THE ASTROPHYSICAL JOURNAL, 543 :764È774, 2000 November 102000. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

DISSOCIATIVE RECOMBINATION OF ANDH3O`, HD2O`, D3O`

M. J. JENSEN, R. C. BILODEAU,1 C. P. SAFVAN,2 K. SEIERSEN, AND L. H. ANDERSEN

Institute of Physics and Astronomy, University of Aarhus, DK-8000 C, DenmarkA� rhus

AND

H. B. PEDERSEN AND O. HEBER

Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100, IsraelReceived 2000 March 1 ; accepted 2000 May 30

ABSTRACTWe present an experimental study of the dissociative recombination (DR) of and its iso-H3O`

topomers and performed at the ASTRID storage ring. DR cross sections have been mea-D3O` HD2O`sured as a function of energy, while complete branching ratios have been measured at E\ 0. The H3O`data yield an accurate determination of the branching ratio for water formation (0.25 ^ 0.01). The threemolecular and a marked resemblance concerning cross sectionsionsÈH3O`, D3O`, HD2O`Èshowand branching ratios. The only observed isotope e†ect is in the fragmentation pattern of whereHD2O`,the release of a light fragment is favored over release of a heavier fragment. As a consequence, anenhanced production of deuterated molecules takes place as a result of the DR process.Subject headings : ISM: molecules È methods : laboratory È molecular data È molecular processes

1. INTRODUCTION

Dissociative recombination (DR) is the reaction in which a molecular ion recombines with an electron and dissociates intoneutral fragments. The process is of great importance for the chemistry of both planetary ionospheres (Bates & Massey 1947 ;Bardsley & Biondi 1970) and interstellar clouds3 (Smith 1992 ; Sternberg & Dalgarno 1995 ; Herbst & Lee 1997). In the lattercase, polyatomic molecular ions are created in a sequence of ion-molecule reactions, initiated by an atom or molecule beingionized by cosmic rays. Since interstellar clouds are rather cold, typically with temperatures less than 50 K, only little energy isavailable for collisions. The DR process, which normally has a high rate coefficient (D10~7 cm3 s~1) at these temperatures, istherefore a key process for the chemistry in these environments.

The hydronium ion is produced in the reaction chain (Dalgarno 1994) :

H2] cosmic ray ] H2`] e~] cosmic ray ,

H2` ] H2] H3`] H ,

H3`] O ] OH`] H2 ,

OH` ] H2] H2O`] H ,

H2O` ] H2] H3O`] H . (1)

Instead of continuing this chain by reacting with molecular hydrogen, undergoes dissociative recombination. FourH3O`di†erent DR channels are energetically allowed at zero collision energy :

H3O`] e~]

4

5

6

00H2O ] H, *E\ 6.4 eV (n

a),

OH] H2, *E\ 5.8 eV (nb),

OH] H ] H, *E\ 1.3 eV (nc),

O ] H2] H, *E\ 1.5 eV (nd),

(2)

where *E is the kinetic energy release for production of ground-state products (Hunter & Lias 1998 ; Herzberg 1989, 1991)and (i\ a, b, c, d) is the branching ratio for channel i.n

iThe branching ratios of the di†erent fragmentation channels in equation (2) are critical parameters for the chemistry ofinterstellar clouds. If DR of primarily leads to the formation of this will be the dominant oxygen-containingH3O` H2O,molecule, whereas if the main product of the DR process is OH, the dominant oxygen-containing species will be (Millar etO2al. 1988). Another important aspect is the fact that the a channel in the DR of is believed to be the only major source ofH3O`water production in interstellar clouds. Water plays a signiÐcant part in the evolution of interstellar clouds and possible starformation (Neufeld, Lepp, & Melnick 1995), and hence there is a demand for knowledge about the water abundance.However, since interstellar water cannot be observed from the Earth because of the water in the atmosphere, its abundance ininterstellar clouds is often determined from the abundance of which can be observed from the Earth. The cross sectionH3O`,for the a channel in equation (2) is required for such a determination.

We here present measurements of both the total cross section and branching ratios for the DR of DR of theH3O`.hydronium ion has been studied previously both in Ñowing afterglow experiments, where the branching ratios have been

1 Present address : Departments of Physics and Astronomy, and Engineering Physics, McMaster University, Hamilton, Ontario, Canada, L8S 4M1.2 Present address : Nuclear Science Center, P.O. Box 10502, Aruna Asaf Ali Marg, New Delhi 110067, India.3 Recently, water was observed in cold interstellar clouds by the SW AS space satellite. See http ://cfa-www.harvard.edu/cfa/oir/Research/swas.html.

764

DISSOCIATIVE RECOMBINATION OF H3O`, HD2O`, AND D3O` 765

obtained (Herd, Adams, & Smith 1990 ; Adams et al. 1991 ; Williams et al. 1996), and in merged beams experiments, yieldingboth cross sections and branching ratios (Mul et al. 19834 ; Andersen et al. 1996 ; Vejby-Christensen et al. 1997).

In the present work, the and isotopomers were also studied. The fragmentation channels for areD3O` HD2O` D3O`equivalent to those of whereas for twice as many channels exist :H3O`, HD2O`

HD2O`] e~ ]

4

5

6

00

D2O ] H, *E\ 6.4 eV (na1),

HDO] D, *E\ 6.4 eV (na2),

OD] HD, *E\ 5.7 eV (nb1),

OH] D2, *E\ 5.7 eV (nb2),

OD] D ] H, *E\ 1.3 eV (nc1),

OH] D ] D, *E\ 1.3 eV (nc2),

O ] D2] H, *E\ 1.4 eV (nd1),

O ] HD] D, *E\ 1.4 eV (nd2).

(3)

Each channel i (i\ a, b, c, d) in or corresponds to two electronically equivalent but isotopically distinctH3O` D3O`channels i1 and i2 in HD2O`.

and are not expected to be of signiÐcance for the chemistry of interstellar clouds. However, in general theHD2O` D3O`abundance of deuterated molecules in interstellar clouds is not negligible. On the contrary, the ratio between the abundancesof singly deuterated and nondeuterated molecules is observed to be on the order of 0.01È0.1 for several molecular species(Turner & Zuckerman 1978). This ratio is orders of magnitude higher than the total cosmic deuterium-hydrogen abundanceratio (Dalgarno & Lepp 1984). Hence, the chemistry of interstellar clouds must favor the formation of deuterated molecularspecies. Ion-molecule reactions are in general known to favor production of deuterated molecules (Tielens 1997), but onlyrelatively little e†ort has been put into studying dissociative recombination of deuterated polyatomic molecules. Full studiesincluding measurements of both cross sections and branching ratios have been performed for and (Datz et al.H3` H2D`1995a, 1995b, 1995c, 1995d) and for and HDO` (Jensen et al. 1999). In both cases, DR is observed to favor theH2O`formation of deuterated molecules, although the e†ect in was less pronounced than in HDO`. In our previous work onH2D`

we argued that an isotope e†ect could be induced by simple kinematics, which would favor H release over DH2O`/HDO`,release and thereby lead to an enhanced production of deuterated molecules. With the present work, we collect moreinformation on the inÑuence of isotope substitution on dissociative recombination, and possibly the abundance of deuteratedmolecules in interstellar clouds.

2. EXPERIMENT

The present experiment was carried out at the heavy-ion storage ring ASTRID in Denmark. The setup is shown inA� rhus,Figure 1. Beams of and were produced in a radio frequency ion source. was produced from aH3O`, D3O`, HD2O` H3O`mixture of vapor and gas, and was produced from vapor, whereas was produced from a 1:1H2O H2 D3O` D2O HD2O`mixture of and vapor. The ions were preaccelerated to 150 keV, injected into ASTRID, and, by means of aH2O D2Oradio-frequency system, further accelerated to 5È6 MeV. Since all vibrational modes of and its isotopomers areH3O`infrared active, the ions had time to relax to the vibrational ground state during the acceleration period, which had a durationof a couple of seconds. After reaching the Ðnal energy, the ion beams were merged with an electron beam provided by anelectron cooler. The electron beam was essentially monoenergetic with transverse and longitudinal temperatures of kT

MB 25

meV and meV. A more detailed description of the electron cooler is given elsewhere (Andersen, Bolko, & Kvist-kTA

B 0.5gaard 1990 ; Vejby-Christensen et al. 1996).

Neutral fragments produced by dissociative recombination and excitation in the electron beam, or by collisions with theresidual gas, were detected by an energy-sensitive solid state detector (SSD) located about 6 m downstream, behind the dipolemagnet following the electron cooler (see Fig. 1). For the measurement, we used a circular detector with a diameter ofH3O`40 mm, whereas for the and measurements, a rectangular 40 ] 60 mm detector was used. An energy spectrumD3O` HD2O`recorded for is shown in Figure 2. After dissociation, each fragment carries a fraction of the beam energy, which isH3O`proportional to the mass of the fragment. Since neutral fragments produced in one event hit the detector simultaneously, aDR event will always deposit the full beam energy in the detector, whereas a dissociative excitation event (and neutralsE0created from dissociative collisions with the residual gas) only deposit a fraction of corresponding to the fraction of theE0total mass carried by the fragments. DR events, in which one or more fragments miss the detector, will also deposit only afraction of In order to subtract background, i.e., neutrals produced by collisions with the residual gas, the electron beamE0.was turned on and o† (chopped) at a frequency of 20 Hz.

In the present experiment, DR events in which one or more fragments missed the detector could not be avoided. Even witha perfectly positioned ion beam, the light fragments produced in channels a and b in the case of and and inH3O` D3O`channels and in the case of would have a Ðnite probability for missing the detector, because of thea1, 2 b1, 2 HD2O`transverse momentum of the fragments and the Ðnite size of the detector. The ion beams were positioned by maximizing theDR signal while minimizing the fraction of light DR fragments being lost. This ensured optimum overlap and alignment of theion and electron beams.

For each molecular ion, two di†erent experiments were conducted. DR cross sections were measured for relative energiesranging from 0 to 20È35 eV, and DR branching ratios were measured at zero relative energy. In the following, these two typesof measurement are described in more detail.

4 The cross sections in this paper are to be divided by a factor of 2.

FIG. 1.ÈSchematic diagram of the ASTRID storage ring. The inset shows a close-up on the detector region.

FIG. 2.ÈEnergy spectrum for with electrons (top graph) and without electrons (bottom graph), measured at E\ 0 without a grid in front of theH3O`detector.

DISSOCIATIVE RECOMBINATION OF H3O`, HD2O`, AND D3O` 767

2.1. DR Cross SectionsDR cross sections were measured as a function of relative energy by varying the electron energy. While scanning the

electron energy, a group of peaks in the energy spectrum, including the full energy peak, were integrated using a single channelanalyzer and a scaler for each peak. Each point in an energy scan was measured using the electron cooler in the choppedmode, and the data recorded with and without electrons were collected separately, enabling the subtraction of the contribu-tion from the residual gas.

Absolute rate coefficients were measured for and In terms of measurable quantities, the absolute rateH3O` D3O`.coefficient is given by

StpT \Ns[ N

bNion

ti

ne*L v

, (4)

where v is the relative velocity and p is the cross section. and are the rates of neutrals in the full energy peak measuredNs

Nbwith and without electrons, respectively, and is the rate of ions passing through the electron cooler, which was measuredNionby a current transformer ; is the ion velocity, the electron density, *L (\0.95 m) the length of the electron cooler, and vv

ine(\1) the detection efficiency. Relative DR rate coefficients as a function of energy were obtained by normalizing the

electron-induced signal in the full energy peak to the electron density and the rate of neutrals in a given peakNs[ N

bneproduced from collisions with the residual gas, i.e., measured when the electron beam was o†. Measurements of relative rate

coefficients as a function of energy were put on an absolute scale using equation (4) at a single energy.As described by the following equation, a measured rate coefficient is given by the velocity-weighted cross section averaged

over the electron velocity distribution in the rest frame of the ions :f (¿)

StpT \P

tp(t) f (¿)d¿ . (5)

The cross sections presented in this paper have been calculated as SpT \ SvpT/*, where is the detuning velocity*\ Â ti[ t

eÂ

between electrons and ions. SigniÐcant deviations from the true cross sections will occur only at energies E[ kTM.

When obtaining cross sections and rate coefficients, the geometry of the electron cooler must be considered. The ratecoefficients consist of contributions not only from the central region of the cooler where the electron and ion beams areparallel, but also from the toroid regions where the beams merge and separate. In the central region, the relative energy is welldeÐned. However, a range of larger relative energies is encountered in the toroid regions, and the rate coefficients measured ata speciÐc energy therefore contain contributions from higher energies. All cross sections presented here were corrected for thetoroid contributions. The DR cross sections were not corrected for loss of light fragments. At E\ 0, light fragments are lost in4%È8% of the DR events (see ° 3.2), and hence these events do not contribute much to the measured DR cross section. Theamount of loss at higher energies is unknown.

2.2. DR Branching RatiosDR branching ratios (eqs. [2] and [3]) for and were measured at E\ 0 by chopping the electronH3O`, D3O`, HD2O`

beam. Energy spectra from the SSD were recorded separately for time intervals with and without electrons, using twomultichannel analyzer cards with 8 ks conversion time analog-to-digital converters. Each spectrum was Ðtted with Gaussians,the integral of each peak calculated, and the DR signal found as the di†erence between peak integrals obtained with andwithout electrons.

In order to separate the di†erent DR channels, a grid with a known Ðnite transmission T was inserted in front of thedetector (see Fig. 1). Thus, each fragment had the probability T for being transmitted by the grid and reaching the detector,whereas the probability for being stopped by the grid was (1 [ T ). Fragments stopped by the grid did not contribute to thesignal, and hence the signal in the full energy peak was redistributed among all peaks. For instance, an event in the a channelof would contribute to the signal in the peak with the probability T 2, in the peak with the probabilityH3O` E0 (18/19)E0T (1[ T ), and in the peak with the probability T (1[ T ). Using this method, it is possible to construct a set of(1/19)E0equations connecting the signal in each peak to the DR branching ratios. In the analysis, we introduced two di†erenttransmission coefficients, for light fragments and lighter) and for heavy fragments (O and heavier). For consistencyT

l(D2 T

hcheck, all measurements were done with two di†erent grids having T B 0.25 and T B 0.70, respectively.When calculating branching ratios, the e†ect of light fragments being lost had to be taken into account. The fractions of

light fragments and lighter) being lost were determined from energy spectra recorded without a grid in front of the(D2detector, since in these spectra, all signals in peaks at fractions of were due to loss of light fragments (at E\ 0, dissociativeE0excitation is energetically forbidden and cannot contribute to peaks at fractions of E0).A more detailed treatment of the branching ratio calculations will be given in the discussions of the individual molecules.

3. RESULTS AND DISCUSSION

3.1. DR Cross SectionsCross sections as a function of energy for dissociative recombination of and are presented in FigureH3O`, D3O`, HD2O`

3, error bars representing the uncertainties in the relative measurements. The uncertainties associated with the absolutemeasurements are ^20% for and ^40% for The cross section, which was measured on a relative scaleH3O` D3O`. HD2O`only, has been arbitrarily scaled to Ðt into the Ðgure.

768 JENSEN ET AL. Vol. 543

FIG. 3.ÈDR cross sections for and The error bars represent the uncertainty in the relative measurement. The cross sectionsH3O`, D3O`, HD2O`.measured previously at ASTRID (Vejby-Christensen et al. 1997) and the cross sections measured by Mul et al. (1983) are shown for comparison. For clarity,all cross sections have been o†set by a factor of 10. The cross section has been arbitrarily scaled to Ðt into the Ðgure.H3O` HD2O`

In the case of and absolute rate coefficients at T \ 300 K were determined by integrating the cross sectionsH3O` D3O`,in accordance with the equation (Mul et al. 1983)

a(T )\ 8nme

(2nmekT )3@2

P0

=p(E)e~E@kTEdE , (6)

yielding

a(300 K) \ 45600(4.3^ 0.6)] 10~7 cm3 s~1, H3O`,(4.5^ 1.8)] 10~7 cm3 s~1, D3O`.

(7)

In the calculations of absolute rate coefficients, the measured cross sections were corrected for the Ðnite energy resolution. Atenergies lower than the ones treated by the experiment, the cross sections were assumed to follow a p P E~1 scaling law.

It is seen in Figure 3 that and its isotopomers have nearly equal cross sections as a function of energy. In principle,H3O`nothing can be said about the absolute value of the cross section, but based on the similar relative behaviors, it seemsHD2O`likely that all isotopomers have essentially the same cross section also on an absolute scale.

Previously published cross sections for and are plotted for comparison (Mul et al. 1983 ; Vejby-Christensen etH3O` D3O`al. 1997). In general, the cross sections recorded in the present experiment agree nicely with the cross sections measured in asingle-pass merged-beams experiment by Mul et al. (1983). The cross section is also observed to be in good agreementH3O`with the previous ASTRID cross section (Vejby-Christensen et al. 1997), except for the valley region (0.6È5 eV) where theprevious ASTRID cross section is higher than those from the present work. The discrepancy is due to the fact thatbackground was not subtracted in the previous work. Usually, the background in the DR channel caused by electron capturefrom the residual gas is negligible ; however, this is not the case in this particular energy region where the DR cross section isparticularly small.

At low energies, the cross sections for all three molecular ions decrease with energy as p P E~1.15. This decrease is fasterthan the p P E~1 scaling law expected to hold for the ““ direct ÏÏ DR mechanism, which may indicate that the ““ indirect ÏÏmechanism proceeding through vibrationally excited Rydberg states plays a signiÐcant role (Bardsley & Biondi 1970 ; Bates1950). We have found similar behavior for other polyatomic molecules (Vejby-Christensen et al. 1997 ; Jensen et al. 1999).

The DR cross sections for and its isotopomers all show structures in the region before the valley (0.2È1 eV). SuddenH3O`drops are observed, most strikingly in the cross sections for and (see Fig. 4). Most likely, these drops can beH3O` D3O`attributed to capture followed by autoionization to a vibrationally excited state of the parent molecular ion, as observed for

and HDO` (Jensen et al. 1999). When the collision energy increases above the energy required for excitation of someH2O`vibrational mode, a new autoionization channel for the neutral molecular system formed by electron capture opens, and thetotal probability for autoionization increases. Autoionization competes with DR and hence decreases the DR cross section.The drops in the cross section appear at lower energies than the corresponding drops for which is consistentD3O` H3O`,with the fact that the vibrational frequencies for are lower than those of Vibrational excitation energies areD3O` H3O`.indicated in Figure 4. In the case, vibrational frequencies have been measured for all modes, symmetric OH stretchH3O` (l1),the umbrella mode asymmetric OH stretch and the deformation mode (Tang & Oka 1999 ; Liu, Haese, & Oka(l2), (l3), (l4)1985 ; Begemann et al. 1983 ; Grubele, Polak, & Saykally 1987), whereas for frequencies have been measured for theD3O`umbrella and asymmetric OD stretch modes (Sears et al. 1985 ; Petek et al. 1990). Because of inversion doubling, two di†erent

No. 2, 2000 DISSOCIATIVE RECOMBINATION OF H3O`, HD2O`, AND D3O` 769

FIG. 4.ÈClose-up on part of the present and cross sections. Vibrational excitation energies are indicated with vertical lines.H3O` D3O`

vibrational frequencies are connected with each mode. The inversion splitting is particularly large for the umbrella mode ; thustwo di†erent energies are indicated for this mode. While no clear features in the cross sections can be associated with thethresholds for exciting the umbrella and deformation modes, the Ðrst drop observed in both and coincides withH3O` D3O`the thresholds for excitation of the OH and OD stretching modes. Since the cross sections for energies below the Ðrst drop arerelatively smooth and scale nicely with energy, as discussed above, the branching ratios are not expected to change drasticallyat these low energies. Assuming that the branching ratios measured at E\ 0 (see Table 1) hold for all energies below D0.3 eV,DR proceeds mainly through the and c(OX] X] X) channels. The nuclear motion associated with thesea(X2O ] X)dissociation channels is expected to have a better Franck-Condon overlap with the excited stretching states than the excitedumbrella and deformation states, and hence as observed in the cross sections, vibrational excitation due to capture followedby autoionization should be signiÐcant only for the stretching modes.

Around 10 eV, the cross sections display a strong peak with a shoulder around 4È5 eV. This type of structure is usuallyexplained by capture into Rydberg states of the neutral molecule pertaining to excited states of the molecular ion. Acalculation by Roszak (1995) predicts a group of excited states between 11 and 18 eV above the ground state,H3O` H3O`and Rydberg states of the neutral system pertaining to some of these states may be at least partly responsible for the observedpeak. The superimposed structure may be a result of a varying Franck-Condon overlap with energy.

3.2. DR Branching Ratios at E\ 03.2.1. H3O`

Figure 5 shows energy spectra from the SSD recorded with a grid in front of the detector. The spectrum displays sevenpeaks in the case. The signal in these peaks can be related to the number of events in each DR channel as described byH3O`the matrix equation

(

t

:

t

t

t

t

t

t

N(O] 3H)N(O] 2H)N(O] H)

N(O)N(3H)N(2H)N(H)

)

t

;

t

t

t

t

t

t

\ TH3O

(

t

:

t

t

Na

Nb

Nc

Nd

)

t

;

t

t

, (8)

where

TH3O \

(

t

:

t

t

t

t

t

t

Th(1[ L H)T

lTh(1[ L H2

)Tl

ThT

l2 T

hT

l2

Th[L H ] (1[ L H)(1[ T

l)] 0 2T

hTl(1[ T

l) T

hTl(1[ T

l)

0 Th[L H2

] (1[ L H2)(1[ T

l)] T

h(1[ T

l)2 T

h(1[ T

l)T

l0 0 0 T

h(1[ T

l)2

0 0 0 (1 [ Th)T

l2

0 (1[ Th)(1[ L H2

)Tl

(1[ Th)T

l2 (1[ T

h)T

l(1[ T

l)

(1[ Th)(1[ L H)T

l0 2(1[ T

h)T

l(1[ T

l) (1[ T

h)(1[ T

l)T

l

)

t

;

t

t

t

t

t

t

. (9)

770 JENSEN ET AL. Vol. 543

and energy spectra recorded at E\ 0 with the 70% grid in front of the detector. The full and dashed curves show theFIG. 5.ÈH3O`, D3O`, HD2O`spectra obtained with and without electrons, respectively. Note that the curves recorded with and without electrons are almost identical for the O peak.

N(X) is the DR signal in the X peak, determined as the di†erence between counts obtained with and without electrons, and(i\ a, b, c, d) is the number of DR events proceeding through channel i. is the probability for losing an H atom formedN

iL Hby DR proceeding through the a channel, and similarly is the probability for losing an molecule produced in the bL H2

H2channel.As an example, the attention is focused on the loss of H fragments. From the energy spectra recorded without a grid in front

of the detector, a loss coefficient deÐned by the following equation can be calculated :

cH \ N(O] 2H)N(O] 3H)] N(O] 2H)] N(O] H)

, (10)

where N(O] 2H) is the signal in the O ] 2H peak etc. This coefficient describes the total fraction of DR events[(18/19)E0],in which an H atom is lost. Since H atoms are being lost only from the a channel, we can write This equation iscH \ L H na.

used to substitute in the matrix given in equation (9). The loss is treated similarly. From the present data, the lossL H H2coefficients and were obtained.cH \ 0.079 cH2\ 0

The matrix equation given in equation (8) describes an overdetermined system of nonlinear equations consisting of sevenequations and six unknowns and (i\ a, b, c, d)]. A numerical s2 minimization routine was used to solve the[T

l, T

h, N

iequation. As in our previous work (Andersen et al. 1996 ; Vejby-Christensen et al. 1997), we treat the transmission coefficientsas free parameters and use the procedure of Ðtting to establish the actual transmission coefficients in each individualmeasurement. There are several reasons for this. Since the transmission depends on the exact angle under which the particlespenetrate the grid, and the grid can rotate slightly when being moved in and out, di†erent transmission coefficients may beobtained in di†erent individual measurements. The transmission may not be uniform over the whole grid, and the actualtransmission coefficients may thus depend on where the beam of particles hits the grid. After installation of the grids in thering experiment, the grids are baked to 150 ¡C to improve the vacuum conditions. The heating and cooling of the grid maya†ect the transmission. Hence, even with a good ““ o†-line ÏÏ measurement of the grid transmissions, we Ðnd that it is better todetermine the transmission coefficients using the Ðtting procedure. The actual transmission coefficients were found to be

and for the grid rated to T \ 70%, while for the 25% grid the valuesTl\ (68.17^ 0.05)% T

h\ (69.4^ 0.6)% T

l\ (23.6

and were found. Branching ratios were obtained after normalization :^ 0.8)% Th\ (23.7^ 0.8)%

ni\ N

i;

kN

k, i \ a, b, c, d . (11)

No. 2, 2000 DISSOCIATIVE RECOMBINATION OF H3O`, HD2O`, AND D3O` 771

TABLE 1

BRANCHING RATIOS FOR THE DISSOCIATIVE RECOMBINATION FRAGMENTATION OF

THE HYDRONIUM MOLECULAR ION AND ITS ISOTOPOMERS : X\ H, D

D3O` HD2O` H3O` H3O` H3O`Channel (This Work) (This Work) (This Work) (Previous ASTRID Work) (Flowing Afterglow)

na(X2O ] X) . . . . . . . . . . 0.25^ 0.04 0.28^ 0.04 0.25^ 0.01 0.33^ 0.08 0.05

nb(OX] X2) . . . . . . . . . 0.15^ 0.03 0.16^ 0.05 0.14^ 0.01 0.18^ 0.07 0.36

nc(OX] X] X) . . . . . . 0.57^ 0.05 0.55^ 0.06 0.60^ 0.02 0.48^ 0.08 0.29

nd(O] X2] X) . . . . . . 0.03^ 0.04 0.01^ 0.02 0.013^ 0.005 0.01^ 0.04 0.30

The Ðnal results are given in Table 1. The three-body dissociation channel c producing OH ] H ] H dominates by taking60% of the Ñux, whereas the Ñux going into the d channel producing is nearly zero. However, our resultsO ] H2] Hestablish the fact that The branching ratio for water formation is 0.25 ^ 0.01. Within uncertainties, then

d(O ] H2] H)[ 0.

present values of the branching ratios are in reasonable agreement with the previous ASTRID results. A number of thingshave been improved in the experiment as compared with the previous measurement (Andersen et al. 1996 ; Vejby-Christensenet al. 1997). This includes improved normalization to the number of stored particles, better alignment of the detector withrespect to the position of the grids, and another type of grid and detector. All together this has reduced the systematic errors.

Only partial agreement can be found between the present branching ratios and the results from Ñowing afterglow experi-ments (Herd et al. 1990 ; Adams et al. 1991 ; Williams et al. 1996). In these experiments, the fractions of DR events leading toOH production and H production have been found to be andf (H)\ n

a] 2n

c] n

d\ 1.0^ 0.3 f (OH)\ n

b] n

c\ 0.65

while the values determined in the present experiment are f (H)\ 1.46^ 0.03 and f (OH)\ 0.74^ 0.02. The O^ 0.15,production has also been determined in a Ñowing afterglow experiment and combined with the values for fractional OH andH production to obtain the full branching ratios (Williams et al. 1996). However, as seen in Table 1, the results of thisprocedure disagree completely with the present experiment.

3.2.2. D3O`

The branching ratios were determined following the exact same procedure as was used for Typical SSDD3O` H3O`.energy spectra for are shown in Figure 5. Similarly to the analysis, loss of D atoms andD3O` H3O` (cD \ 0.047) D2molecules was taken into account. The actual transmission coefficients determined by solving the matrix(cD2

\ 0.004)equation equivalent to equation (8) were andT

l\ (68.0^ 0.6)%, T

h\ (65.4^ 1.1)% T

l\ (24.0^ 0.3)%, T

h\ (22.9^ 0.4)%

for the 70% and 25% grids, respectively. The branching ratios resulting from the analysis are given in Table 1.

3.2.3. HD2O`

The fragmentation of the molecule is more complex with eight di†erent channels (see eq. [3]) and 11 peaks in theHD2O`energy spectra, as shown in Figure 5. Moreover, four di†erent loss coefficients, andcH \ 0.047, cD \ 0.030, cHD \ 0.003,

were introduced.cD2\ 0.001,

The matrix equation relating the signal in each peak N(X) to the number of DR events in each channel is as follows :Ni

(

t

:

t

t

t

t

t

t

t

t

t

t

N(O] 2D ] H)N(O] 2D)

N(O] D ] H)N(O] D)N(O] H)

N(O)N(2D] H)

N(2D)N(D] H)

N(D)N(H)

)

t

;

t

t

t

t

t

t

t

t

t

t

\ THD2O

(

t

:

t

t

t

t

t

t

Na1

Na2

Nb1

Nb2

Nc1

Nc2

Nd1

Nd2

)

t

;

t

t

t

t

t

t

, (12)

where the matrix for is given in Table 2.THD2OBecause of the complexity of this matrix equation, we preferred to Ðx the transmission coefficients when solving theequations. Thus, the transmission coefficients determined in the analysis of the experiment, which was conducted inD3O`direct connection with the experiment, were adopted. Accordingly, a system consisting of 11 equations with eightHD2O`unknowns had to be solved. However, the H peak was hidden in the noise, and the Ðts of the 2D peak and the (2D ] H) peakwere uncertain and therefore were discarded, leaving only eight equations with eight unknowns. This system of equations wassolved using the same s2 minimization routine as for and The resulting branching ratios are listed in Table 3.H3O` D3O`.

When considering possible isotope e†ects, the branching ratios must be corrected for the statistical predominance of Datoms in Hence, the branching ratios of channels a2, b1, c1, and d2 are divided by a factor of 2. Using theseHD2O`.statistically corrected values, ratios between branching ratios corresponding to two electronically equivalent channels are

TA

BL

E2

MA

TR

IXO

FT HD

2OT h(1

[LH)T

lT h(1

[LD)T

lT h(1

[LHD

)Tl

T h(1[

LD2

)Tl

T hTl2

T hTl2

T hTl2

T hTl2

T h[LH]

(1[

LH)(1

[T l)]

00

0T hT l(1

[T l)

0T hT l(1

[T l)

00

T h[LD]

(1[

LD)(1

[T l)]

00

T hT l(1[

T l)2T

hT l(1[

T l)0

T hT l(1[

T l)0

0T h[L

HD]

(1[

LHD

)(1[

T l)]0

T h(1[

T l)20

0T hT l(1

[T l)

00

0T h[L

D2]

(1[

LD2

)(1[

T l)]0

T h(1[

T l)2T hT l(1

[T l)

00

00

00

0T h(1

[T l)2

T h(1[

T l)20

00

00

0(1

[T h)T

l2(1

[T h)T

l20

00

(1[

T h)(1[

LD2

)Tl

0(1

[T h)T

l2(1

[T h)T

l(1[

T l)0

00

(1[

T h)(1[

LHD

)Tl

0(1

[T h)T

l20

0(1

[T h)T

l(1[

T l)0

(1[

T h)(1[

LD)T

l0

0(1

[T h)T

l(1[

T l)2(

1[

T h)Tl(1

[T l)

0(1

[T h)T

l(1[

T l)(1

[T h)(1

[L

H)Tl

00

0(1

[T h)T

l(1[

T l)0

(1[

T h)Tl(1

[T l)

0

DISSOCIATIVE RECOMBINATION OF H3O`, HD2O`, AND D3O` 773

TABLE 3

THE DISSOCIATIVE RECOMBINATION BRANCHING

RATIOS FOR HD2O`

Channel Branching Ratios

na1(D2O ] H) . . . . . . . . . . . 0.15 ^ 0.05

na2(HDO] D) . . . . . . . . . . 0.13 ^ 0.04

nb1(OD] HD) . . . . . . . . . . 0.13 ^ 0.02

nb2(OH] D2) . . . . . . . . . . 0.03 ^ 0.04

nc1(OD] D ] H) . . . . . . 0.42 ^ 0.06

nc2(OH] D ] D) . . . . . . 0.13 ^ 0.07

nd1(O] D2] H) . . . . . . . . 0.00 ^ 0.01

nd2(O] HD] D) . . . . . . 0.01 ^ 0.015

calculated :

na1(D2O ] H)

na2(HDO] D)

\ 2.3^ 1.1 ,

nb1(OD] HD)nb2(OH] D2)

\ 2.2^ 2.9 ,

nc1(OD] D ] H)

nc2(OH] D ] D)

\ 1.6^ 0.9 ,

nd1(O] D2] H)

nd2(O] HD] D)

\ 0.0^ 1.0 . (13)

Isotope e†ects are observed in the a, b, and c channels where and although in channels b and c,na1[ n

a2, nb1 [ nb2, n

c1[ nc2,the uncertainties are as large as the apparent isotope e†ects. A deÐnite conclusion can be derived only for the a channel, in

which the branching ratio for H release is about a factor of 2 higher than that of D release. Still, the general trend seems to bethat a light fragment is more likely to be released than a heavier fragment. Similar e†ects have been observed in the DR ofHDO`, where the probability for H release is about a factor of 2 higher than the probability for D release (Jensen et al. 1999),and less pronounced in the DR of where the ratio between H and D release is 1.2 (Datz et al. 1995b).H2D`,

Since H and D are electronically equivalent, the observed isotope e†ects can originate only in asymmetries in the nuclearmotion caused by the mass di†erence between H and D. In connection with the study of and HDO` (Jensen et al.H2O`1999), two simple kinematic e†ects that could be responsible for the observed isotope e†ects, not only in HDO`, but also inthe present system were discussed. BrieÑy, after electron capture a wave packet is formed on a neutral potentialHD2O`,energy surface. Based on a simple classical model, it was argued that if two electronically equivalent dissociation pathwaysthat lead to di†erent DR channels (e.g., a1 and a2) exist, then pure kinematics tends to favor release of the lighter fragment(e.g., H). In addition, when dissociating along the pathway leading to release of the lighter fragment, the neutral system hasless time to decay by autoionization and hence a higher probability for completing the DR process. The key parameter inboth e†ects is the reduced mass corresponding to dissociation along a given pathway. The larger the di†erence in the reducedmasses corresponding to two electronically equivalent pathways, the larger we could expect the isotope e†ects to be. For

the reduced masses corresponding to motion along the and HDO ] D dissociation pathways are 0.95HD2O`, D2O ] Hand 1.81, respectively. For the OD] H and OH ] D dissociation pathways in HDO`, the reduced masses are 0.95 and 1.79.In on the other hand, the di†erence is smaller, with reduced masses of 0.75 for the HD] H dissociation pathway and 1H2D,for the pathway. The fact that the isotope e†ects observed in and HDO` are larger than observed inH2] D HD2O` H2D`supports the kinematic model. It may also be argued, however, that the isotope e†ect is caused by di†erences in Franck-Condon overlaps corresponding to H release and D release, as adopted in models for photodissociation (Butler & Neumark1996 and references therein). Accordingly, as discussed in relation to HDO` (Jensen et al. 1999), di†erent e†ects may beimportant, and a full explanation is likely to require more detailed knowledge about the speciÐc molecules.

3.2.4. Comparison

For comparison with and the energy spectra from the SSD were analyzed ignoring the di†erenceH3O` D3O`, HD2O`between H and D; i.e., the signals in the O] 2D and O ] H ] D peaks, the O ] D and O ] H peaks, etc., were added inpairs. An analysis similar to the analysis performed for and was then carried out, yielding the branching ratiosH3O` D3O`

(i\ a, b, c, d). As can be seen in Table 1, the branching ratios (i \ a, b, c, d) are remarkably similar forni\ n

i1] ni2 n

iand Within the uncertainties, the three molecules have identical branching ratios. The only observedH3O`, D3O`, HD2O`.isotope e†ect is for where channels a, b, c, and d are each split up into two channels, which do not have equalHD2O`,branching ratios even after correcting for the statistical predominance of D atoms in However, this isotope e†ectHD2O`.a†ects only the splitting of channels a, b, c, and d and does not redistribute the Ñux between them. The same conclusion hasbeen derived for the DR of and HDO` (Jensen et al. 1999). Consequently, even though the branching ratiosH2O` HD2O`show that isotope substitution does a†ect the nuclear motion on the potential energy surface(s) of the neutral system, the

774 JENSEN ET AL.

branching ratios (i\ a, b, c, d) are not altered by a measurable amount. Thus, it may seem that the four di†erent channelsniare separated immediately after electron capture, before the nuclei start moving. A possible reason could be that these

channels correspond to capture into four (or more) di†erent potential energy surfaces, which do not couple.

4. CONCLUSION

The dissociative recombination of the hydronium ion and its isotopomers and shows a markedH3O` D3O` HD2O`resemblance. Except for Ðne details due to di†erences in the vibrational frequencies, the DR cross sections measured as afunction of energy are identical for and On a relative scale we have also established that the DR cross sectionsH3O` D3O`.are the same for all three molecular ions. Likewise, the branching ratios (i \ a, b, c, d) are identical within the uncertainties.n

iThe only signiÐcant isotope e†ect observed in this experiment is in the DR of where the Ñux is unequally sharedHD2O`,between electronically equivalent but isotopically distinct channels. Dissociative recombination of deuterated polyatomicmolecules, in particular those containing a heavy atom, appears to favor the formation of deuterated over nondeuteratedmolecules, because release of a light fragment (e.g., H) is favored over release of a heavier fragment (e.g., D).

Concerning the results, both the cross section and branching ratios have been improved compared with the previousH3O`storage ring experiment (Andersen et al. 1996 ; Vejby-Christensen et al. 1997). In particular, the branching ratios have beendetermined more accurately. With a branching ratio of 0.60^ 0.02, the OH ] H ] H channel dominates, whereas thebranching ratio for water production is 0.25 ^ 0.01. This value is somewhat lower than the value 0.35, which is the typicalvalue adopted when modeling the chemistry of interstellar clouds (Smith 1992).

This work has been supported by the Danish National Research Foundation through the Aarhus Center for AtomicPhysics (ACAP). We thank the ASTRID sta† for their assistance during the experiment.

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