Influence of superfluidity on recombination reactions of H + T → HT and T + T → T2 in 3He-4He quantum media under saturated vapor pressure at 1.6 K

Article abstract of DOI:10.1021/jp021765r

An influence of superfluidity on chemical reaction has been studied in the recombination reactions of hydrogen (H) and tritium (T) atoms, H + T → HT and T + T → T₂, in ³He-⁴He mixture solutions at 1.6 K. The reactive species, H and T atoms, were produced in the mixture through the nuclear reaction, ³He + n → p(H) + T. Experimental yield ratio of HT to T₂ was 110 ± 17 in normal-fluid solution. However, in superfluid solution, the value decreased to 60 with a decrease in atomic fraction of ³He. A two-fluid model was applied to estimate the contribution of superfluidity. The calculated yield of HT to T₂ in the superfluid component became almost a constant value of 56 ± 14 over the whole range of superfluid solution studied. On the basis of preferential formation of HT over T₂ and a computer simulation of relative rate constants, formation of hydrogen isotope bubbles and their tunneling recombination were proposed.

Full text of DOI:10.1021/jp021765r

J. Phys. Chem. A 2003, 107, 3741-3746
3741
Influence of Superfluidity on Recombination Reactions of H + T f HT and T + T f T2 in
3He-4He Quantum Media under Saturated Vapor Pressure at 1.6 K
Yasuyuki Aratono,*,† Kazunari Iguchi,†,‡ Kenji Okuno,‡ and Takayuki Kumada†
AdVanced Science Research Center, Japan Atomic Energy Research Institute,
Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan, and Faculty of Science, Shizuoka UniVersity,
Ohya, Shizuoka 422-8529, Japan
ReceiVed: July 31, 2002; In Final Form: February 28, 2003
An influence of superfluidity on chemical reaction has been studied in the recombination reactions of hydrogen
3
(H) and tritium (T) atoms, H + T f HT and T + T f T2, in He-4He mixture solutions at 1.6 K. The
reactive species, H and T atoms, were produced in the mixture through the nuclear reaction, 3He + n f p(H)
+ T. Experimental yield ratio of HT to T2 was 110 ( 17 in normal-fluid solution. However, in superfluid
solution, the value decreased to 60 with a decrease in atomic fraction of 3He. A two-fluid model was applied
to estimate the contribution of superfluidity. The calculated yield of HT to T2 in the superfluid component
became almost a constant value of 56 ( 14 over the whole range of superfluid solution studied. On the basis
of preferential formation of HT over T2 and a computer simulation of relative rate constants, formation of
hydrogen isotope bubbles and their tunneling recombination were proposed.
1. Introduction
Although several techniques such as laser sputtering, ion
beam, hot filament, pick-up by He droplet, etc., have been used
for the studies mentioned above,2,3 no experiment has been
reported on the hydrogen isotopes (H, D, and T) and their
molecules (H2, HD, D2, HT, and T2). This is a result of
difficulties in introducing them into liquid helium and in
spectroscopic investigation.
To solve these problems about hydrogen isotopes, the authors
developed a nuclear transformation method, 3He(n,p)T, to
introduce H and T into liquid helium as well as a radiochemical
analysis of the reaction products using radio-gas chromatogra-
phy10,11 and applied this method to the study of the recombina-
tion reactions of H + T f HT and T + T f T2 in liquid helium
at 1.6 K.
An attempt to observe the chemical reaction in liquid helium
was first reported in the reaction of Ba + N2O f BaO + N2
inside helium droplets by Lugovoj et al. in 2000.12 Although
they observed enhancement of the reaction rate in the droplet
compared to that in the gas phase, it is not clear how the reaction
will be affected by the fluidity.
The purpose of the present study is to investigate the
recombination reaction of H and T atoms in superfluid and
normal-fluid solutions by the experimental method developed
by the authors and make the features of the chemical reaction
in superfluid solution clear in comparison with that in normal-
fluid solution.
Since helium is a nonreactive rare gas element, its role in
the chemical field has been very minor. Contrary to this, its
very unique characters in condensed states have attracted many
physicists because of its extremely low temperature, the largest
quantum parameter, and so on. The most exciting property of
liquid helium is, of course, superfluidity and many investigations
have been focused on the phenomena associated with super-
fluidity itself from a physical point of view.
On the other hand, the influence of quantum properties of
liquid and solid helium on physicochemical behaviors of guest
atoms and molecules has been one of the current topics because
impurities embedded into liquid helium take very unique
chemical forms such as a bubble atom, which is produced by
the repulsive force between helium and an impurity having an
open shell like alkali atoms or in an electronically excited state
due to the Pauli exclusion principle, and snowball.1-7 The
straightforward approach to the above problems is to examine
the change of spectroscopic features induced by pressure,
temperature, phase transition from normal-fluid to superfluid
and so on. Tabbert et al.8 investigated the influence of fluidity
1
1
1
upon optical transitions of Ca(4p P1 f 4s S0), Mg(3p P1 f
3s 1S0), and Ag(5p P1/2 f 5s S1/2) by a bath cryostat
experiment at 1.4-2.4 K, but they could not observe a
significant line shift against phase transition at 2.17 K. The
recent progress of spectroscopy of molecules picked up into a
He-droplet has been giving evidence for superfluidity of helium
clusters on the basis of the highly resolved vibrational and
rotational spectra.3 However, no experiment has been carried
out on the change of spectroscopic features over the phase
2
2
2. Experimental Section
Helium-3 gas was purchased from Isotec Inc. and its isotopic
enrichment was more than 99.9 atom %. Tritium content in the
gas was below the detection limit for the present T counting
transition except by Grebenev et al. in a He-3He mixture
4
droplet9 because the temperature of the helium cluster is about
0.38 K and cannot be changed easily.
3
system. The mixture gas with predetermined ratio of He to
4He (purity of more than 99.99%) was prepared using a glass-
made vacuum line operated at 10-3 Pa. The superfluid or
normal-fluid state was chosen by changing the atomic fraction
* Corresponding author. Tel: +81-29-284-3515. Fax: +81-29-282-5927.
E-mail: aratono@popsvr.tokai.jaeri.go.jp.
† Japan Atomic Energy Research Institute.
‡ Shizuoka University.
3
3
of He(f He) (Figure 1). The experimental setup of the irradiation
10.1021/jp021765r CCC: $25.00 © 2003 American Chemical Society
Published on Web 04/15/2003

3742 J. Phys. Chem. A, Vol. 107, No. 19, 2003
Aratono et al.
and 576 keV, respectively, according to the following nuclear
reaction:
3He + n f T** + p**
(1)
where T** and p** show translationally excited states. Tritium
is also produced as a bare nucleus, triton(positive charge),
because the initial translational velocity of recoil tritium is very
much larger than the velocity of a Bohr orbital electron. These
species are thermalized efficiently by collisional deactivation
with surrounding He owing to close masses among T**, p**,
4
3He, and He and to the high density of He. According to the
calculation, 100 collisions are sufficient for T** and p** to reach
thermal energy at 1.6 K(1.37 × 10-4 eV). Neutralization of a
triton and a proton during the deactivation process in liquid
helium has not been well-known. In helium gas, the possibility
of reionization of neutralized hydrogen isotopes is theoretically
predicted due to higher ionization potential of He(24.6 eV) than
that for hydrogen isotopes(13.6 eV).14 However, this prediction
is based on the pure charge-transfer process in gas phase. In
the present experimental condition, the electrons produced
through the deactivation process are considered to play a
prominent role for neutralization. Even if a snowball is formed,
the mutual reaction of the snowball will be impossible due to
the repulsive force because a snowball has positive charge. It
will be neutralized to the atomic state at first and then will
recombine. After thermalization and neutralization, H and T
react with each other to form H2, HT, and T2 by the following
recombination reactions:
Figure 1. Phase diagram of a 3He-4He mixture solution under
saturated vapor pressure.
kHH
Figure 2. Experimental setup of irradiation apparatus.
H + H + (He) 8 H2 + (He)
(2)
apparatus is shown in Figure 2. The reaction irradiation cell is
a stainless steel box with inner dimensions of 2 mm × 15 mm
× 20 mm. A Polaroid neutron camera with a BC-704 detector
kHT
H + T + (He) 8 HT + (He)
(3)
(4)
6
kTT
(a phosphor screen based on ZnS(Ag) and Li) and Fujifilm
T + T + (He) 8 T2 + (He)
FP-3000B was used to monitor the position and condition of
the sample under irradiation. Particular attention was paid to
keep the reaction cell clean. The mixture gas of 3He-4He with
a predetermined ratio was introduced into the reaction cell
through a charcoal column cooled at 77 K and lowered to 1.6
K by evaporative cooling of liquid helium. After the vapor
pressure attained equilibrium value and the reaction cell was
filled with the liquefied mixture, thermal neutron irradiation was
performed at the neutron beam guide of JRR-3M (Japan
Research Reactor No. 3M)13 for about 40 h. The maximum
thermal neutron flux measured by the Au-foil activation method
was (3-4) × 1010 m-2 s-1. However, in the actual irradiation
condition, the average neutron flux changed from 1.43 × 1010
where kHH, KHT, and kTT are rate constants for each reaction
and (He) is a third body for removal of reaction energy released
in the recombination reaction.
It has been known that hot H and T atoms, which are
produced in the vicinity of the wall, abstract hydrogen from
small amounts of hydrogen-containing impurity on the wall of
the reaction cell to give H2 and HT (so-called wall effect).
Therefore contribution of H2 and HT from the wall effect to
that from reactions 2 and 3 was estimated as described below.
If the wall effect contributes to the H2 and HT yield
significantly, dependence of the yield on fluidities of the solution
will not be observed. From this point of view, the experimental
results shown later (Figure 4) qualitatively suggest that the wall
effect does not play a significant role in HT formation. To
evaluate the wall effect more quantitatively, the fractions of
H(proton) and T formed within their recoil ranges from the wall
against total H(proton) and total T, Hw and Tw, were evaluated
by using neutron intensity and their recoil ranges. The neutron
intensity was calculated as a function of depth from the surface
to which neutron impinges by the computer code of SRAC.15
The ranges of proton and T were estimated to be 168 µm for
the former and 22 µm for the latter from the stopping power.16
m-2 s-1 at f He ) 1.0 to 1.63 × 1010 m-2 s-1 at f He ) 0.1. Since
the irradiation port is 60 m away from reactor core, the γ-ray
dose rate at the irradiation port is very low and radiolysis of
the reaction products is negligibly small. After irradiation, the
solution was recovered by warming the reaction cell to room
temperature and subjecting it to radio-gas chromatographic
analysis. The reaction products, HT and T2, were separated with
a γ-alumina column chilled at 77 K, and their radioactivity was
measured by gas flow proportional counter. The atomic fraction
of 3He in the solution was determined with a quadrupole mass
spectrometer.
3
3
3
The values of Hw and Tw were 0.15 and 0.04 at f He ) 1.0,
respectively. In case of f He ) 0.1, the values of 0.05 and 0.01
were obtained for Hw and Tw, respectively. From the above
qualitative and quantitative considerations, it is concluded that
the main processes to yield H2 and HT are reactions 2 and 3.
3
3. Results and Discussion
3.1. Thermalization of Energetic Tritium and Proton.
Tritium and protons are produced with recoil energies of 192

Recombination Reactions of H + T f HT and T + T f T2
J. Phys. Chem. A, Vol. 107, No. 19, 2003 3743
3
0.35 and begin to change with a decrease in f He. This turning
point corresponds to the transition from normal-fluid solution
3
to superfluid solution at 1.6 K (f He ) 0.35, see Figure 1).
It has been reported that OCS and SF6 in a mixed cluster of
4
3
3He/4He are surrounded by a shell of He and that He atoms
are on the outside due to the finite size effects.9,17 It has been
also reported that the phase diagram of the He-4He mixture
3
inside the aerogel is different from that of the bulk mixture
solution.18 This was theoretically explained by confinement and
substrate-3,4He interaction potential effects.19 Since our results
are from a bulk experiment, these effects induced by the
environment will not be significant. Thus the present experi-
mental result strongly suggests that superfluidity affects the
chemical reaction.
The two-fluid model predicts that liquid 4He solution below
2.17 K at saturated vapor pressure, He II, is composed of two
interpenetrating fluidssnormal-fluid and superfluid.20 According
to the model, the total density of liquid (F) is given by
Figure 3. Typical radio-gas chromatogram of neutron-irradiated
sample.
F ) Fn + Fs
(5)
where Fn and Fs are the densities of normal-fluid and superfluid
components and their ratio depends on the temperature. The
superfluid does not contribute to the entropy of the liquid and
thus thermal phenomena are attributable to the normal-fluid.
The model has been successfully applied to the explanation of
transport properties of He II. It has been proved by theoretical
and experimental studies that a similar picture can be applied
3
to the superfluid solution of the He-4He mixture shown in
Figure 1. In the case of the mixture solution, the ratio Fn/Fs
depends on both the temperature and the fraction of 3He.
Although the picture of the model is rather based on the physical
viewpoints, the entropy, thermal phenomena, and transport
properties are closely related to chemical processes. Therefore
the authors attempted to apply the model to the experimental
results in order to learn how the recombination reaction is
influenced by the superfluidity.
As seen in Figure 4, (YHT exp
)
and (YT )exp are constant over
2
3
the whole range of normal-fluid solution (f He ) 0.95-0.35).
This indicates that normal-fluidity does not influence the
reaction. On the basis of this experimental fact, the authors
assumed that (YHT exp
is kept constant over the whole range of He fraction studied
)
/(YT )exp obtained in normal-fluid solution
2
3
Figure 4. Experimental mol % yield of HT and T2 against the atomic
3
fraction of He.
and the change of (YHT)exp/(YT )exp in superfluid solution is
2
attributed to superfluidity. To estimate the contribution of
superfluidity, the authors used Fn/F in 3He-4He mixture
solutions at various temperatures under saturated vapor pressures
which were obtained experimentally by Pogorelov et al. and
Sobolev et al.21,22 Figure 5 shows relative densities of normal-
fluid and superfluid components, Fn′ ) Fn/F and Fs′ ) Fs/F, under
saturated vapor pressure at 1.6 K.21,22 The superfluid component
increases with f He, from 0 at f He ) 0.35 to 0.85 at f He ) 0.
Experimental yields of HT and T2 given in Figure 4 can be
expressed as follows:
3.2. Relative Yields of HT and T2 Molecules as a Function
of the Superfluid Component. Figure 3 shows a typical radio-
gas chromatogram of a neutron-irradiated sample. Two peaks
were identified as HT and T2 by the retention time of the
standard HT, DT, and T2 mixture gas. The amount of H2 could
not be analyzed due to very low concentration below the
detection limit but is equal to that of T2 from a material balance.
3
3
3
The experimental mol % yields of HT ((YHT)exp) and T2
3
((YT )exp) are presented in Figure 4 as a function of f He. (YHT exp
)
2
and (YT )exp are defined as follows:
2
(YHT exp
)
) (YHT)n + (YHT)s ) (YHT)Fn′)1 × Fn′ + (YHT s
)
(6)
(YHT exp
)
) {(radioactivity of HT)/[(radioactivity of HT) +
(radioactivity of T2)/2]} × 100
and
(YT )exp ) {[(radioactivity of T2)/2]}/
(Y )exp ) (Y )n + (Y )s ) (Y )Fn′)1 × Fn′ + (Y )s (7)
2
T2
T2
T2
T2
T2
{[(radioactivity of HT) + (radioactivity of T2)/2]} × 100
where (YHT)n and (YHT)s are yields of HT in normal-fluid and
3
It is interesting to compare Figure 4 with the phase diagram
(see Figure 1). As shown in Figure 4, (YHT exp
independent of the atomic fraction of He over f He ) 0.95 to
superfluid components at f He < 0.35, and (YHT)Fn′)1 and
3
)
and (YT )exp are
(YT )Fn′)1 are the mean values of (YHT exp
)
and (YT )exp at f He
>
2
2
2
3
3
0.35, respectively. On the basis of eqs 6 and 7, the experimental

3744 J. Phys. Chem. A, Vol. 107, No. 19, 2003
Aratono et al.
Figure 5. Relative density of superfluid and normal-fluid components
3
in a He-4He mixture solution at 1.6 K.
data in Figure 4 were recalculated and the results are plotted in
Figure 6. The yield ratios of (YHT)n/(YT )n ) 110 ( 17 and (YHT)s/
2
(YT )s ) 56 ( 14 were obtained for normal-fluid and superfluid
2
components from Figure 6.
3.3. Proposal of H and T Bubbles and Their Tunneling
Recombination. The large yield ratios of HT to T2 both in
superfluid and normal-fluid solutions cannot be explained by a
gas-phase reaction where the isotope effect is negligible due to
nonbarrier reaction and suggest that reactions 2-4 are the
processes having the reaction barrier and proceed through
tunneling mechanism because the reactions proceed in the
solution at very low temperature. If so, rate constants of the
reactions 2-4, kHH, kHT, and kTT, will be very different from
each other. The authors attempted to estimate probable rate
Figure 6. Yield of HT and T2 in superfluid and normal-fluid
3
components. (Because the superfluid component at f He > 0.35 is zero,
the scatter of the values around the yield of 0 is due to variation of
experimental values.)
bubbles. Saarela and Krotscheck25calculated the radial distribu-
tion functions of D and T atoms and effective masses of
hydrogen isotopes in liquid 4He. According to the radial
distribution function, the nearest-neighbor peaks of D and T
atoms are moved from about 0.35 nm for He-He to about 0.4
nm for both He-D and He-T. Although the distribution
function of H is not given due to the lack of convergence of
their iteration scheme for the Euler equation below 10 atm, the
equilibrium distance of the He-H pair potential is around 0.36
constants to yield YHT/YT ) 60-110 by computer simulation.
2
The rate equations for reactions 2-4 are given by
d[H]/dt ) AH - 2kHH[H]2 - kHT[H][T]
(8)
and
d[T]/dt ) AT - kHT[H][T] - 2kTT[T]2
(9)
4
nm and is longer than that of He-4He due to a short-range
repulsive force.26,27 The effective mass of hydrogen isotopes in
liquid helium is roughly 10 for H, D, and T atoms.25 On the
basis of these calculations, we can briefly draw a picture of the
ground state of a hydrogen isotope bubble in liquid helium as
a radius of about 0.4 nm, effective mass of about 10, the
spherical square well potential a result of the s structure of the
valence electron, and lower ground state for T than H a result
of lower zero-point energy.
The formation of a bubble of impurity embedded into liquid
helium has been well established for electron and some alkali
and alkaline-earth elements by theoretical and experimental
investigations.2 For example, the electron resides in the square
well potential of about 1 eV in depth with the bubble radius of
1.72 nm at zero pressure at 1.3 K.28 The radius of a Cs bubble
at 1.5 K under saturation vapor pressure is experimentally
obtained to be 0.65 nm and coincides well with the theoretical
calculation employing the pair potential of the Lennard-Jones
form.29,30
where AH and AT are the generation rates of H and T atoms by
nuclear reaction and are expressed as follows:
AH ) AT ) Nσthf
(10)
where N is the concentration of 3He atoms at the experimental
3
point, σth is the cross section for He(n,p)T (5.5 × 10-25 m2),
and f is the neutron flux. Since f is a function of depth at each
3
f
He, the average value was used at the experimental point. The
3
values of AH () AT) at f He ) 1.0 and 0.1, for example, are 2.10
× 10-10 mol m-3 s-1 and 2.39 × 10-11 mol m-3 s-1
,
respectively.
In the above mathematical treatment, the absolute values for
k
HH, kHT, and kTT cannot be obtained but their ratio, which
satisfies YHT/YT ) 60-110 and YH /YT ) 1 can be calculated.
2
2
2
Since the rate constant of the H-H recombination reaction in
liquid helium is expected to be smaller than that in the gas phase,
the values less than 2.30 × 107 m3 mol-1 s-1, which is the
mean volume rate constant in the gas phase at around 1 K,23,24
were used for calculation. The results were kHH > kHT . kTT
and differed by one or four orders of magnitude.
In order for hydrogen isotopes in the bubble state to
recombine, the barrier should be overcome either by thermal
motion or tunneling. If the dissociation energy in the H-He
pair potential is taken as a measure of minimum activation
energy as the first approximation, 7-8 K would be necessary
for the bubble-atom reaction.26,27 Since the reaction temperature
is 1.6 K, it seems reasonable to consider that reactions 2-4
The most plausible process with a barrier is considered to be
the recombination of H and T atoms in the bubble state. Though
the bubble structure of hydrogen isotopes has not been reported,
the theoretical calculation seems to predict the hydrogen isotope

Recombination Reactions of H + T f HT and T + T f T2
J. Phys. Chem. A, Vol. 107, No. 19, 2003 3745
proceed through the tunneling process. Since the zero-point
energy of T is lower than that of H, the tunneling distance for
reaction 4 would be longer than that of reaction 3. This would
result in the preferential formation of HT over T2 in liquid
helium, being different from the volume recombination reaction
mechanism in the gas phase at around 1 K.
It has been supposed that the neutralization process between
Ba+ and the electron in liquid helium proceeds via the tunneling
mechanism.2,31,32 Since the neutralization process has no reaction
barrier in general, the bubble state of the reactants is considered
to be responsible for the tunneling reaction. In fact, their bubble
states in liquid helium are strongly supported by optical
investigations.8,28,33
(0.38 K) spectroscopically and found great enhancement of the
reaction rate over the gas-phase reaction.12 Though they could
not compare the reaction rate with that in normal-fluid solution
due to experimental difficulty in making normal-fluid He-
droplet, the results obtained both in the authors’ work and in
their experiment predict very unique features of the chemical
reactions in superfluid solution.
4. Conclusion
Chemistry in quantum media has been gaining attention as a
field of low-temperature chemistry.37 Liquid and solid hydrogen
constitute one of the typical quantum media, and chemical
reactions in the solid hydrogen have been widely investigated
focusing on the tunneling phenomena in chemical reactions.38-40
The quantum parameter of helium is 2-3 times larger than that
of hydrogen41 and hence many physicochemical effects associ-
ated with quantum character, especially with superfluidity, will
be expected. Chemical phenomena concerning hydrogen iso-
topes are very fundamental and thus the chemical behavior of
hydrogen isotopes in liquid helium will lead to a very unique
field of low-temperature chemistry. From this point of view,
investigations of temperature and pressure effects upon recom-
bination reactions of H and T atoms in superfluid and normal-
fluid solutions are in progress by the radiochemical methods
developed by the authors.
3.4. Reactivity in Superfluid and Normal-fluid Solutions.
The different preference in formation of HT and T2 over phase
transition from normal-fluid to superfluid solutions, {(YHT)n/
(YT )n}/{(YHT)s/(YT )s} ≈ 2, is the next point of interest. Two
2
2
factors seem to influence the results. One is the change of bubble
3
structure against the atomic fraction of He, and the other one
is coherence of the system.
The total energy of the bubble atom, Et, is given by following
equation:34,35
Et ) Efa + Eint + Ec
(11)
where Efa is the electronic energy of the free atom, Eint is the
energy of the interaction with the surrounding helium atoms,
and Ec is the energy to form the bubble atom. As the first
approximation, Ec is expressed by the sum of surface energy
(Esurf) and pressure volume work (Epv),
Acknowledgment. The authors thank Mr. B. Komukai and
Dr. S. Kubo for their extensive advice in computer calculations
of neutron intensity and rate equations. The authors also express
their appreciation to Drs. S. Shimizu and M. Nomura for their
helpful discussions.
2
3
Ec ) Esurf + Epv ) 4πRb σ + [4πRb /3]p
(12)
References and Notes
where Rb, σ, and p represent radius of bubble, surface tension,
(1) Proceedings of the 128th WE-Heraeus-Seminar on Ions and Atoms
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and pressure of liquid helium. In the present experimental
conditions, these parameters vary with f He and it may lead to
3
the change of total energy of the bubble. However, (YHT exp and
)
(3) Toennies, P. J.; Vilesov, A. F. Annu. ReV. Phys. Chem. 1998, 49,
3
(YT )exp are constant over the wide range of f ) 0.95 to 0.35
and thus drastic change in its structure at f He ) H0e.35 to 0.1 would
2
1.
3
(4) Takahashi, N.; Shigematu, T.; Shimizu, S.; Horie, K.; Hirayama,
Y.; Izumi, H.; Shimoda, T. Physica B 2000, 284, 89.
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K. J. Nucl. Sci. Technol. 1990, 27, 1138.
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not be expected. Therefore the bubble structure might not exert
a substantial effect upon the yield ratios of HT to T2 both in
superfluid and normal-fluid solutions. This seems to be con-
sistent with a spectroscopic study by Tabbert et al. who did not
observe change of spectroscopic features of Ca, Mg, and Ag in
the bubble state upon phase transition from superfluid to normal-
fluid.8
Recently, Kumada et al. studied the H-H recombination
reaction in quantum solid p-H2 which contains various amount
of o-H2 by ESR, ENDOR, and ESE at 4.2 K.36 They changed
relative concentration of o-H2(x0) from 0.001 to 0.75(normal
H2) and found that the reaction is controlled by different
mechanisms, depending on the concentration of o-H2. At x0 >
0.1, the reaction was well explained by the usual diffusion-
controlled process. However, at concentrations lower than 0.1,
the reaction proceeded with a much slow rate than expected
from the diffusion coefficient. They attributed the absence of
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3
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Lugovoj et al. studied the rate of the chemiluminescent Ba
+ N2O f BaO + N2 reaction inside a superfluid He-droplet-

3746 J. Phys. Chem. A, Vol. 107, No. 19, 2003
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