction dynamics it is important to 

note that the low lying N 3 � states have collinear centrosymmetric 

equilibrium geometry. Another interesting result from 

the calculations and from spectroscopic studies is that several 

excited states, e.g., the A 3 � u state, are separated by 

rather high barriers from the dissociation asymptotes. The 

question of how these states determine the collision process 

stimulated part of the present experiment. Is it possible that a 

long lived collision complex �i.e., a resonance� is formed at 

elevated collision energies? 

In order to get an answer to this question, we have extended 

the previous GIB and GIB-TOF experiments using 

isotopically labeled reactants. With 14 N 2 gas in the ion source 

and 15 N 2 as target gas, the following three reaction channels 

can be distinguished with the mass spectrometer: 

14 N � � 15 N 15 N→ 15 N � � 14 N 15 N, �I� 

→ 15 N 15 N � � 14 N, �II� 

→14N15N��15N. �III� 

For the corresponding integral cross sections the symbols 

�I , �II , and �III will be used. Reaction I, which is essentially 

thermoneutral, is usually called ion–atom interchange 

or isotopic exchange. For processes II and III the names 

electron- and atom-transfer �or atom abstraction� are common; 

however, it will be shown in this paper that this terminology 

does not describe the actual reaction mechanism 

which is more complicated. Nonetheless, we will use these 

simple names as long as it does not causes confusion. 

In the following some hints to the experimental procedure 

are given with special emphasis on the GIB-TOF 

method. The results section contains product velocity distributions 

and branching ratios for channels II and III. Also for 

channel I, the ion–atom interchange, integral cross sections, 

and velocity distributions are mentioned. For all channels, 

these results obviously also provide information on the internal 

excitation of the products and on their laboratory energy, 

an important information for modeling plasmas. In the discussion 

section it is shown that for II and III at least four 

mechanisms have to be distinguished. This is qualitatively in 

accord with the fact that the molecular ion can be formed via 

complicated nonadiabatic interactions involving several potential 

energy surfaces. 

II. EXPERIMENT 

The schematic diagram of the universal Guided Ion 

Beam �GIB� apparatus used in the present study is shown in 

Fig. 1. Since a complete description of the apparatus, its 

operation principle, and the routinely performed tests measurements 

are given elsewhere 9 only a very short summary is 

presented here. 

As indicated in Fig. 1, an rf storage ion source is used to 

produce the primary ions by electron impact. The ions leaving 

the ion source via an extraction electrode �diameter 3 

mm� enter the quadrupole which is operated in the effective 

FIG. 1. Schematic view of the universal guided ion beam �GIB� apparatus. 

Ions are produced by electron impact in an rf storage ion source operating in 

a pulsed mode. In the quadrupole the ions are mass selected and also energy 

preselected by pulsing input and output lenses of the quadrupole. An einzellens 

focuses the ions onto the octopole injection electrode. The first octopole 

guides the ions through the 300 K scattering cell. The second, much longer, 

octopole guides primary and product ions toward the entrance slit of a 90° 

magnetic mass spectrometer. After mass selection the ions are detected with 

nearly 100% efficiency by a Daly detector. The second octopole is used also 

for time-of-flight analysis of the axial velocity of the primary and product 

ions. 

potential mode �high frequency� and which pre-selects the 

primary ion beam according to mass and energy making use 

of the focusing and guiding properties �see Ref. 9�. The 

transmitted ions are injected into a twin-octopole system 

with a defined kinetic energy. Octopole 1 �length 13.6 cm, 

rod diameter 2 mm� guides the primary ions into and through 

the scattering cell �effective length 4.6 cm�. Octopole 2 

�length 46.8 cm, rod diameter 2 mm� guides the reactant and 

product ions toward the detector. The two ion guides are 

coupled to the same rf generator �frequency 12 MHz, amplitude 

typically 150 V� source but they can be operated with a 

different dc bias. Typically the second octopole is floated 

0.1–0.5 V below the first octopole in order to avoid discrimination 

of slow ions in the transition region or due to potential 

distortions inside the second octopole. At the end of the second 

octopole, ions are accelerated to 2 keV, pass some electrostatic 

optics and the magnetic mass spectrometer, and are 

converted into short negative pulses using a Daly detector, 

amplifier, and discriminator system. 

For getting reliable results for the title reaction, special 

attention has to be paid to the preparation of the primary N � 

ions. It has been shown in paper II that minor contaminations

J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Reactions in 14 N � � 15 N 2 

of the primary ion beam with electronically excited atomic 

ions or with doubly charged molecular ions, N 2 2� , lead to 

erroneous cross sections in the threshold region. In the 

present experiment, N � ions were produced from N 2 by using 

low-energy electrons ��25 eV�, and operating the rf storage 

ion source with a mean storage time of 1 ms and high 

gas pressure �up to 10 �3 Torr�. Comparison of the present 

results with those from paper I allows the conclusion that, for 

quenching excited atomic N � ions or doubly charged molecular 

ions, the storage ion source is slightly more efficient 

than the flow-tube ion source used in the Utah GIB apparatus. 

One of the key features of the GIB technique for measuring 

integral cross sections is that the octopole can allow 

for 4� collection of product ions, independent of their flight 

direction. Necessary conditions are that the rf amplitude is 

high enough and that ions which are backward scattered in 

the laboratory frame are reflected toward the detector by a 

suitable voltage pulse on the octopole injection electrode. 

The absolute values of integral cross section are determined 

in the usual way from count rates, target gas density, and the 

effective length of the scattering cell. By introducing the 

reactant gas directly into the scattering cell or alternatively 

into the vacuum chamber the background signal due to collisions 

outside the scattering cell is taken into consideration 

�chopper like principle�. The absolute pressure in the scattering 

cell is measured using a Baratron or a Viscovac. Usually 

the primary ion beam is only weakly attenuated. In most 

cases statistical errors are negligible in comparison to systematic 

uncertainties, which are estimated conservatively to 

be 20%. 

For preparation and calibration of the actual ion energy 

with an accuracy better than 10 meV and for getting information 

on the axial product velocity by TOF, the ion beam is 

operated in a pulsed mode using an adequate pulse sequence 

at the exit electrode of the source, the lens system after the 

quadrupole, and the octopole entrance electrode. The repetition 

period used in the present experiment was 2 ms. TOF 

spectra are recorded with a multichannel scaler, in this work 

with a time resolution of 2 �s. The obtained TOF spectra are 

transformed into axial velocity distributions of the ions. 

For a detailed discussion including the numerical procedure 

and the evaluation of the influence of the target motion and 

the finite length of the scattering cell see Refs. 10, 9, and 

paper II. 

As discussed in detail in paper II the octopole beam 

guide can also be used to measure absolute doubly differential 

cross sections with high sensitivity and at low laboratory 

energies. Briefly, this method requires a primary ion beam 

moving with a small angular divergence parallel to the axis 

of the octopole, a short scattering cell, and a long second 

octopole for analyzing the product velocity. The data evaluation 

and the presentation of the results make use of the fact 

that the mean value of the target velocity is zero �scattering 

cell�, and that the total scattering problem is rotationally 

symmetric to the axis of the octopole. Under these conditions 

the laboratory velocity vector of the ionic product, v1� , is 

fully specified by the two components v1p � and v1t � , the parallel 

and the transverse one �the primed symbols refer to 

7013 

FIG. 2. Axial velocity distribution of 15 N � product ions for the nearly ther- 

moneutral isotope exchange process �channel I�, plotted as a function of the 

laboratory velocity, v1p � . Velocities are given in units of cm/�s�104 m/s. 

The dashed line marks v CM the dash-dotted line at the right corresponds to 

E T��E T�2 eV. Products are formed both in the forward direction �indicated 

by the Gaussian� and in the backward direction �left side from the dashed 

line�. Note that E T� of most products is smaller than 1 eV. Concerning 

experimental problems with very slow products �kinetic energy below 20 

meV� and ions which are backward scattered in the laboratory frame; see 

text. 

products, for a complete summary of our standard nomenclature 

see Ref. 10 and paper II�. Transformation of the velocities 

into the center-of-mass frame, u1p � �v 1p � �v CM and u1t � 

�v 1t � , is obvious. For the relationship between measured 

count rates and the doubly differential cross section, 

d2�/du1p � du1t � , see Eq. �4� of paper II. Note that the favorable 

geometry also leads to a very simple transformation of 

intensities from the center-of-mass �CM� into the laboratory 

�LAB� frame �see Eq. �5� of paper II�. Operating the octopole 

at a large enough rf amplitudes automatically results in an 

integration over the transverse velocity distribution. This 

leads to axial velocity distributions which are proportional to 

the differential cross section d�/du1p � . It is a special feature 

of the GIB scattering geometry, that this information is already 

sufficient to decide, whether the reaction dynamics 

lead to a preference of forward or backward scattering. 

As a typical example, Fig. 2 shows an axial velocity 

distribution measured for the reaction channel I at a collision 

energy of 2 eV. As described in detail in paper II, the TOF 

distributions recorded with a multichannel scaler are transformed 

into a laboratory velocity distribution. Important for 

the understanding of such a distribution are the dashed and 

the dash-dotted lines which mark the velocity of the centerof-mass 

of the collision system, v CM , and the product velocity 

for the special case E T��E T �see upper scale�. Another 

important problem for understanding such results and for 

their interpretation is the increase of intensity toward very 

low laboratory velocities, which are due to ions with very 

long flight times. Such peak intensities often appear at product 

velocities, v1p � �0.05 cm/�s, corresponding to laboratory 

energies below 20 meV. The reason for such a peak is that 

potential distortions in the octopole ion guide can lead to ion 

reflections or that ions which are backward scattered in the


laboratory frame appear at very long flight times if they are 

reflected on the octopole entrance. For a detailed discussion 

of such effects, see paper II and especially Fig. 6 therein. 

Inspection of the results plotted in Fig. 2 directly reveals 

that the nearly thermoneutral isotope exchange leads to two 

groups of 15 N � products, one in the forward direction which 

can be approximated by the indicated Gaussian �dotted line� 

and one in the backward direction, i.e., on the left side from 

the dashed line. Comparison of the distribution with the scale 

on the upper part of the figure reveals that a significant fraction 

of the initial translational energy, E T�2 eV, is converted 

into internal excitation. Some more details of reaction 

I will be discussed below. 

III. RESULTS 

A. Differential cross section for channels II and III 

The present study is the extension of our previous measurements 

of the axial velocity distribution of the title reaction 

performed with three identical 14N atoms �paper II�. 

Here we combine the high sensitivity of the GIB-TOF 

method with isotope labeling in order to characterize the 

reaction mechanism in more detail. The type of information 

one can get is illustrated in Fig. 3, which shows four different 

distributions obtained all at the same collision energy, 

ET�6.41 eV. The two upper panels �a and b� show the results 

for channels II and III. It can be seen that the shapes 

differ substantially indicating that the products 15 � 

N2 and 

14 15 � N N are formed in different ways. Channel II exhibits a 

clear dominance of backward scattering with respect to the 

center-of-mass velocity, vCM whereas forward scattering prevails 

for channel III. Another characteristic feature of both 

results is that there is also a nonnegligible part of products 

appearing on the opposite side of vCM . 

The plots in panels �c� and �d� of Fig. 3 illustrate why 

one obtains pronounced forward–backward symmetry if one 

does not distinguish between the isotopes. Panel �c� shows 

the sum of channels II and III. Note that the GIB-TOF 

method determines distributions in absolute units which can 

be converted directly into absolute differential cross sections 

�see above and paper II�. This has been accounted for when 

we combined the two isotopic channels II and III �panel �c��. 

For better comparison of the shapes, all four distributions in 

Fig. 3 are plotted normalized to the maximum. The lowest 

panel shows an axial velocity distribution measured for the 

collision system 14N��14N2, i.e., without isotope labeling. 

In this case all produced molecular ions have mass 28 amu 

�atomic mass unit� and one cannot distinguish between contributions 

from charge transfer and atomic interchange. It is 

evident that the sum of the two isotopes �c� and the results 

without using the isotope labeling �d� are very similar. 

The energy dependence of the differential cross sections 

d�/du1p � has been recorded for channels II and III at center- 

of-mass collision energies from E T�4.5 eV up to 10 eV. 

Typical results are shown in Fig. 4�a� for the product channel 

15 N 15 N � and in Fig. 4�b� for channel 14 N 15 N � . For all dis- 

tributions the u1p � velocity scale is the same, the dashed line 

marks vCM , and the scale of the kinetic energy after the 

collision, ET� , is also valid for all results. Note the slight 

differences in the individual v1p � velocity scales. Also here 

the data have been normalized to the maximum of the individual 

curves in order to facilitate the comparison of the 

shapes. In addition, absolute values for the differential cross 

section are given by the vertical scales of the particular plot 

on the right �units: Å 2 /cm �s �1 �. The maximum of the distributions 

changes from 0, 7 Å 2 /cm �s �1 at low collision 

energies to 10 Å 2 /cm �s �1 at 10 eV. The differences between 

channels II and III which have been discussed in Fig. 3 are 

evident over the full energy range. A careful inspection of 

the energy dependence reveals that for both channels there is 

a trend to prefer the direct processes at higher collision energies 

ET . This will be evaluated more quantitatively in the 

discussion section. 

B. Branching ratios for channels II and III 

As it was already mentioned in paper I, the absolute 

cross sections measured for the two channels II and III, e.g., 

� II and � III can be used to define a criterion for distinguishing 

between charge transfer and atom interchange. In addition 

the ratio � III /� II was used to discuss possible structures 

of the intermediate complex formed in the course of the reaction. 

In order to determine this ratio with high accuracy we 

derived this value directly from the counts corresponding to 

masses 29 amu ( 15 N 14 N � ) and 30 amu � 15 N 15 N � ) at otherwise 

identical conditions, i.e., without relating them to the 

number of counts corresponding to the primary ions. In Fig. 

5 the energy dependence of the obtained ratio � 29 /� 30 is 

plotted as a function of the collision energy �crosses�. At 

E T�5 eV, where the cross sections � II and � III are very 

small (�0.1�10 �16 cm 2 ) a fraction of ions with mass 28 

( 14 N 14 N � ) amu was also produced from traces of the doubly 

charged ions 14 N 2 2� contaminating the primary 14 N � beam. 

Since in such a collision two molecular ions, 14 N 2 � and 15 N2 � , 

are formed by a single electron transfer, the data � 28 /� 30 

�open triangles in Fig. 5� can be used to correct the measured 

ratio � 29 /� 30 in order to obtain � III /� II . At energies above 5 

eV, the influence of doubly charged ions in the primary ion 

beam can be neglected. Below 3 eV the cross sections � II 

and � III are so small that production of 15 N 15 N � is dominated 

by the reaction of doubly charged 14 N 2 2� �see Fig. 7 in paper 

II�. 

The branching ratio � III /� II was also derived from velocity 

distributions �Fig. 4� by integrating over the suitable 

velocity interval. This procedure is not influenced by the 

presence of 14 N 2 2� , because the product ions formed in a 

transfer of a single charge from N 2 to 14 N 2 2� are very fast due 

to the coulomb repulsion. They either escape with their high 

kinetic energy from the octopole or they arrive at the detector 

at different times �see Fig. 8 of paper II�. The ratios 

� III /� II obtained from the TOF distributions at energies between 

4.5 and 10 eV are also included in Fig. 5 �open 

squares�. AtE T�6.5 eV the value of the branching ratio is 

approaching 0.7, and is nearly constant. Below 4.5 eV the 

cross section of the reactions is so small that the scatter of 

the data became too large. The fact that the charge transfer 

channel II increases in weight with increasing energy than 

the isotopic exchange channel III will be discussed below. It


FIG. 3. Axial product ion velocity distributions for reactions II and III 

measured at E T�6.41 eV. The dashed line marks v CM , the dash-dotted line 

is at the position where E T��E T . Velocities are given in units of 

cm/�s�10 m/s. Panel �a� shows the results for 15 N 15 N � products; panel �b� 

for 14 N 15 N � products. Panel �c� is the weighted sum of �a� and �b�, whereas 

panel �c� shows 14 N 2 � products from a measurement without isotopic labeling 

�i.e., one cannot distinguish between II and III�. All four plots are normalized 

to the maximum of the curve. The plots are embedded in a box 

showing on the lower scale the axial velocity of the product ions in the CM 

frame, u�1p �parallel to the axis, indicated by subscript p�. The upper scale 

gives, here only for 14N��14 � 

N2 , the translational energy of the products in 

the CM frame, ET� . Note that the other isotopes have slightly different ET� scales. 

should be noted that not only the results from our two different 

measuring procedures are in good accordance, but that 

there is also an overall agreement with the ratio � III /� II reported 

in paper I. 

C. Channel I: Isotopic interchange 

7015 

Although it has not been the dominant aim of this work, 

we have also measured integral cross sections and velocity 

distributions for reaction I, the isotope exchange channel. 

The absolute cross sections, determined in the energy range 

from 0.07 eV to 10 eV, are plotted in Fig. 6. Special attention 

was given to collect all backward scattered product ions, 

a problem which has been briefly discussed above in connection 

with Fig. 2. By pulsing the entrance electrode of the 

octopole in a suitable way, the product ions can be forced to 

exit the octopole only at the end toward the detector. For 

reaction channel I this leads to an increase of the count rate 

of up to 20% at an energy below 0.5 eV. From 0.2 eV up to 

1.5 eV, the results can be fitted with the function � l 

�7.5 E T �0.5 �units of �l and E T are Å 2 and eV, respectively�. 

This corresponds to a rate coefficient k�(1.9�0.4) 

�10 �10 cm 3 s �1 . These data can be compared with a flowing 

afterglow result, k�(1.8�0.7)�10 �10 cm 3 s �1 reported by 

Fehsenfeld et al., 7 and with k�(1.6�0.3)�10 �10 cm 3 s �1 

given in paper I. All three results agree within the claimed 

experimental uncertainties. At collision energies above 1.5 

eV the cross section declines faster than �E T �0.5 . 

Also for channel I, axial velocity distributions have been 

measured at energies from 0.6 eV up to 10 eV. Similar to the 

results shown in Fig. 2, all results clearly indicate two distinguishable 

groups of products, a backward scattered one, 

I B , and a forward scattered one, I F . Forward scattering 

dominates with about 60% at energies up to 4 eV. At higher 

energies backward scattering becomes more important and it 

prevails with 65% above 6 eV. Both parts of the distribution 

show more or less pronounced peaks the position of which 

move with collision energy. Some tentative evaluation of the 

velocity distributions will be discussed below. 

IV. DISCUSSION 

A. Definition of subchannels IIC ,IID , IIIC , and IIID As can be seen from Fig. 3, isotopic labeling clearly 

reveals that electron transfer and atom transfer lead to significant 

differences in the velocity distributions. From this it 

is also obvious that the forward–backward symmetry reported 

in paper II for 14N��14N2 collisions was not due to a 

collision complex which lived longer than several rotational 

periods but due to the indistinguishableness of the three atoms 

involved. Nonetheless, it can be presumed that a certain 

fraction of the ionic product molecules is formed via a statistical 

complex. This presumption is not only motivated by 

the experimental observation that products appear on both 

sides of vCM but it is also supported by ab initio calculations. 

The rather complex potential curves and their avoided crossings, 

shown in Fig. 1 of Ref. 8, can be used as a qualitative 

argument that some of the trajectories may get caught in a 

strongly coupled �may be also long-lived� collision complex, 

also at total energies above 5 eV.


FIG. 4. Axial product ions velocity distributions measured for the reaction 14 N � � 15 N 2 at the indicated collision energies E T . For details concerning the 

representation and the scales see Fig. 3. The curves are all plotted normalized to the same height; however, for comparison of the actual product yields, the 

vertical scales on the right side of the plots show the differential cross section, d�/du� 1p , in absolute units, e.g., in Å 2 /cm �s �1 . The product distribution of 

reaction channel II � 15 N 15 N � , left panel� shows a clear preference for backward scattering, whereas in reaction III � 14 N 15 N � , right panel� forward scattering 

prevails. The slight but significant change of the shape of the distributions with increasing collision energy E T is discussed in the text.


In order to evaluate the results shown in Fig. 4 in more 

detail, we postulate that channels II and III can be further 

divided into two subchannels which are briefly named ‘‘direct’’ 

and ‘‘complex.’’ Inspection of the results reveals that 

the extraction of the direct part is rather obvious; for simplicity 

we used a Gaussian with three free parameters. Also for 

FIG. 4. �Continued.� 

7017 

the second part we suppose that its velocity distribution can 

be represented with a Gaussian; however, here we assume 

that the function is centered at v CM �two additional parameters�. 

This assumption is based on the hypothesis that a 

statistical collision complex is formed leading to more or less 

rotationally symmetric angular distribution and to an effi-


FIG. 5. The branching ratio of the atom transfer �III� and electron transfer 

�II� channel as a function of collision energy E T . The ratio � 29 /� 30 

�crosses� was determined directly from the two count rates obtained at mass 

29 amu ( 14 N 15 N � ) and at mass 30 amu ( 15 N 15 N � ). Below 5 eV, this value 

is slightly affected by contributions from doubly charged 14 N 2 2� ; this contribution 

is characterized by � 28 /� 30 �open triangles, for details see text�. By 

open circles are indicated values of � III /� II obtained after correction of 

� 29 /� 30 taking into account contribution produced from 14 N 2 2� . The corrected 

values are in good agreement with the ratio � III /� II obtained from the 

TOF distributions �open squares�, which are not affected by the presence of 

14 N2 2� . 

cient excitation of all internal degrees of freedom. Integration 

of such a distribution over the transverse component of 

the product velocity leads to an axial velocity distribution 

which usually peaks at v CM . The use of Gaussians is also 

motivated by the fact that simulations of GIB-TOF measurements 

which account for the thermal motion of the target gas 

and the finite length of the scattering cell lead to such curves 

�see, for example, Figs. 5 and 6 of paper II�. 

A few typical results of the described evaluation procedure 

�five parameter fit� are plotted in the upper and lower 

panel of Fig. 7 for E T�5.5 eV and E T�10.0 eV, respectively. 

Shown are the absolute values of the single differen- 

FIG. 6. Integral cross section for 14 N– 15 N isotope exchange �reaction channel 

I� as a function of the collision energy E T . Below E T�0.5 eV �symbol 

*� the measured values have been corrected for product loss due to backward 

scattering in the laboratory frame �see text�. The solid line indicates 

the function �(E T)�7.5 Å 2 �(E T /eV) �0.5 , corresponding to about 1/5 of 

the Langevin cross section. 

FIG. 7. Differential cross sections, d�/du1p � , for the two reaction channels 

II and III �15N15N� : filled squares; 14N15N� : open circles�, measured at ET �5.5 and 10 eV. For details concerning the representation see Fig. 3. The 

experimental data were fitted by two independent Gaussians. One Gaussian 

was chosen such that it has its maximum at u1p � �0. This corresponds to the 

assumption that a part of the velocity distribution has forward–backward 

symmetry. For reaction channel II, the fit and the two individual contributions 

are plotted by full lines. Dashed lines are for channel III. This fitting 

procedure is used to distinguish between subchannels of reaction II and III, 

which are called direct and complex. Note that at ET�5.5 there is a preference 

for the complex part while at ET�10 eV direct scattering is more 

pronounced. 

tial cross sections for channels II �solid squares� and III 

�open circles� as a function of the velocity in the CM frame, 

u1p � . It is evident that each set of experimental data is nicely 

reproduced by the sum of two Gaussians. The quality of the 

fit validates our assumption that both reaction channels, 

which are usually called ‘‘electron transfer’’ and the ‘‘atom 

transfer,’’ can be decomposed into a ‘‘direct’’ part and a 

‘‘complex’’ part. Note, however, that the resulting precise 

branching ratios should not be overinterpreted. In the following 

we will use the subscripts D and C for marking these 

subchannels �IID , IIC , IIID , and IIIC�. By using these 

branching ratios we obtain �at particular ET� four differential 

cross sections, (d�/du1p � ) IID ,(d�/du1p � ) IIC ,(d�/du1p � ) IIID , 

and (d�/du1p � ) IIIC which are indicated by lines in Fig. 7. By 

integrating these differential cross sections we obtained the 

absolute cross sections for particular subchannels, �IID , 

�IIC , �IIID , and �IIIC . The maximum of the fitted Gauss 

function gives the most probable velocity of the products of 

the particular subchannel, which is identical with the mean 

product velocity �u 1p � �. Comparison of the individual Gaus-


sians reveals that �i� the complex part is more dominant at 

5.5 eV than at 10 eV, �ii� that the complex part is more 

dominant for channel III than II, and �iii� that the ‘‘position’’ 

of the direct part is different for the two channels II and III 

and depends on collision energy. 

It must be noted that in general the fitting procedure 

would be more sensitive to the reaction mechanism if one 

would measure the doubly differential cross section, 

d2�/du1p � du1t � . In the present case, however, we have shown 

by some tests �variation of the guiding field� carried out at a 

collision energy of 6.41 eV that no significant intensity is 

scattered in sidewards direction. This means that both the 

direct and the complex part is located close to the vector of 

relative velocity. Therefore, d�/du1p � already provides most 

of the information. 

B. Branching ratios 

The procedure discussed in Sec. IV A has been applied 

to all velocity distributions recorded at collision energies between 

4.5 eV and 10 eV. Some of the resulting parameters 

are plotted in Fig. 8. The upper panel of this figure shows the 

branching ratios of individual subchannels, II D ,II C , III D , 

and III C , distinguished by isotopic labeling �II and III� and 

by TOF �subscript D and C�. In addition the sum of the two 

‘‘direct’’ contributions and of the two ‘‘complex’’ ones are 

also plotted. They show �solid lines� that at low E T the 

‘‘complex’’ channels are dominant �70%� whereas at higher 

E T the direct channels become more important �60%�. 

In order to find correlation between channels II �‘‘electron 

transfer’’� and III �‘‘atom transfer’’�, several ratios are 

plotted in the lower panel of Fig. 8. The ratio of the overall 

cross sections, � II /� III , slowly increases with increasing energy. 

This result, derived here from the TOF distributions, is 

in accordance with the values determined from the count 

rates on mass 29 amu ( 14 N 15 N � ) and mass 30 amu 

( 15 N 15 N � ) which are plotted in Fig. 5 �note that Fig. 5 shows 

the reciprocal value on a logarithmic scale�. This energy dependence 

is in agreement with the simple expectation that 

electron transfer becomes more dominant at higher collision 

energies. Nevertheless, one has to realize that the actual reaction 

mechanisms are more complicated and that the ratio 

� II /� III has no simple interpretation. This is stressed by the 

fact that the ratio � IID /� IIID is larger than 4 at low energies 

and that it falls with increasing energy. This is a clear indication 

that charge transfer is here not a simple ‘‘large distance 

electron jump’’ but determined by a complicated interplay 

of several potential energy surfaces. 8 Interesting is the 

energy dependence of the ratio � IIC /� IIIC which remains 

rather close to 1/2 over the full range of energies shown in 

Fig. 8. This is in clear contrast to the ratio 1/1 which has 

been derived in paper I and in Fig. 5 from the count rates of 

the two product masses 29 amu and 30 amu. A ratio 1/2 

instead of 1/1 can indicate that in the strongly coupled �or 

long-lived� complex all three N atoms are equivalent, and 

subchannels II C and III C are given just by dissociation of this 

complex. Note, however, that this statement is based on our 

model assumption. Exploration of the collinear potential 

curves, shown in Figs. 1–3 of Ref. 8, may results in some 

FIG. 8. Various branching ratios as function of collision energy. The upper 

panel shows the fraction of the four subchannels II D ,II C �circles�, and 

III D ,III C �squares�. The symbols �� and �� indicate the overall direct 

(II D�III D) and overall complex (II C�III C) fraction of the reaction, respectively. 

At low energies atom transfer via the complex (III C) is dominant; 

above 7 eV the direct electron transfer (II D) prevails. In the lower panel, the 

ratio � II /� III �open squares� is compared with the corresponding ratio for 

the subchannels, � IIC /� IIIC and � IID /� IIID . The dashed lines indicate the 

value expected for simple statistical assumptions. � II /� III�1 is expected for 

a linear ( 15 N– 14 N– 14 N) � complex, where the central atom has to remain in 

the middle, whereas �II /� III� 1 

is expected for a complex where full scram- 

2 

bling can take place. The fact that �IIC /� IIIC approaches this value at low 

energies is discussed in the text. Note that the high value of �IID /� IIID at 

low ET is due to very low value of �IID , below 10% of the sum of the cross 

sections of the reactions II and III. 

speculative predictions; however, we believe that for a reliable 

interpretations of our detailed results, more theoretical 

studies are required such as potential curves in three dimensions 

and dynamical studies accounting for all the avoided 

crossings and conical intersections. 

C. Internal excitation, product kinetic energies 

7019 

A hint that reactions II and III most probably require 

formation of excited products is given by the delayed onset 

of the integral cross sections. In paper I an apparent threshold 

energy of 3.41 eV has been derived by fitting the measured 

data up to 9 eV using the function �units are Å 2 and


FIG. 9. Product translational energy ET� and translational endoergicity �E� 

for the direct process of channels II and III as function of collision energy 

ET . The energies ETII � and ETIII � �open symbols� have been extracted from 

the results shown in Fig. 4. The evaluation procedure is described in Fig. 7 

and in the text. The values �E II ��E T�E TII � and �E III � �E T�E TIII � are the 

energies used for overcoming the endoergicity of the reaction and for internal 

excitation of the products. The solid lines are linear fits of the data. 

Linear extrapolation of the lines to ET��0 leads to ET values which can be 

interpreted as apparent threshold energies for direct processes. The results, 

obtained for the two subchannels IID and IIID , are 3.47 eV and 3.67 eV, 

respectively. 

eV� ��1.9 (E T�3.41) 1.4 /E T . In paper II, where data points 

up to 8 eV have been evaluated, a slightly smaller threshold 

value has been obtained, ��0.9 (E T�3.1) 2 /E T . If one analyzes 

only the extremely small cross sections measured below 

3 eV �see Fig. 9 from paper II�, one obtains � 

�0.034 (E T�2.32). Comparison of these three functions 

rises the question whether these apparent thresholds are correlated 

to accessible product states. More information can be 

obtained from product velocity distributions. A few typical 

examples are shown in Fig. 10 of paper II. Such measurements 

allow the conclusion that at E T�2.95 eV a significant 

fraction of both products, N 2 � and N, are formed in the electronic 

ground state while at E T�3.95 eV the velocity distribution 

provide evidence that there is a high probability to 

form the atom in the N( 2 D) states, which requires at least 

3.43 eV. 

More detailed information on the product kinetic energies 

can be extracted from the Gaussians fitted to the axial 

velocity distributions as described above. It is obvious that 

for the complex part the mean product velocity is zero by 

construction. For characterizing the energetic positions of the 

direct parts of the velocity distributions �subchannel II D or 

III D�, we define E T� as the translational energy of the products 

�in CM frame� corresponding to the maximum of the 

velocity distribution �for subchannel II D or III D�, i.e., E T� is 

not the mean product translational energy but given by ET� ��/2�u 1p � � 2 . In Fig. 9 the resulting values ETII � and ETIII � �for 

the two reaction channels IID and IIID� are plotted as function 

of ET . Ignoring the small transverse velocity component 

�see the remark at the end of Sec. IV A� and making use of 

energy conservation, allows one to calculate the translational 

endoergicity, �E II ��E T�E TII � and �E III � �E T�E TIII � i.e., the 

energy which is used to overcome endoergicity of the reac- 

FIG. 10. Product translational energies E T� and translational endoergicities 

�E� for reaction channel I �thermoneutral atom interchange, leading to 

15 N � � as a function of collision energy ET . The upper part is for forward 

scattering �subscript F�, the lower one for backward scattering �subscript B�. 

The plotted mean values, ETF � and ETB � , have been determined by fitting the 

measured velocity distribution with two Gaussians �see text�. It can be seen 

from the values �E F��E T�E TF � and �E B��E T�E TB � �solid symbols� that 

most of the available energy �solid lines� is converted into internal excitation 

of the products. The dashed lines are mainly for guiding the eyes. 

tion and is converted into internal excitation of the products. 

It can be seen from Fig. 9 that linear extrapolation of these 

data indicates that subchannel III D starts at E T�3.7 eV, 

whereas subchannel II D has an onset at a slightly lower energy, 

E T�3.5 eV. All of these results clearly indicate that 

formation of N( 2 D)�N 2 � (X), which becomes energetically 

possible above 3.43 eV, plays a dominant role. Coupling of 

the input channel to channel N( 4 S)�N 2 � (A), which is accessible 

on the triplet surfaces at energies above 2.16 eV, seems 

to be very inefficient. 

D. Branching ratios and product energies 

for channel I 

In order to understand the low energy behavior of the 

reaction the nearly thermoneutral reaction channel I has also 

been studied in the present work. The axial velocity distributions, 

which have been measured at energies between 0.6 eV 

and 10 eV, were fitted by two Gaussians. As already discussed 

above in connection with Fig. 2, the evaluation procedure 

was more complicated and less accurate than for the 

other product channels because a significant fraction of backward 

scattered 15N� ions �indicated by subscript B� appear in 

the neighborhood of v 1p 

� �0. The forward scattered products 

�indicated by subscript F� showed a very broad and flat distribution 

and, especially at energies above 5 eV, it was difficult 

to fit the data. Therefore the results shown in Fig. 10 

have to be taken with some precaution. The derived product 

translational energies ETF � and ETB � �see definition in Sec. 

IV C� and the translational endoergicities, �E F��E T�E TF � 

and �E B��E T�E TB � show the clear overall trend that translational 

energy is efficiently converted into internal excitation 

of products during atomic scrambling. At collision energies 

below 2–3 eV this can be explained with the 

formation of a strongly coupled collision complex, i.e., the


atomic exchange proceeds via the more than 3.5 eV deep 

N 3 � ( 3 � � ) ground state. At higher energies, however, the 

situation becomes more complex, and many other reaction 

paths become accessible. Therefore it is somewhat surprising 

that the data in Fig. 10 rise monotonously without obvious 

steps. This may be a hint that most products of channel I are 

formed via the lowest surface, where energy is efficiently 

converted into rovibrational motion while a jump to an upper 

surface leads to other products. This is consistent with the 

steep fall of � I at collision energies where the other channels 

open up. 

V. CONCLUSIONS 

The GIB-TOF method has been used to study the interaction 

of 14 N � with 15 N 2 at collision energies up to 10 eV. In 

addition to absolute cross sections measured for the three 

channels I–III, axial product velocity distributions were recorded 

for determining absolute differential cross sections. It 

has been shown that isotopic exchange �channel I� results in 

products with high internal excitation. A detailed evaluation 

of the differential cross sections measured for the formation 

of molecular ions showed that these products are formed via 

several, well-distinguishable processes: electron transfer with 

backward scattering, atom stripping with forward scattering, 

and formation of a long-lived collision complex with isotopic 

exchange. Some of the experimental results can be qualitatively 

understood with the help of the ab initio calculations 

from Bennett et al. 8 Nonetheless, more theoretical work including 

potential energy surfaces for three dimensions and 

their coupling is required to get more insight into these elementary 

reactions. 

The results of this paper provide detailed data for modeling 

material flow and energy balance in ionosphere and 

nitrogen containing discharges and plasmas, including reentry 

of cosmic vehicles through atmosphere. In this context 

we want to emphasize that the information contained in Figs. 

8, 9, and 10 not only describes the distribution of the initial 

translational energy between internal degrees of freedom and 

relative motion, but that it also can be used to derive laboratory 

velocities. Note, for example, that in reaction II D most 

of the collision energy is converted into internal excitation; 

nevertheless transformation into the LAB system reveals that 

the produced N atoms have a large laboratory energy, e.g., 

7021 

almost 8 eV at E T�10 eV. Also, reaction I B leads to fast 

14 N 15 N molecules �e.g., at ET�10 eV, the laboratory energy 

is almost 6 eV� although also for this reaction channel, most 

of the collision energy is converted into internal excitation. 

The history of the studies of the N � and N 2 reaction 

nicely demonstrates how, with the advance of experimental 

techniques, the information on the reaction was increasing 

from a single thermal rate coefficient, energy dependent absolute 

cross sections, detailed studies of the threshold region, 

via differential cross sections to the details provided in the 

present experiment. Nonetheless, we are far from full understanding 

of the mechanism of the reaction of N � and N 2 on a 

state-to-state level, a very complicated task in the energy 

range of the present experiment. Especially at low collision 

energies, studies with ions prepared in specific fine structure 

states are required in order to understand the mechanism of 

isotope exchange on the various surfaces. Also challenging is 

the study of the reverse reaction of N 2 � (v, j) with N atoms in 

the ground or an excited state for exploring the potential 

surfaces and their nonadiabatic interactions. 

ACKNOWLEDGMENTS 

J.G. and A.L. wish to express their thankfulness for the 

hospitality during their visit at the Institut für Physik of the 

Technische Universität Chemnitz. This work was supported 

in part by the VW foundation �Schwerpunkt Intra- and intermolekulare 

Elektronenübertragung, Az.: I/72 593� and by a 

grant from the Agency of Czech Republic �Project No. 

GACR 203/98/0508�. 

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F. Vedel and M. Vedel, J. Mod. Opt. 36, 431�1992�. 

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Knudsen �Aarhus, Denmark, 1993�, p. 699. 

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W. Freysinger, F. A. Khan, P. B. Armentrout, P. Tosi, O. Dmitriev, and D. 

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S. Mark and D. Gerlich, Chem. Phys. 209, 235 �1996�. 

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W. B. Maier II and E. Murad, J. Chem. Phys. 55, 2307 �1971�. 

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F. C. Fehsenfeld, D. L. Albritton, Y. A. Bush, P. G. Fournier, T. R. 

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D. Gerlich, in State Selected and State-to-State Ion-Molecule Reaction 

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Guided ion beam studies of electron and isotope transfer in N+N ...

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