doi: 10.1098/rsta.2012.0097
, 5101-5108370 2012 Phil. Trans. R. Soc. A  Johnsen and J. Glosík P. Dohnal, M. Hejduk, J. Varju, P. Rubovic, S. Roucka, T. Kotrík, R. Plasil, R.
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Phil.Trans.R.Soc.A(2012)370,5101–5108
doi:10.1098/rsta.2012.0097
Binary recombination of para-and ortho-H+
3 with electrons at low temperatures
B Y P.D OHNAL1,M.H EJDUK1,J.V ARJU1,P.R UBOVIˇC1,*,Š.R OUˇCKA1,
T.K OTRÍK1,R.P LAŠIL1,R.J OHNSEN2AND J.G LOSÍK1
1Faculty of Mathematics and Physics,Department of Surface and Plasma Science,Charles University,Prague,Czech Republic 2Department of Physics and Astronomy,University of Pittsburgh,
Pittsburgh,PA15260,USA
Results of an experimental study of binary recombination of para-and ortho-H+
3ions with
electrons are presented.Near-infrared cavity-ring-down absorption spectroscopy was used
to probe the lowest rotational states of H+
3ions in the temperature range of77–200K
in an H+
3-dominated afterglow plasma.By changing the para/ortho abundance ratio,
we were able to obtain the binary recombination rate coefficients for pure para-H+
3and
ortho-H+
3
.The results are in good agreement with previous theoretical predictions.
Keywords:H+
3
;dissociative recombination;cavity ring down spectroscopy;afterglow plasma
1.Introduction
The fundamental characteristics of the H+
3dissociative recombination(DR)[1]
have been the subject of much interest for both theoretical and experimental
physicists[2].The discrepancies between measurements of the binary dissociative
reaction rate and the theoretical complexity of this seemingly simple reaction
led to a great deal of fruitful research on this process.The history of H+
3 recombination studies has been adequately covered in several review articles[3–9].
Recently,both theory and experiment have converged to a value for the rate of
this particular reaction.The theoretical treatment took a crucial leap forward in
the understanding of the DR process after including the Jahn–Teller mechanism
as the critical step in the initial electron-capture step of the DR reaction
[10].This resulted in a convergence with experimental DR data reported from
ion storage rings where experimentalists had realized the impact of rotational
excitation of the H+
3ions on the DR reaction rate,especially with respect
to the importance of the DR process in interstellar molecular clouds[11–13]. Final convergence between theory and the remaining important experimental techniques,stationary andflowing afterglow,was reached after recognizing that a *Author for correspondence(peter.rubovic@gmail).
One contribution of21to a Theo Murphy Meeting Issue‘Chemistry,astronomy and physics of H+
3
’.
5102P.Dohnal et al.
fast third-body reaction,not previously considered,stabilizes the recombination process in such plasmas[4,14,15].However,recently it has been shown[16,17]
that the assumption of rotationally cold H+
3ions in storage rings was not
entirely correct[17].This is important if we realize that the quantum mechanical calculations[18]predict a large difference in the low-temperature recombination
of ions in para-H+
3and ortho-H+
3
states.This has been qualitatively confirmed in
storage-ring experiments using hydrogen with an enriched para fraction[12,13,19]. However,as has just been stated,the actual rotational population of the recombining ions has not been proved experimentally.In the present experiments, the stationary afterglow(SA)technique with spectroscopic in situ determination of the abundances of the recombining ions was used.Near-infrared cavity-ring-down absorption spectroscopy(NIR-CRDS)enabled in situ determination of the spin states,together with the kinetic and the rotational temperatures of the recombining ions.A similar approach was used in our recent study of binary
recombination of para-H+
3and ortho-H+
3
ions at temperatures close to77K[20].
In the present studies,we have extended the range of temperatures up to200K.
Our previous measurements in H+
3-and D+
3
-dominated plasmas at conditions
similar to those in the present experiment[4,14,15,21,22]have shown that the
H+
3ions recombine by both a binary process with a rate coefficient a bin,and a
ternary helium-assisted recombination mechanism,with a rate coefficient K He. The plasma decay can then be described by an overall effective recombination rate coefficient:
a eff=a bin+K He[He].(1.1) Both rate coefficients can be obtained by measuring the dependence of a eff on the helium density[He].The possible effects of another ternary process—collisional radiative recombination(CRR)[23,24]—are discussed in detail elsewhere[25].
In the following,we will use left indices p,o,n and e to denote‘para’,‘ortho’,‘normal’and‘para-enriched’p H2,o H2,n H2and e H2)and p f2and
o f2to denote para and ortho fractions.p H+
3and o H+
3
stand for para-H+
3
and
ortho-H+
3,while p f3and o f3denote their p f3=[p H+3]/[H+3]and o f3=
[o H+3]/[H+3]).If an index is missing,then the spin modification is not specified. Assuming that the plasma is quasi-neutral and that it contains no ions other
than H+
e=[p H+3]+[o H+3]),then following the derivation in the study of
Varju et al.[20],we can write the continuity equation for the electron number density n e:
d n
e d t =−(p a ef
f p f3+o a eff o f3)n2e−n e
t D
=−a eff n2e−n e
t D
,(1.2)
where o a eff and p a eff are the state-selected effective recombination rate coefficients
for o H+
3and p H+
3
,respectively,a eff=p f3p a eff+o f3o a eff is the overall(apparent
binary)recombination rate coefficient for a given mixture of ortho and para ions, and t D is the characteristic time constant of the ambipolar diffusion.A linear relation similar to equation(1.2)holds also for p a eff and o a eff[20].
The data(see§3)show that at the H2and He densities used in the experiment, the fractions p f3and o f3are nearly constant during the afterglow.A measurement of a eff for two or more different values of p f3,but under otherwise identical conditions(temperature,and density of He and H2),then permits a determination
Binary recombination of para-and ortho-H+
3
5103
of the individual recombination rate coefficients p a eff and o a eff.The fraction p f3 can be enhanced from about0.5to0.8by using para-enriched hydrogen instead of normal hydrogen(for details,see[20,26]).
2.Experimental apparatus
The experimental apparatus is the same as that in our previous studies[20,26].
A pulsed microwave discharge generates a plasma in a tube(inner diameter of approx.1.5cm)cooled by liquid nitrogen.A mixture of He/Ar/H2with a typical composition1017/1014/1014cm−3flows continuously along the discharge tube.Details of the ion formation reactions are given elsewhere[4,5,27].‘A para-hydrogen generator’prepares samples of para-enriched H2(e H2)[26].The enrichment was measured by nuclear magnetic resonance spectroscopy(RNDr Jan Lang PhD2010,personal communication).NIR-CRDS in the continuous wave modification(based on the confi
guration described by Romanini et al.[28])was developed in our laboratory for time-resolved studies[26,29,30].The light source is afibre-coupled distributed feedback laser diode with a central wavelength of 1381.55nm,line-width less than2MHz,and maximum output optical power of 20mW.During the experiment,the time-dependent optical absorption signals from the discharge and the afterglow are recorded.The measured absorption is
then converted to ion concentrations.The kinetic temperature of the H+
3ions and
its evolution during the discharge and in the early afterglow were determined from the Doppler-broadened absorption line profiles by tuning the wavelength of the laser diode.All spectroscopic absorption measurements were performed on the second overtone transitions originating from the ground vibrational level
of H+
3.The lowest rotational levels(1,0)(ortho,transition3v1
2
(2,0)←0v0
2
(1,0))
and(1,1)(para,transition3v1
2(2,1)←0v0
2
(1,1))of the vibrational ground state
were monitored routinely.In some experiments,we also probed the higher-lying
level(3,3)(ortho,transition3v1
2(4,3)←0v0
2
(3,3)).Here,and in the following
discussion,the energy levels are labelled(J,G)by their quantum numbers J and G.
3.Experimental results:binary recombination of para-H+
3and ortho-H+
3
The measured electron density decay curves were analysed to obtain a eff for two particular values of p f3(further details can also be found in the study of Varju et al.[20]).We carried out a systematic set of measurements that differed only in the value of p f2(p f2=0.25when using n H2and p f2=0.87using e H2),but under otherwise very similar conditions.The densities of the para(1,1),ortho(1,0)and
ortho(3,3)states of H+
3were monitored.Examples of data measured at140K
with n H2and with e H2are plotted infigure1a,b,respectively.The middle panels offigure1a,b show a large difference in the measured populations of the particular
rotational states of H+
3in both experiments.In this set of experiments,we
reaction to a book or an articleobtained p f3∼0.5for n H2,and p f3∼0.7for e H2(see the lower panels).Note that in both experiments,the values of p f3are nearly constant during the afterglow.
Assuming thermal equilibrium(TDE)within the para and ortho manifolds, we calculated from the densities of the ions in the(1,1)and(1,0)states the
5104
P.Dohnal et
al.10(a )
(b )10p o p u l a t i o n  (%)p f 3 (%)n  (c m –3)t  (µs)t  (µs)Figure 1.(a )Upper panel:a typical example of the ion and electron decay curves measured during the afterglow in a He/Ar/n H 2gas mixture.The time t =0is taken to be at the beginning of the afterglow when the discharge is switched off.The measurements were made at 140K and 1000Pa of He and at the indicated densities of H 2and Ar.Middle panel:the measured relative populations of the para (1,1),ortho (1,0)and ortho (3,3)states of H +3.Lower panel:the measured fraction of p f 3of p H +3.Note the constant value of p f 3during the afterglow.(b )Similar to (a ),but for data measured in a He/Ar/e H 2gas mixture.(Online version in colour.)
total densities [p H +3],[o H +3]and n e .We have proved experimentally [25,26]
that the assumption of TDE under our experimental conditions is correct.To obtain a eff from the measured electron density decay curves,we used direct fits to the data and,in addition,the more advanced ‘integral analysis’technique
[31].We deliberately excluded the first 50–150m s of the afterglow decay from the data analysis because some new ions were probably still being formed (for details see [4,20,26,31]).The observed dependences of n a eff and e a eff on [He]at 140K are shown in figure 2a .The corresponding fractions p f 3are shown in figure 2c .Because n a eff and e a eff increase linearly with increasing [He],we can use equation (1.1)to obtain binary and ternary recombination rate coefficients for known para/ortho ratios.The values obtained with normal hydrogen (p f 3=0.5)correspond to those expected under TDE.The present experiments with n H 2also confirmed that p f 3was 0.5in our previous flowing afterglow with Langmuir probe (FALP)experiments [4,14,15,32].Hence,the values of a bin and K He from these experiments correspond to TDE.
The dependences of n a eff and e a eff on [He]were measured for four temperatures in the 77–200K range.From those dependences and from the corresponding p f 3,we calculated the values of p a eff and o a eff for pure p H +3and for pure o H +3,respectively.The binary recombination rate coefficients for pure p H +3and for
pure o H +3were obtained by fitting the values of p a eff and o a eff (figure 2b )using equation (1.1).For further details on the data analysis,see Varju et al.[20].The measured values of p a bin ,o a bin ,n a bin and values of n a bin from previous FALP experiments [4,14,15]are plotted in figure 3.The displayed errors of rate coefficients are 1s errors,and systematic errors (mainly from determination of ion number densities)were estimated to be less than 10per cent.
Binary recombination of para-and ortho-H+
3
5105 4
(a)
(b)
(c)
3
2
1
4
5
3
2
1
75
50
[He] (×1017 cm–3) p
f
3
(
%
)
a
e
f
f
(
×
1
–
7
c
m
3
s
–
1
)
a
e
f
f
(
×
1
–
7
c
m
3
s
–
1
)
Figure2.The measured dependences of the effective recombination rate coefficients on the He density at140K.(a)a eff measured using n H2(open circles)and a eff measured using e H2(filled
circles).(b)The measured values p a eff and o a eff for pure p H+
3(filled triangles)and pure o H+
3
(open
triangles),respectively.(c)The fractions p f3of p H+
3measured in the experiments with n H2and
e H2.(Online version in colour.)
4.Discussion and conclusion
By using either normal or para-enriched hydrogen gas,we were able to form
plasmas with different partial populations of p H+
3(fractions,p f3)and o H+
3
,
and from the measured decay of the ion density,we evaluated the binary
recombination rate coefficients for pure p H+
3and o H+
3
ions.The temperature
range covered in this study was77–200K.The results of this study show a
strong dependence of the low-temperature binary recombination of H+
3ions on the
nuclear spin states of the ions.The agreement between the experimental values
(n a bin,p a bin and o a bin)and the theoretical values(n a DR,p a DR and o a DR)[18]is
very good.Moreover,though the electron number density used in the present
experiment was by an order of magnitude higher than in our previous FALP
experiments using Langmuir probes[14],the agreement between the present n a bin values and those from the FALP experiments is very good over the whole temperature range.Because of this agreement at higher temperatures,where
CRR is negligible,we conclude that the measured rate coefficients at77K do not
depend on the electron density.From this,it follows that CRR has little to no
effect on the plasma decay and that the obtained recombination rate coefficients

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