electronic states

JOURNAL OF CHEMICAL PHYSICS

VOLUME 118, NUMBER 14

8 APRIL 2003

Dissociative recombination of NO¿ : Dynamics of the X 1 ⌺ ¿ and a 3 ⌺ ¿ electronic states Fredrik Hellberg, Stefan Roseń, Richard Thomas, Anita Neau, and Mats Larsson Department of Physics, Albanova, Stockholm University, SE 106 91 Stockholm, Sweden

Annemieke Petrignani and Wim J. van der Zande FOM–Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands

共Received 8 July 2002; accepted 15 January 2003兲 We have studied the dissociation dynamics of NO⫹ ions in their ground, X 1 ⌺ ⫹ , and first excited metastable, a 3 ⌺ ⫹ states, induced by the capture of electrons of variable collision energy in the dissociative recombination 共DR兲 process. The branching over the different dissociation channels has been measured in a merged-beam experiment on the heavy-ion storage ring, CRYRING. In accord with previous observations, NO⫹ (X 1 ⌺ ⫹ , v ⫽0) ions dissociate dominantly to the N( 2 D) ⫹O( 3 P) product limit at 0 and 1.2 eV collision energies. In contrast to earlier reports, the spin-forbidden N( 4 S)⫹O( 1 D) dissociation limit contributes 0共⫾2兲% at 0 eV. At 5.6 eV a new channel coupled to the production of ground-state atoms becomes more important, but no increase in the production of ground-state product atoms was observed. All observed branching fractions compare very favorably with predictions from a simple statistical model, which is based on the multiplicity of each dissociation limit in combination with spin conservation during the dissociation and the initial electron capture. We also report the distribution of fragment pairs from the DR reaction involving the metastable a 3 ⌺ ⫹ state. This state is found to dissociate to nearly all of the energetically allowed product pairs. The lifetime of the a 3 ⌺ ⫹ state is found to be 730共⫾50兲 ms, in agreement with earlier, sometimes indirect, observations. The experimental observations have been complemented with ab initio calculations on the different radiative decay processes both for the X 1 ⌺ ⫹ and the a 3 ⌺ ⫹ states. It is found that vibrational relaxation via infrared radiation is faster for NO⫹ (a 3 ⌺ ⫹ , v ⬎0) ions than the electronic decay of these metastable-state ions to the ground state. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1557917兴

共⬍0.81 eV兲. The kinetic energies of the fragments are increased by the electronic, vibrational, and rotational excitation energy of the parent ion. In the Earth’s atmosphere, the following properties of the DR process are important. First, the total DR rate coefficient involving ground-state ( v ⫽0) ions is of interest, as this determines the absolute importance of NO⫹ as a sink for electrons. Second, the branching fractions deserves attention, as the product atoms are fast and reactive species. Also of great importance, for example, is that O( 1 D) is a source of the red airglow near 633 nm 共Ref. 1兲 and is relevant in reactive collisions forming the OH radical. N( 2 D) is the most reactive of the three lowest states of nitrogen.2 For these reasons it is important to accurately determine the branching fractions. Furthermore, the N( 2 D) →N( 4 S) transition is responsible for airglow emission at 520 nm. Using satellite observations of neutral and ion concentrations, together with the local electron temperature and the 520-nm airglow emission profile in the ionosphere and ground-based measurements of the emission line, a quantum yield for N( 2 D) of 0.8 –1.0 was inferred.3 Both the DR thermal rate coefficients and branching fractions have been the subject of earlier research. Thermal rate coefficients of NO⫹ have been determined using flowing afterglow measurements.4,5 For example, Dulaney, Biondi, and Johnsen5 reported a value of 4.2⫻10⫺7 (T/300) ⫺0.75 cm3 /s, T being the electron temperature. The

I. INTRODUCTION

One of the major constituent ions in the D, E, and F regions of the Earth’s ionosphere is the nitric oxide ion, NO⫹ . Both NO⫹ and O2 ⫹ act as important sinks for lowenergy thermal electrons in these regions via the dissociative recombination reaction 共DR兲. For NO⫹ this reaction has a number of product channels: NO⫹ ⫹e ⫺ →N共 4 S 兲 ⫹O共 3 P 兲 ⫹2.7 eV

共 Na兲

N共 4 S 兲 ⫹O共 1 D 兲 ⫹0.80 eV

共 Nb兲

N共 2 D 兲 ⫹O共 3 P 兲 ⫹0.38 eV

共 Nc兲

N共 2 P 兲 ⫹O共 3 P 兲 ⫺0.81 eV

共 Nd兲

N共 S 兲 ⫹O共 S 兲 ⫺1.42 eV

共 Ne兲

4

1

N共 2 D 兲 ⫹O共 1 D 兲 ⫺1.59 eV

共 Nf兲

N共 2 P 兲 ⫹O共 1 D 兲 ⫺2.78 eV

共 Ng兲

N共 2 D 兲 ⫹O共 1 S 兲 ⫺3.81 eV

共 Nh兲

N共 2 P 兲 ⫹O共 1 S 兲 ⫺5.00 eV

共 Ni兲

N共 4 S 兲 ⫹O共 5 S 兲 ⫺6.38 eV

共 Nj兲 .

The minus sign on channels (Nd – Nj) indicates that these channels are energetically closed for low-energy electrons 0021-9606/2003/118(14)/6250/10/$20.00

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© 2003 American Institute of Physics

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Dissociative recombination of NO⫹

J. Chem. Phys., Vol. 118, No. 14, 8 April 2003

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TABLE I. Experimental results of the radiative lifetime of the a 3 ⌺ ⫹ state. Lifetime 共ms兲 730⫾50 760⫾30 720⫾70 465⫾69/90 330⫾30/60 680⫾91/87 100⫾20 135⫾25 530⫾300/100 1450⫾1150/450

Level ( v ⫽0) ( v ⫽0) ( v ⫽1) ( v ⫽2) ( v ⭓0) ( v ⭓1) ( v ⭓0)

Method

References

Dissociative recombination Collisional loss in an ion trap Optical experiment

Present work Wester et al.a Calamai and Yoshinob

FT-ICR FT-ICR

Marx et al.c Marx et al.d

FT-ICR FT-ICR, single cell

Kuo et al.e O’Keefe and McDonaldf

a

Reference 15. Reference 14. c Reference 10 共improved measurement of Ref. 11兲. d Reference 11. e Reference 12. f Reference 13. b

kinetic temperature of the ions in these experiments was 295 K. A similar thermal rate coefficient was deduced from a recent merged-beam experiment using the heavy-ion storage ring ASTRID by Vejby-Christensen et al.6 共VC from here on兲. VC determined DR rates as a function of electron collision energy. In these measurements a broad local maximum was found around 5 eV. At a collision energy of 5 eV, it is possible for the electron to be captured by the positive ion into the repulsive A 2 ⌺ ⫹ state. This target state is connected with N( 4 S)⫹O( 3 P) ground-state fragments and may produce nitrogen and oxygen atoms with kinetic energies of 4.1 and 3.6 eV, respectively, sufficiently high to allow escape from planetary bodies such as Mars.7 VC also determined branching fractions of the different energetically allowed channels for collision energies over the range 0–1.35 eV. In another experiment Kley, Lawrence, and Stone used flash photolysis of NO to determine the yield of N( 2 D) atoms from the DR of NO⫹ , and they report a yield of 0.76共6兲.8 Theoretical calculations have been performed by Schneider et al.9 to try to explain the resonant feature in the cross section at 5 eV collision energy. Their calculations suggest that the branching fraction generating ground-state atoms may be as large as 30% at these energies. The first electronically excited state in NO⫹ is the a 3 ⌺ ⫹ state, which is metastable by virtue of the spin-selection rule, ⌬S⫽0. Having a lifetime of the order of 1 s, the properties

of this state of the NO⫹ ion is of atmospheric importance. For example, this state has an excitation energy of 52 190 cm⫺1 共⬎6 eV兲 and is therefore of special interest in the search for processes causing a loss of atoms in the ionosphere due to escape from the planetary gravitational field. DR is one of very few reactions occurring at these heights with sufficient exothermicity. The different properties of the metastable NO⫹ state have been subject to both experimental and theoretical research. The lifetime has been reported in the literature before and these data are listed in Tables I and II. The first experimental results concerning the lifetime of the a 3 ⌺ ⫹ electronic state used Fourier-transform ion cyclotron resonance 共FT-ICR兲 spectrometer techniques10–13 in which the reaction rate of NO⫹ ions with different monitor gases was studied as a function of storage time in single or triple ICR cells. The different techniques showed large differences in the determined lifetimes. Calamai and Yoshino14 used a different technique to measure the radiative decay of the a 3 ⌺ ⫹ state. They monitored uv photons emitted in a rf ion trap, which was a direct measurement of the decay. Furthermore, they were able to distinguish between different vibrational levels. Wester et al.15 used a different type of ion trap in which the ions were stored at energies of a few keV. The time-dependent rate of the stored ions undergoing charge-exchange collisions with residual gas was monitored.

TABLE II. Theoretical results of the radiative lifetime of the a 3 ⌺ ⫹ state. Lifetime 共ms兲

Level

Perturber

183→190 270→250 455→495 758 780 989

( v ⫽0→4) ( v ⫽0→5) ( v ⫽0→4) ( v ⫽0)

Predominantly A 1 ⌸ B 1 ⌸ more than A 1 ⌸ A 1 ⌸ dominates Rotationally averaged Extended calculation of Ref. 13 A 1⌸

References Bearpark et al.a Palmieri et al.b Manaa and Yarkonyc Kuo et al.d O’Keefe and McDonalde

a

Reference 17. Reference 16. Reference 18. d Reference 12. e Reference 13. b c


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The results of Wester et al. agree well with those of Calamai and Yoshino and the most recent FT-ICR measurements.10 Calculation of the metastable-state lifetime has turned out to be difficult. For example, the calculations do not agree on which singlet excited state provides the necessary dipole moment for the metastable state to decay to the singlet electronic ground state.12,13,16 –18 It is of interest to note that in all these theoretical calculations, the vibrational radiative relaxation within the a 3 ⌺ ⫹ state has not been discussed in connection to the lifetime of metastable vibrationally excited levels. The present paper contains such calculations, indicating that the intrastate decay is significant. To the best of our knowledge the metastable state has never been an explicit subject of experimental DR studies. In short, in the present paper, experiments to determine the DR behavior of the metastable state and to use this DR reaction as direct probe for the lifetime of this state are reported. For ground-state ions, improved branching fractions are reported as well as branching fractions at nonzero electron collision energies. II. EXPERIMENT

The experiment was performed using the ion storage ring CRYRING located at the Manne Siegbahn Laboratory in Stockholm, Sweden. The experimental setup has been described in detail before19 and therefore only a brief explanation will be presented here. An internal discharge filament ion source 共MINIS兲 was used to create the NO⫹ ion using NO gas. Electrons are emitted from the filament and ionize NO molecules. For protection of the filament, a mixture of NO and Ar was used. The gas is heated locally due to the temperature of the filament, which in combination with the electron-impact ionization mode, means that the ions are most likely electronically and vibrationally excited when they are extracted from the ion source. After extraction from the ion source, the ions are mass selected and accelerated to 40 keV before injection into the storage ring. CRYRING has a circumference of 51.6 m. A beam cycle starts when ions are injected into the ring. During the first second of the cycle, the ions are further accelerated to the maximum energy of 3.15 MeV. In one of the twelve sections of CRYRING, the electron cooler, the ions are merged with a continuously renewed monoenergetic electron beam. The electron beam in the cooler region has an interaction length of 85 cm and a diameter of approximately 4 cm. The electrons have a well-defined velocity distribution and the velocity spread is described by a longitudinal temperature kT e 储 ⫽0.1 meV and a transversal temperature kT e⬜ ⫽1.5– 3 meV. The velocity of the electron beam ( v e ) can be matched to the velocity of the ion beam ( v i ). An advantage of storing the ions for several seconds is the possibility of vibrational relaxation via radiation to the lowest vibrational level. In these experiments, the electron energy can be changed from this velocity-matched condition, giving a different center-of-mass energy. The velocity of the electron beam can then be expressed as v e ⫽ v i ⫹ v d , where v d is the electron detuning velocity. If an ion recombines with an elec-

Hellberg et al.

FIG. 1. The imaging detector system used to determine distance separation between DR products. The detected interfragment distances are proportional to the kinetic energy release in the process.

tron and dissociates into two neutral fragments, the neutrals are not deflected by the bending magnets and leave the storage ring tangentially. A position-sensitive imaging detector1,20 is situated 6.3 m from the center of the electron cooler 共see Fig. 1兲. The two neutral fragments hit a stack of three Hamamatsu microchannelplates 共MCPs兲, with a phosphor screen 共Hamamatsu兲. Light emitted from the phosphor screen is detected by a photomultiplier tube 共PMT兲, which triggers a Proxitronic image intensifier 共II兲 and a charge-coupled device 共CCD兲 camera. The phosphor screen is imaged onto the II, and the output phosphor of the II is focused onto the CCD chip of the Dalsa camera (64⫻64). A spot-finding routine in software gives information about the positions of the detected flashes, and their separation in the CCD frame is determined. In some previous experiments a position- and time-sensitive detector has been used.1 However, in this experiment, a high count rate was considered to be more important than timing information, and so data sets of dissociation events without timing information were recorded. The projected distance distribution is a measure of the kinetic energy release in the DR process. The available energy in the process and the internal energy of ground-state atoms determine the kinetic energy release, which is directly related to the maximum interfragment distance measured on the CCD camera. Production of internally excited atoms gives a lower kinetic energy release compared to that for ground-state atoms. The measured distances are presented in histogram form and have been fitted with analytical distance distributions using the ion beam energy, the kinetic energy release, and the distance between the interaction region and the detector as parameters.6 DR is assumed to occur randomly throughout the electron cooler, and, in most cases, the dissociation process is found to be isotropic. Furthermore, the rotational temperature of the ions and the demagnification factor between the phosphor screen and the CCD chip were determined for all simulations. The least-squares fit, taking into account the statistical error bars, determines the branching fractions to the available channels. Apart from the 85 cm in the electron cooler, where the velocity vector of the electrons and the ions are parallel, the




electron beam is deflected into and out of the ion beam. Each of these two toroidal sections consists of two parts, each being approximately 12.5 cm long. The first part, closest to the straight section, has a maximum deflection between the ion beam and electron beam of 75 mrad. The ion beam is more rapidly deflected out of the electron beam in the second part and the maximum deflection is 280 mrad. As the angle between the ion beam and the electron beam increases, the relative collision energy increases. This so-called toroidal effect has been taken into account in DR cross-section measurements,21 but it has not been applied to distance distributions. For the numerical implementation of this correction, the toroidal sections were divided into small segments. For each segment the relative collision energy was determined. For each collision energy, a number of product channels are energetically allowed. As much as possible, experimentally determined branching values were used. At elevated energies an equal branching between the open channels was assumed. Various branching ratios were used to check the sensitivity of that assumption. The DR signal generated in each segment of the toroidal parts of the electron cooler depends on the DR cross section of NO⫹ . The relative values measured by VC were used. The estimated contribution of the toroidal part was subtracted from the signal before the distance distributions were fitted with analytical distributions, assuming monoenergetic electron collisions. III. THEORETICAL CALCULATIONS

Calculations were performed in order to estimate the rotational radiative lifetime of the lowest vibrational level ( v ⫽0) of the 1 ⌺ ⫹ ground electronic state and the vibrational radiative lifetime of the metastable 3 ⌺ ⫹ state. The radiative lifetime ␶ of a rovibrational state with vibrational and rotational quantum number v ⬘ and J ⬘ , respectively, can be expressed as

␶ ␯⬘J⬘⫽

1 , A ␯⬘J⬘

共1兲

where A v ⬘ J ⬘ is the sum of all Einstein coefficients which correspond to all possible radiative transitions v ⬘ J ⬘ to v ⬙ J ⬙ . The Einstein coefficient A (s ⫺1 ) can be expressed as22

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FIG. 2. Potential curves of NO⫹ taken from Ref. 9. The a 3 ⌺ ⫹ potential curve has been calculated in the present work. Energies are in atomic units. The bold lines are the ionic curves and only the lowest diabatic energies are indicated.

calculations were performed at the complete active-space self-consistent field 共CASSCF兲 level, including 8 electrons and 8 molecular orbitals as an active space. The basis set used was 6-311G* . The potential energy and the dipole moment were calculated for 21 internuclear distances in the interval 0.9– 4.0 Å. The calculated potential curve is presented in Fig. 2 and the dipole moment in Fig. 3. IV. RESULTS

Figure 2 shows a potential energy diagram of the ionic and some of the neutral states that play a role in the DR process involving the X 1 ⌺ ⫹ and first a 3 ⌺ ⫹ states of NO⫹ . The ionic ground-state curve was taken from Schneider et al.9 That paper also contained the neutral doubly excited curves shown in Fig. 2. All these doubly excited states have been invoked in the theoretical treatments of the DR of NO⫹ . The metastable potential energy curve has been calculated as described earlier. The curves in Fig. 2 explain the choices made in the present experiment: 共1兲 For the X 1 ⌺ ⫹ state at 0 eV, three channels are available of which the N( 4 S)⫹O( 1 D) first excited channel is spin-forbidden. As this dissociation limit only correlates with quartet molecular states, a spin flip is

A⫽3.136 186 1⫻10⫺7 关 S 共 J ⬘ ,J ⬙ 兲 / 共 2J ⬘ ⫹1 兲兴 ␯ 3 ⫻円具 ␺ ␯ ⬘ ,J ⬘ 兩 M 共 R 兲兩 ␺ ␯ ⬙ ,J ⬙ 典円2 ,

共2兲

where M (R) is the dipole moment function 共in debye兲, ␯ is the emission energy 共in cm⫺1兲, S(J ⬘ ,J ⬙ ) is the Ho¨nl–London rotational intensity factor, and ␺ v ⬘ ,J ⬘ and ␺ v ⬙ ,J ⬙ are the initial- and final-state wave functions. The FORTRAN program 22 LEVEL 7.4 by Le Roy was used to calculate the transition probabilities. LEVEL 7.4 solves the one-dimensional Schro¨dinger equation numerically and determines the initial- and final-state wave functions. The potential curve and dipole moment function of the 1 ⌺ ⫹ ground state were taken from Fehe´r and Martin.23 Not only rovibrational transitions but also pure rotational transitions have been calculated. Ab initio calculations were performed, using the GAUSSIAN 98 program,24 in order to calculate the potential curve and dipole moment function of the metastable a 3 ⌺ ⫹ state. The

FIG. 3. Dipole moment of the a 3 ⌺ ⫹ state of NO⫹ determined by ab initio calculations.


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Hellberg et al.


TABLE III. Calculated rotational lifetime of NO⫹ (X 1 ⌺ ⫹ ) ions.

␶ 共s兲

FIG. 4. Histogram of distances between N and O fragments measured by the present imaging detector. The break up of NO was due to DR at the 0 eV collision energy. 䊏 are experimental data points. The bold curve is a fit from an optimized simulation spectrum using the branching fractions as parameter and the thinner curve is the magnitude and shape of the toroidal correction 共see text兲. The peaks are labeled with the dissociation limits.

required during the electron capture or the dissociation process. Nevertheless, VC observed this channel.6 For the upper atmosphere, channels producing O( 1 D) atoms are very important, and therefore it is of interest to try to find details on this channel. 共2兲 The overlap with the A ⬘ 2 ⌺ ⫹ state becomes significant at 5 eV electron energy. 共3兲 The metastable state can decay to many different dissociation limits. Ground-state fragments would have kinetic energies of 4.9 eV for the nitrogen and 4.3 eV for the oxygen fragment. 共4兲 The availability of a direct probe for the metastable state would provide a direct method to assess the lifetime of this state. A. Branching behavior of the X 1 ⌺ ¿ state

Figure 4 shows a particle distance spectrum taken at 0 eV collision energy. The ion beam was produced in the MINIS source. Data were collected after a storage time of NO⫹ in the ring of 4 s. This storage time removes possible signal from ions in electronically or vibrationally excited states 关the vibrational radiative lifetime of the X 1 ⌺ ⫹ ground state is less than 100 ms 共Ref. 25兲兴. Dissociation events with small particle distances are not detected in our spot-finding routine, which explains the cutoff below 3 mm 共⬃3 pixels兲. One peak dominates the spectrum and a much smaller peak is observed at larger particle separation. The dominant peak reflects dissociation to the N( 2 D)⫹O( 3 P) product pair. The small peak is due to N( 4 S)⫹O( 3 P) ground-state atoms. The position of the spin-forbidden N( 4 S)⫹O( 1 D) channel is very close to the dominant peak. In our analysis of the spectrum, we noticed two aspects. First, the peak shape was fitted with a rotational temperature of 1300 K 共as done by VC兲, whereas the temperature of the MINIS ion source is estimated to be of the order of 900 K. The rotational state lifetimes are very long 共see Table III兲. For example, the X 1 ⌺ ⫹ ( v ⫽0, J⫽40) level, which has an energy of about 0.4 eV, has a radiative decay time of 23 s. Hence, storage of the NO⫹ ions does not change the population of these highly excited levels. Second, it was realized that the high-energy side of the dominant peak was affected by the toroidal effect.

J⫽10

J⫽20

J⫽30

J⫽40

J⫽50

J⫽60

J⫽70

1559

189

55

23

11

6

4

A corrected spectrum as well as the magnitude of the correction is shown in Fig. 4. The final branching was found to be 5共2兲%:0共2兲%:95共3兲% over the first three allowed dissociation limits, i.e., 关 N( 4 S),O( 3 P) 兴 : 关 N( 4 S),O( 1 D) 兴 : 关 N( 2 D), 3 O( P) 兴 . Without including the toriodal correction, the spinforbidden channel was found to be of the order of 1.5共2兲%. The effect of the toroidal regions is complicated. The particle separation on the detector depends on the place of dissociation in the electron cooler. Being on either side of the parallel section, the toroidal sections give extra counts at small and at large particle separation. The enhanced collision energy due to the nonzero angle between the electron and the ion-beam velocity vectors, means a shift to higher apparent kinetic energy release values and, hence, larger particle separations. VC reported a significantly higher contribution of the spinforbidden channel. In their analysis also a signal from a metastable state was inferred. The difference with our results is due to an ill-understood effect operating in the ion sources, producing NO⫹ . In the MINIS ion source and in another ion source, a hollow-cathode ion source, distance spectra were observed that depended on the ion-source conditions and that resembled strongly the structure reported by VC. Although the product mechanism is unknown, we conclude that a small fraction of the NO⫹ ions is formed with large internal rotational energy. We stress that this is a problem probably intrinsic to NO and that this effect has not been observed in other diatomic species studied before at CRYRING. As this aspect does not effect the results presented in this paper, this detail is left for future research. At 1.25 eV collision energy, the N( 2 P)⫹O( 3 P) channel opens and is observed. A spectrum obtained from the data taken at this energy is shown in Fig. 5 together with a fit to the distance distribution. The dominant N( 2 D)⫹O( 3 P) channel was best fitted using a nonisotropic sin2 ␪ distribution,6 which suggests a preference for the ions to dissociate perpendicularly to the relative collision vector. This preference has implications for the possible symmetries of the target states, as has been described by Dunn26 and also O’Malley and Taylor27 共see later兲. The toroidal correction shows two peaks, associated with dissociations in the region before the electron cooler 共large separations兲 and after the cooler 共smaller interparticle separations兲. Also, in this case, the toroidal correction reduces the branching to the spinforbidden N( 4 S)⫹O( 1 D) channel and, after this correction, it decreases from 18共10兲% to 10共10兲%. The cross section decreases steeply as function of electron energy and the experiments become more difficult to perform because the signal-to-background ratio decreases. As a consequence, the branching fractions are less accurate at elevated energies. All branching fractions are collected together and presented in Fig. 7. At 5.6 eV collision energy, we hoped to observe a clear




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FIG. 5. Histogram of interparticle distances due to the DR of NO⫹ at the 1.25 eV collision energy. 䊏 are the experimental data points, and the bold curve is the optimized simulation spectrum using the branching fractions as parameter. The thinner curve is the magnitude and shape of the toroidal correction 共see text兲.

nonzero branching fraction to ground-state atoms. The presence of this channel was suggested by Schneider et al.9 Figure 6 shows the interparticle distance spectrum of this energy. The arrow indicates the maximum separation of the ground-state atoms. We conclude that either the A ⬘ 2 ⌺ ⫹ state is not dominant as a capture state or the A ⬘ 2 ⌺ ⫹ state does not correlate uniquely with ground-state atoms as was suggested by the potential curve given in Fig. 2. Nine different dissociation channels are open at 5 eV and the wide range of detected interparticle distances 共Fig. 6兲 indicates that several of these channels are populated. The distributions of the different channels are assumed to be isotropic except for the N( 2 P)⫹O( 1 S), for which a cos2 ␪ distribution was used to yield a more accurate fit to the experimental data points at low kinetic energy release. This cos2 ␪ distribution indicates a larger probability for the ions to dissociate parallel to the

FIG. 6. Histogram of DR fragments taken at the 5.6 eV collision energy. The arrow indicates the maximum distance where ground-state fragments are to be detected. 䊏 are the experimental data points and the curve is the result of a simulation including all but the spin-forbidden channels.

FIG. 7. Experimental and model branching fractions for the ground X 1 ⌺ ⫹ state at the 共i兲 0 eV, 共ii兲 1.25 eV, 共iii兲 5.6 eV collision energy, and 共iv兲 the metastable a 3 ⌺ ⫹ state at the 0 eV collision energy. In each case, three data sets are plotted. 共I兲 shows the branching ratio determined from the multiplicity of available states. 共II兲 is 共I兲 but also accounts for spin selection rules. 共III兲 is the experimental data. These results are compared to statistical models. The histogram bars correspond to the branching fractions of 共a兲 N( 4 S) ⫹O( 3 P), 共b兲 N( 4 S)⫹O( 1 D), 共c兲 N( 2 D)⫹O( 3 P), 共d兲 N( 2 P)⫹O( 3 P), 共e兲 N( 4 S)⫹O( 1 S), 共f兲 N( 2 D)⫹O( 1 D), 共g兲 N( 2 P)⫹O( 1 D), 共h兲 N( 2 D) ⫹O( 1 S), 共i兲 N( 2 P)⫹O( 1 S), 共j兲 N( 4 S)⫹O( 5 S). The asterisk means that the N( 4 S)⫹O( 5 S) channel could not be detected due to the small particle separation.

relative velocity vector. A rotational temperature of 1300 K was used for all channels. A least-squares fit weighted to the statistical error bars of the experimental data points, though not including the spin-forbidden channels N( 4 S)⫹O( 1 D) and N( 4 S)⫹O( 1 S), gives rise to the branching fractions presented in Fig. 7. It is of interest to note that inclusion of the spin-forbidden channel N( 4 S)⫹O( 1 S) reduces the quality of the fit and that the N( 4 S)⫹O( 1 D) channel only contributes with a few percent if included. We varied a number of parameters 共for example, rotational temperature and collision energy兲 within the accuracy to get a better estimate of the error. The anisotropy has been kept fixed for all channels.


6256


FIG. 8. Distance spectra taken at different time intervals after ion injection into CRYRING in order to detect DR events from the metastable a 3 ⌺ ⫹ state.

It has been noted earlier that the branching behavior in DR compares favorably with the results of a statistical model, in which the number of molecular states connected to a certain dissociation limit determines the probability to reach this limit.28,29 For example, if the spin multiplicity and the orbital angular momentum degeneracy of both atoms are multiplied, N( 4 S)⫹O( 3 P) yields a multiplicity of (4⫻1 ⫻3⫻3⫽) 36, N( 4 S)⫹O( 1 D) yields 20, and N( 2 D) ⫹O( 3 P) yields 90. If a NO⫹ (X 1 ⌺ ⫹ ) ion captures an electron, it forms a repulsive state with spin S⫽ 21 , and so a multiplicity of 2. Hence, if only dissociation products of spin-allowed transitions are considered, the N( 4 S)⫹O( 1 D) channel will not contribute at all and branching fractions of 17%, 0%, and 83% are obtained. These numbers compare well with the observations at 0 eV, 5共2兲%:0共2兲%:95共3兲%. The results of the statistical behavior for NO⫹ at 0 eV collision energy has been reported before.28 The expectations from the statistical model are presented in Fig. 7. In each of the panels 共i兲–共iii兲 in Fig. 7 the experimental results 共III兲 are plotted together with the expectations from the spin unconstrained 共I兲 and spin-constrained models 共II兲. In all cases, the dominant dissociation limit is correctly predicted by the spin-constrained model. B. Branching behavior and dynamics in the a 3 ⌺ ¿ state

Figure 8 shows a series of spectra in which data have only been taken during different time windows after injection. The aim of this experiment was to observe DR products from metastable states in NO⫹ . The intensity in each spectrum was normalized using the intensity of the dominant N( 2 D)⫹O( 3 P) peak formed from ground-state ions. From this analysis a time-dependent signal is observed at large particle separations, i.e., those for which the DR products have large kinetic energy release values. The arrow indicates the separation of ground-state fragments if starting from the a 3 ⌺ ⫹ state. The associated kinetic energy in the spectrum is as high as 9 eV. As in nearly all molecular systems, this state can also dissociate to many different limits. Figure 9 shows

Hellberg et al.

FIG. 9. The distance distributions of DR events from the metastable a 3 ⌺ ⫹ state used to determine branching fractions of the nine lowest open channels. The solid line is the result of a simulation used to determine the branching fractions. The dotted line is the result of a simulation using branching ratios obtained by the spin statistical model.

the result of the least-square fit together with the predicted distance distribution using the statistical model discussed earlier. As the collision energy is 0 eV, all channels are described using an isotropic distribution. The last panel 共iv兲 in Fig. 7 shows the similarities between the parameter-free statistical model and the results from the least-square fit. Since the energy difference between the X 1 ⌺ ⫹ and the a 3 ⌺ ⫹ states is 6.3 eV, the statistical prediction using the spin unconstrained model 共I兲 of the a 3 ⌺ ⫹ state at 0 eV collision energy is similar to the prediction for the 5.6 eV collision energy of the X 1 ⌺ ⫹ ground state. The a 3 ⌺ ⫹ state is a triplet and so can form doublet and quartet states when recombining with an electron. Therefore, none of the open channels are spin forbidden. Implementation of the spin-selection rules affects the predicted branching of ground-state ions and improves agreement with the experiment considerably 关see Figs. 7共iii兲 and 7共iv兲兴. The highest excited channel N( 4 S) ⫹O( 5 S) has not been included in the simulation since it cannot be detected due to the small particle separation. Discrepancies between the statistical model and the fit is larger for the two highest observed excited channels. The discrepancies could be related to the difficulties in obtaining reliable branching to these two channels due to the poor signal-tonoise ratio. It is noted that the statistical model predicts a small contribution from these two channels. Overall, the experimental branching ratios and the predictions from statistical arguments agree well. Figure 8 shows the contribution from ground-state molecular ions and from the metastable a 3 ⌺ ⫹ state. By normalizing the metastable signal with respect to the ground-state counts within each time window, it is possible to extract the lifetime of the metastable state. Figure 10 shows the relative number of counts from the total number of counts 共at all observed distances兲 as well as for two selected distance regions 共high and low distance values兲. The decay time is found to be 730共50兲 ms, independent of the selected part of the distance spectrum. In the ion source, vibrational excited




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FIG. 10. The number of DR events from the metastable a 3 ⌺ ⫹ state taken at different time intervals after injection in the ring. The different data sets correspond to different distance intervals in the spectrum 共see Fig. 8兲.

levels will probably be populated in the metastable a 3 ⌺ ⫹ state. The decay of the a 3 ⌺ ⫹ state may be dependent on the vibrational level. From the absence of a dependence on interparticle separations, we could conclude that the branching over the possible dissociation limits does not strongly depend on the vibrational level. Alternatively, the vibrational excited levels may decay quickly to the vibrational ground state 共intrastate decay兲, followed by a decay of the a state ( v ⫽0) level to the NO⫹ ground state. In our experiment, it is clear that we have no vibrational resolution in the distance spectra. In order to estimate the intrastate decay rate, associated radiative lifetimes have been calculated. These results 共see Table IV兲 indicate that the intrastate decay will be faster than the spin-forbidden radiative decay to the electronic ground state. At present, a delay exists between the formation of the ions in the ion source and the data acquisition due to the acceleration time required, which is about 1.1 s. During this time, most of the vibrationally excited states have already decayed. The only experiment that has reported a vibrational state-dependent lifetime is the optical experiment by Calamai and Yoshino.14 These authors reported a lifetime that strongly depended on the vibrational level, 720 ms for v ⫽0, 465 ms for v ⫽1, and 330 ms for v ⫽2. Table IV shows the expected vibrational lifetimes combining the observed decay of the v ⫽0 state with the calculated vibrational decay using ␶ eff⫽␶intra␶ inter /( ␶ intra⫹ ␶ inter). The trend reported by of Calamai and Yoshino is reproduced in the calculations here. TABLE IV. Calculated vibrational decay lifetimes, ␶ intra( v ), within the NO⫹ a 3 ⌺ ⫹ state and also estimated and reported lifetimes adding the interstate lifetime of 730 ms, ␶ inter( v ).

a

a 3⌺ ⫹( v )

␶ intra( v ) 共ms兲

␶ eff(v) 共ms兲

␶ (v)a 共ms兲

1 2 3

522 272 190

304 198 151

465⫾69/90 330⫾30/60

Reference 14.

We have performed a series of experiments to determine the product formation in the DR of NO⫹ . The N( 2 D)-containing channel has a branching fraction close to unity near 0 eV collision energy. In aeronomical applications quantum yields are usually used to express branching fractions, i.e., the number of atoms formed in a specific state per dissociating molecule. At small collision energies, the branching fraction of the N( 2 D)⫹O( 3 P) channel equals the N( 2 D) quantum yield. The spin-forbidden channel at 0 eV, N( 4 S)⫹O( 1 D), is virtually closed, and the present value differs significantly from earlier reported values.6,8 At elevated collision energies, new dissociation channels open up and the present experiments reveal that these limits are also populated. Within our experimental accuracy we have no indication that spin-forbidden channels are populated. At 5.6 eV collision energy the production of ground-state fragments is only a few percent, and this is in contrast to recent predictions, in which Schneider et al. proposed that a significant fraction of 30% would populate the 2 ⌺ states.9 It has been shown in numerous cases that the dissociation behavior in the DR process is very complicated. Nearly all channels are populated, even in those cases for which only a limited number of capture states seems to be relevant. The complexity of the dissociation behavior seems to be described in an empirical way by the simple statistical model applied to the observed branching. Figure 7 shows the remarkable agreement with the branching obtained from fittings to experimental data and branching predicted empirically. At the moment, it is not clear why these prediction are accurate. The theoretical approach to the DR process requires accurate calculations of states that have to cross the vibrational wave function of the ionic state. Such a calculation excludes many neutral doubly excited states. To determine the capture efficiency demands a second independent calculation, which again selects specific states on the requirement of a sufficiently large capture matrix element.30 The complexity of DR branching calculations is large. To date, no complete calculation exists for the branching behavior for molecules heavier than H2 and HeH.31–33 In DR studies of molecular oxygen, spin–orbit coupling has been invoked to explain the product O( 1 S) atoms at near 0 eV collisions. The spin flip associated with this coupling was mediated by the formation of a triplet Rydberg state and increased the O( 1 S) yield from near 0% to 5%.1,34 So, although, spin changes and the involvement of spin–orbit coupling cannot be completely ruled out, the impact on product branching is expected to be small. DR is not always an isotropic process and, at collision energies larger than 0 eV, a well-established relative collision vector is established in the experiment. As a consequence, for example, capture processes that favor a molecular axis orientation parallel to the relative velocity vector will dissociate preferentially perpendicular to the detector and are described by a cos2 ␪ distribution. Figure 6 shows such an example at small interparticle separations. Figure 5 shows an example of a sin2 ␪ distribution. Dunn26 and O’Malley and Taylor27 have addressed this problem in electron-capture processes, using conservation of symmetry before and after the


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reaction. O’Malley and Taylor 关Eq. 共14兲 in Ref. 27兴 provide an attractive approximate prediction. The sin2 ␪ distribution for the dominant N( 2 D)⫹O( 3 P) channel at the 1.25 eV collision energy is in agreement with the formation of a 2 ⌸ state by a p ␲ partial electron wave. The cos2 ␪ distribution found for the N( 2 P)⫹O( 1 S) channel suggests a product state of 2 ⫹ ⌺ symmetry in a collision reaction in which the p ␴ partial wave has a larger cross section than the s ␴ partial wave. If a large kinetic energy resolution could be achieved in combination with accurate anisotropy determination, much more insight could be gained about the dynamics of the DR process. At present, for reasons of data acquisition, the length of the electron target 共85 cm兲 is an important resolution-limiting factor. DR from the metastable a 3 ⌺ ⫹ state has been studied and the radiative lifetime of this state measured. It cannot be ruled out that the ion source will produce other electronically excited ions in several more states other than the a 3 ⌺ ⫹ state. The two states that are closest in energy to the a 3 ⌺ ⫹ state are the b 3 ⌸ and the w 3 ⌬ states.35 However, results from experiments studying uv photon emission from electronically excited states of NO⫹ 共Ref. 14兲 indicate that the b 3 ⌸ and w 3 ⌬ states of NO⫹ have much shorter lifetimes and would not influence the population of the a 3 ⌺ ⫹ state in our experiment. Tables I and II summarize the experimental and theoretical results for several properties of the a 3 ⌺ ⫹ state. The experimental10–15 as well as theoretical12,13,16 –18 work concentrated on the direct decay channels to the electronic ground state. It seems that the decay of vibrationally excited levels through ir radiation within the metastable state has never been treated, in spite of the importance of this decay channel with respect to the lifetime on a vibrational-stateresolved level. Our calculations reveal that the intrastate decay of vibrationally excited levels is faster than the decay to the ground state. Thus, the 1.1-s delay between ion generation and the start of our experiment is sufficient for an almost complete loss of vibrationally excited states. In the future, experimental improvements will allow for a reduction of this delay to 200 ms.36 The data in Tables I and II also illustrate the variation in both theoretical calculations and in experimental lifetime determinations. Recent experimental determinations14,15 agree on a v ⫽0 lifetime of about 730 ms. The most recent theoretical calculations predict lifetimes that are much shorter than the observed values. It is of interest to note that the different calculations do not agree on those states that cause the finite radiative decay on the triplet state. The dissociation behavior has been determined for the metastable state. For these data also the statistical model seems to describe the observed distance distribution well. Fragments are formed with energies up to 5 eV for nitrogen and 4.3 eV for oxygen and with a total kinetic energy release as high as 9.3 eV. This observation may make metastable NO⫹ a source of hot atoms in the geocorona and in other relevant plasmas. VI. CONCLUSIONS

This paper presents experimental and theoretical results on the behavior of NO⫹ (X 1 ⌺ ⫹ ) ground-state ions and the

NO⫹ (a 3 ⌺ ⫹ ) metastable ions in reactions with electrons at different collision energies. Our results provide an improved upper limit on the absence of the spin-forbidden dissociation channel in the dissociative recombination reaction involving ground-state NO⫹ at 0 and 1.2 eV collision energies. The branching behavior has also been studied at 5.6 eV for the X 1 ⌺ ⫹ state and at 0 eV for the a 3 ⌺ ⫹ state. Those results show a complex branching to a large number of open channels. In all cases the DR dissociation dynamics can be compared favorably with the results of a model that involves only statistical arguments and spin-conservation rules during electron-capture and dissociation processes. The radiative lifetime has been determined for the a 3 ⌺ ⫹ metastable state. These results together with ab initio calculations indicate that vibrational excited levels in the a 3 ⌺ ⫹ metastable state first decays via intrastate radiative decay to v ⫽0, prior to radiative relaxation to the electronic ground state. ACKNOWLEDGMENTS

This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie 共Foundation for Fundamental Research on Matter兲 and was made possible from financial support from the Stichting voor Nederlands Wetenschappelijk Onderzoek 共Foundation of Netherlands Scientific Research兲. Support is acknowledged from EU research training network ETR No. HPRN-CT-2000-00142. The authors gratefully acknowledge the support from the staff of the Manne Siegbahn Laboratory. 1

R. Peverall, S. Roseń, J. Peterson, M. Larsson, A. Al-Khalili, L. Vikor, J. Semaniak, R. Bobbenkamp, A. Le Padellec, A. N. Maurellis, and W. van der Zande, J. Chem. Phys. 114, 6679 共2001兲. 2 M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, and G. G. Volpi, in Molecules in Astrophysics: Probes and Processes, edited by E. F. van Dishoeck 共Kluwer, Amsterdam, 1997兲, pp. 271–280. 3 M. R. Torr, R. G. Burnside, P. B. Hays, A. I. Stewart, D. G. Torr, and J. C. G. Walker, J. Geophys. Res. 81, 531 共1976兲. 4 T. Mostefaoui, S. Laube´, G. Gaultier, C. Rebrion-Rowe, B. R. Rowe, and J. B. A. Mitchell, J. Phys. B 32, 5247 共1999兲. 5 J. L. Dulaney, M. A. Biondi, and R. Johnsen, Phys. Rev. A 36, 1342 共1987兲. 6 L. Vejby-Christensen, D. Kella, H. B. Pedersen, and L. H. Andersen, Phys. Rev. A 57, 3627 共1998兲. 7 R. P. Wayne, Chemistry of Atmospheres, 3rd ed. 共Oxford University Press, Oxford, 2000兲. 8 D. Kley, G. M. Lawrence, and E. J. Stone, J. Chem. Phys. 66, 4157 共1977兲. 9 I. F. Schneider, I. Rabadan, L. Carata, L. H. Andersen, A. Suzor-Weiner, and J. Tennyson, J. Phys. B 33, 4849 共2000兲. 10 R. Marx, S. Fenistein, G. Mauclaire, J. Lemaire, and M. Heninger, Int. J. Mass Spectrom. Ion Processes 132, 143 共1994兲. 11 R. Marx, Y. M. Yang, G. Mauclaire, M. Heninger, and S. Fenistein, J. Chem. Phys. 95, 2259 共1991兲. 12 C. H. Kuo, T. Wyttenbach, C. G. Beggs, P. R. Kemper, and M. T. Bowers, J. Chem. Phys. 92, 4849 共1990兲. 13 A. O’Keefe and J. R. McDonald, Chem. Phys. 103, 425 共1986兲. 14 A. G. Calamai and K. Yoshino, J. Chem. Phys. 101, 9480 共1994兲. 15 R. Wester, K. G. Bhushan, N. Altstein, D. Zajfman, O. Heber, and M. L. Rappaport, J. Chem. Phys. 110, 11830 共1999兲. 16 P. Palmieri, R. Tarroni, G. Chambaud, and P. Rosmus, J. Chem. Phys. 99, 456 共1993兲. 17 M. J. Bearpark, N. C. Handy, P. Palmieri, and R. Tarroni, Mol. Phys. 80, 479 共1993兲. 18 M. R. Manaa and D. R. Yarkony, J. Chem. Phys. 95, 6562 共1991兲. 19 C. Stro¨mholm, J. Semaniak, S. Roseń, H. Danered, S. Datz, W. J. van der Zande, and M. Larsson, Phys. Rev. A 54, 3086 共1996兲.


J. Chem. Phys., Vol. 118, No. 14, 8 April 2003 Z. Amitay and D. Zajfman, Rev. Sci. Instrum. 68, 1387 共1997兲. Z. Amitay and D. Zajfan, Phys. Rev. A 54, 4032 共1996兲. 22 R. J. Le Roy, University of Waterloo, Chemical Physics Research Report No. CP-642 R3 共2001兲. 23 M. Fehe´r and P. A. Martin, Chem. Phys. Lett. 215, 565 共1993兲. 24 M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 98, Revision A.3, Gaussian, Inc., Pittsburgh, PA, 1998. 25 H. Partridge, S. R. Langhoff, and C. W. Bauschlicher, Jr., Chem. Phys. Lett. 170, 13 共1990兲. 26 G. H. Dunn, Phys. Rev. Lett. 8, 62 共1962兲. 27 T. F. O’Malley and H. S. Taylor, Phys. Rev. 176, 207 共1968兲. 28 W. J. van der Zande, in Dissociative Recombination: Theory, Experiment, 20 21


6259

Applications IV, Stockholm, 1999兲, edited by M. Larsson, B. Mitchell, and I. F. Schneider 共World Scientific, Singapore, 2000兲, p. 251. 29 W. J. van der Zande 共private communication兲. Note that there is a printing error in Fig. 2, Ref. 28. 30 S. L. Guberman and A. Guisti-Suzor, J. Chem. Phys. 95, 2602 共1991兲. 31 ˚ A. Larsson and A. E. Orel, Phys. Rev. A 64, 062701 共2001兲. 32 S. L. Guberman, Phys. Rev. A 49, R4277 共1994兲. 33 ˚ A. Larsson and A. E. Orel, Phys. Rev. A 59, 3601 共1999兲. 34 S. L. Guberman, Science 278, 1276 共1997兲. 35 D. L. Albritton and A. L. Schmeltekopf, J. Chem. Phys. 71, 3271 共1979兲. 36 CRYRING staff 共personal communication兲.
