Crossed-beam study of the Al( 2P1/2, 3/2 )+O2( X 3Σ-g ) → AlO( X 2Σ+ )+O( 3PJ ) reaction at low and very low kinetic energies

Article abstract of DOI:10.1016/S0009-2614(99)00759-9

The title reaction is revisited at kinetic energies between 255 and 6 meV with a new crossed-beam apparatus. The AlO dissociation energy is evaluated to be D₀(AlO)=5.27±0.01 eV. Al(²P_1/2) and Al(²P_3/2) spin-orbit reactivities are shown to be different. The relative cross-section of Al(²P_1/2)+O₂ is found to increase monotonically when decreasing kinetic energy. The variation of the calculated thermal rate constant is in agreement with kinetic measurements performed between 1083 and 23 K. Good agreement is also found with theoretical treatment based on the adiabatic capture centrifugal sudden approximation.

Full text of DOI:10.1016/S0009-2614(99)00759-9

3
September 1999
Chemical Physics Letters 310 Ž1999. 231–239
www.elsevier.nlrlocatercplett
Crossed-beam study of the
2
3
2
3
y
q
ž
/
ž
/
ž
/
ž /
Al P
qO X S ™ AlO X S qO P reaction at low
1
r2, 3r2
2
g
J
and very low kinetic energies
Christian Naulin, Michel Costes )
UMR 5803 CNRS - UniÕersit e´ Bordeaux I, Laboratoire de Physico-Chimie Mol e´ culaire, UniÕersit e´ Bordeaux I,
F-33405 Talence Cedex, France
Received 6 April 1999; in final form 2 July 1999
Abstract
The title reaction is revisited at kinetic energies between 255 and 6 meV with a new crossed-beam apparatus. The AlO
2
2
dissociation energy is evaluated to be D ŽAlO.s5.27"0.01 eV. AlŽ P . and AlŽ P . spin–orbit reactivities are shown
0
1
r2
3r2
2
to be different. The relative cross-section of AlŽ P .qO is found to increase monotonically when decreasing kinetic
energy. The variation of the calculated thermal rate constant is in agreement with kinetic measurements performed between
083 and 23 K. Good agreement is also found with theoretical treatment based on the adiabatic capture centrifugal sudden
approximation. q 1999 Elsevier Science B.V. All rights reserved.
1
r2
2
1
1
. Introduction
Several experimental and theoretical studies have
been reported since. An intriguing, strong effect of
spin–orbit selective reactivity was revealed in the
crossed-beam experiment of Chen et al. in which
fluorescence imaging techniques were used w3x. In
In a former crossed-beam study of the reaction
2
3
y
2
q
3
AlŽ P .qO ŽX S . ™ AlOŽX S .qOŽ P ., we
J
2
g
J
determined the dependence of the reactive cross-sec-
tion on the kinetic energy between 41 and 420 meV
Ž1 eVs96.485 kJrmol. w1x. The excitation function
that work, experimental results concluding that
2
ground-state AlŽ P . is the only reactive spin–orbit
1
r2
curve appeared to be monotically increasing with
decreasing kinetic energy, i.e. with no energy barrier.
Averaging this excitation function over a Maxwell
distribution of velocities allowed us to calculate
a variation of the rate constant in very good agree-
ment with the kinetic measurements of Garland
and Nelson performed in the 298–1083 K tempera-
ture range w2x.
component were presented and explained by an elec-
trostatic interaction model. The electrostatic model,
however, appeared insufficient to describe the long-
range interaction potential of this reaction fully. The-
oretical work based on the adiabatic capture centrifu-
gal sudden approximation ŽACCSA. method, with a
long-range potential made up of the sum of the
quadrupole–quadrupole, dispersion and spin–orbit
2
contributions w4x, showed that AlŽ P . does react
3
.
r2
2
)
Ž
with O , although less than Al P
. Furthermore,
Corresponding author. Fax: q33-5-6846645; e-mail:
2
1r2
costes@cribx1.u-bordeaux.fr
ACCSA rate constants fit well with experimental
0
009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S0009-2614Ž99.00759-9

2
32
C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
kinetic results concomitantly obtained at tempera-
tures between 295 and 23 K w5x. The thermal rate
constant increases by a factor of 2.6 between these
temperatures, which is very different from that which
would be derived from an extrapolation of our calcu-
lated curve.
ular beam sources, as well as laser ablation for
generating of transient species, and laser-induced
fluorescence ŽLIF. for detection. The beam intersec-
tion angle, now variable from uspr2 or 3pr4
down to uspr8 replaces the former, conventional,
rigid configuration at right angles ŽFig. 1.. Variation
In a recent communication devoted to the CqO
of the beam intersection angle, employed by Gentry
and co-workers w9,10x, and latterly by Liu and co-
workers w11x, is a powerful method which allows for
2
™
COqO reaction w6x, we gave the first results
from a new crossed beam apparatus, specially de-
signed for the study of neutral atom – neutral
molecule atom-exchange reactive collisions, AqBC
scanning of the relative velocity and the relative
translational energy, z and ´ , of A and BC colli-
r
tr
™
ABqC, at low and very low kinetic energies.
sion partners with reduced mass m, without having
to change the laboratory beam velocities zA and
zBC , and hence the molecular beam source condi-
tions:
2
The new aspects of the AlŽ P
.qO reactivity
1
r2, 3r2
2
are re-examined with this apparatus and described in
this Letter.
1
2
2
r
1
2
2
A
2
´tr s mz s m
Ž
z qz y2zAzBC cos u
.
.
1
Ž .
BC
2
. Experimental
The vacuum chamber is a stainless-steel horizon-
tal cylinder 450 mm long with 480 mm inner diame-
ter divided in three parts: two lateral source cham-
As with our former crossed molecular beam in-
strument w7,8x, the new apparatus uses pulsed molec-
Fig. 1. Schematic cutaway through the molecular beam axes plane of the experiment ŽPV1 and PV2, pulsed valves for the A-atom beam and
the BC molecular beam; ALB, ablation laser beam; PLB, probe laser beam; PMT, photomultiplier tube..

C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
233
bers and a central scattering section. The right-hand
side, beam A, is sealed by a lid which has a fixed
position whereas the left-hand side, beam BC, is
sealed by a rotating lid supported by a ball bearing
w9x. Each lid has an internal O-ring sealed partition
increasing the gas output emitted by the pulsed valve
y4
3
y4
3
to 6=10
per pulse.
Pa m per pulse from 3=10
Pa m
Each beam escaping its wedge-shaped chamber is
collimated by a skimmer, at 40 mrad half-width at
1re ŽHWE. in this study, and the beams are crossed
disk attached to it and terminates in the central
scattering volume with a wedge-shaped chamber
which contains the skimmed pulsed beam source.
Each source chamber is differentially pumped
on the horizontal axis of the chamber with an attenu-
ation factor -8%. Other beam characteristics are
summarised in Tables 1 and 2. The base pressure in
3
y1
y4
through a hole in the partition disk by a 0.35 m s
turbopump and the central scattering section is evac-
the central scattering section reached Ps2=10
Pa with both valves operated at 5 Hz.
3
y1
uated by a 0.9 m s turbopump.
LIF detection of the Al reactant and AlO product
at the crossing point was achieved with a pulsed
Nd:YAG pumped Ž3rd harmonic. dye laser operated
The central scattering volume, 230 mm wide, has
eight 153 mm diameter portholes ŽISO 160., equally
spaced at pr4 angles, and centred on the scattering
plane which is vertical. In standard operation, two
fast-ionization gauges ŽFIGs., each mounted on a
with a mixture of C460–C480 dyes. The probe laser
beam propagated along the horizontal axis of the
vacuum chamber, thus always at right angles to the
relative velocity vector when scanning the intersec-
tion angle, which avoids detuning by the Doppler
shift. Al atoms were monitored using the doubled-dye
vacuum feedthrough translator stage with a 200 mm
path, are positioned on the flanges at p and 3pr2 to
measure the velocity distributions of the beams; ul-
traviolet–visible fluorescence collecting optics are
positioned at 3pr4. This configuration limits the
widest beam intersection angle to uspr2. If an
extended range of kinetic energies is required as in
this work, the FIG at 3pr2 is removed and replaced
by the collecting optics: the widest beam intersection
angle then increases to us3pr4. Fluorescence de-
tection in the vacuum ultraviolet Žnot shown here. is
also possible w6x: in this case, a solar-blind photo-
2
output in the saturation regime of the 5d D § 3p
3
r2
2
0
2
2
0
P1
and 5d D §3p
P
absorption transi-
r2
3r2
3r2
tions at 236.705 and 237.335 nm, respectively; fluo-
rescence arising from these two transitions was at-
tenuated by a neutral density filter of optical density
2.3 to avoid saturation of the photomultiplier tube.
2
q
The AlO product was probed on the ŽB S
§
2
q
X S . DÕsq1 sequence between 465 and 470
nm, again in the saturation regime; fluorescence
above 490 nm was collected with a high-pass type
multiplier is directly placed under vacuum at 3pr4,
the photons being collected by a concave mirror
positioned at 7pr4.
filter. The O internal-state distribution was not mea-
2
sured but assumed to be very cold, with a mean
internal energy -1 meV by analogy with NO beams
obtained under similar operating conditions and
characterized by LIF w13x. Assuming the same rota-
As previously, Gentry–Giese pulsed valves are
used to generate the beams w10,12x. The distance
from the nozzle to the crossing collision centre is
1
41 mm for the atom beam and 120 mm for the
beam of molecules. The atom-beam source, exten-
sively described in Ref. w8x, has been redesigned.
Table 1
Characteristics of the Al beam
Laser ablation at 266 nm of a rod maintained in slow
helical motion is again the preferred choice, but no
extension channel can now be used due to the steric
limitations imposed by the wedge-shaped chamber.
Nonetheless, satisfactory operating conditions in
terms of intensity and velocity resolution have been
found when focusing the ablation laser 1 mm below
the nozzle, lowering the laser ablation energy to
a
b
Carrier gas
P1
P
zAl
DzAl rzAl
r2
3r2
Žm sy1.
1
2
3
4
neat N2
neat Ne
0.94
0.54
0.06 1030
0.46 1030
0.03
0.11
0.09
0.10
0.12
Xe:N s0.20:0.80 0.97
780
2
c
He:N s0.90:0.10 n.m.
n.m. 1800
2
a
2
P swAlŽ P .xrwAlx.
J
J
b
Velocity spread ŽHWE.; uncertainty on ÕAl determination is
2%.
0
.5–0.8 mJrpulse from 3–10 mJrpulse in the old
"
c
design Žin a 0.16 mm diameter circular waist., and
Not measured.

2
34
C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
Table 2
The excitation limit which corresponds to the
Characteristics of the O2 beam
separation of AlO in the rovibrational state of high-
DzO2 rzO2 a
est energy with O in its ground P state with almost
3
Gas mixture
zO2
Žm s
2
y1
.
no recoil energy gives the closest value of ´ . Such
tot
A
B
O :Hes0.55:0.45
955
740
-0.08
-0.08
2
an excitation limit is clearly identifiable in the P
O :Ars0.45:0.55
2
Ž
.
Ž
.
branches of the 1–0 and 2–1 bands. Taking the
a
spectrum at ´ s12 meV which has the largest
Velocity spread ŽHWE.; uncertainty on ÕO2 determination is
tr
"
2%.
signal-to-noise ratio, the highest populated levels are
Y
N s45 Žcalculated to be at ´s163.3 meV from
Y
molecular constants w15x. in the Õ s0 manifold, and
Y
Y
N s24 Ž´s166.7 meV. in the Õ s1 manifold,
tional temperature as for NO would result in the
following relative rotational populations: 0.60, 0.35,
respectively. The excitation limit thus lies in between
Y
Y
Y
N s45 and 46 levels in Õ s0, and N s24 and
Y
0
.05, and -0.002 for Js1, 3, 5, and 7, respec-
2
5 levels in Õ s1. Equating the AlO internal energy
tively.
to ´ yields D´ sy155"4 meV. The absolute
tot
0
uncertainty in the determined value also arises from
the kinetic energy spread Žoverestimated as "33%,
i.e. "4 meV. and can thus be consistently consid-
ered as "8 meV. Introducing D ŽO .s5.1156"
3
. Results and discussion
0
2
3
.1. LIF excitation spectra at low kinetic energy and
0
.0019 eV w16x yields D ŽAlO.s5.27"0.01 eV.
0
AlO dissociation energy
This value is in agreement with our former determi-
nation: D ŽAlO.s5.26"0.03 eV w7x.
0
In previous work, the quantum-state populations
of AlOŽX S ., PŽÕ , N ., given by the title reac-
tion were determined from LIF excitation spectra
The enhancement of the Ž2–1. bandhead at low
2
q
Y
Y
energy is in our opinion not a dynamical feature, but
rather an artifact due to a LIF detection efficiency
which increases slightly with decreasing recoil en-
ergy w17x. Indeed, the Ž2–1. bandhead occurs for
obtained at kinetic energies between ´ s83 and
tr
4
90 meV w7,14x. Spectra at much lower kinetic ener-
Y
gies could be recorded in this study. The signal-to-
noise ratio at low energy was very large and the
spectra presented in Fig. 2 were acquired with re-
stricted averaging Ž2 shots per point. over short
N s14 Ž´s136 meV., and according to Eq. Ž2., at
Y
Y
3
´
s6 meV, AlOŽÕ s1, N s14. and OŽ P . frag-
tr
2
ments share a mere 15 meV in recoil energy, and
OŽ P1, 0. fragments cannot be produced since their
3
acquisition times, i.e. 1800 s at ´ s6 and 12 meV
tr
energies are 20 and 28 meV, respectively. However,
it is important to notice that such effects are small in
the present case of a reaction with a low exoergicity,
and thus do not induce significant errors in the
derived rovibrational distributions. An experimental
proof of this was found with spectra at a selected
kinetic energy which look identical when being
recorded with different velocity vectors and intersec-
tion angles Ždifferent Newton diagrams.. Hence, the
spectrum of Fig. 2 at ´ s74 meV Žz s1800 m
and 2250 s at ´ s74 meV.
tr
2
q
The manifold of the accessible AlOŽX S . rovi-
brational states depends on the total energy available
to reaction products:
´tot s´ q´
Ž
Al
.
q´i
Ž
.
O2 yD´0
tr
i
X
s´ q´iŽAlO
.
q´i
Ž
O
.
,
Ž .
2
tr
where ´ stand for the respective internal energies,
i
D´0 for the reaction ergicity taken as the energy
tr
Al
y1
y1
difference between the zero point energies of reac-
s
, z s955 m s , and uspr8. was found to
be identical to another spectrum at the same energy
O
2
X
tants and products, and ´ for the recoil energy.
tr
2
y1
y1
Nearly pure AlŽ P . beams were used at low ki-
netic energy Žsee Table 1. and, since the O internal
Žz s780 m s , z s740 m s , and us1.52
1
r2
Al
O
2
rad Ž878... The latter spectrum is not shown here due
2
energy was negligible, the total energy of the reagents
was restricted to the kinetic relative translational
energy.
to space limitations but it looks the same as a
previous one ŽFig. 2 in Ref. w7x. obtained with the
former crossed beam machine at a comparable ki-

C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
235
2
q
Fig. 2. Excitation spectra of the AlOŽX S . product at selected kinetic energies. Beam conditions: ´ s6 meV Ž3 collided with B at
tr
uspr8., ´ s12 meV Ž1 collided with A at uspr8., ´ s74 meV Ž4 collided with A at uspr8..
tr
tr
y1
netic energy, ´ s83 meV Žz s810 m s , z s
gases. This remarkable feature prompted us to re-ex-
amine the problem of the spin–orbit selective reac-
tivity. The method is fairly simple. With two Al
tr
Al
O
2
y1
6
60 m s , and uspr2..
3
.2. Spin–orbit reactiÕity
beams, beam 1 ŽN carrier gas. of spin–orbit popula-
2
1
1
tions P1 and P , beam 2 ŽNe carrier gas. of
r2
3r2
2
2
3r2
As can be seen in Table 1, Al beams of the same
spin–orbit populations P1 and P
collided with
r2
velocity but with markedly different populations of
spin–orbit states were obtained with different carrier
the same O beam, ŽA entry, Table 2., one had to
2
2
measure: Ž1. the LIF intensity of AlŽ P ., I1r2; Ž2.
1
r2

2
36
C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
then at each selected kinetic energy, i.e. at each
selected beam intersection angle, the LIF intensity of
AlO at the Ž1–0. bandhead, IAlO; and Ž3. solve the
simplified two-linear-equation system:
1
1
1
1
I
A I
A I
Ž
Ž
s
s
qs3r2 =P rP
.
.
,
Ž
Ž
3a
3b
.
.
AlO
1r2
1r2
1r2
3r2
1r2
2
AlO
2
1r2
2
2
1r2
I
qs3r2 =P rP
3r2
to extract the ratio s3r2rs1r2. Each measurement,
however, required a set of 4 LIF intensities deter-
mined with low dispersion values and no systematic
errors at all. The measurements were thus conducted
as follows: Ž1. the laser was tuned at the AlOŽ1–0.
bandhead and a batch of 100 shots was acquired at
Fig. 3. Relative spin–orbit reactivity. Symbols: open circles, this
Letter; dashed line, ACCSA calculations in the highrlow energy
limits ŽRef. w18x..
uspr8 with beams 1 and A on; Ž2. the laser was
2
2
0
tuned to the centre of the 5d D § 3p P
tran-
3
r2
1r2
sition and a batch of 500 shots was acquired with
beam 1, then a batch of 500 shots with beam 2, and a
batch of 500 shots with beam 1 again to be sure that
no drift had occurred; Ž3. the laser was tuned back to
the AlOŽ1–0. bandhead, and batches of 100 shots
2
The results plotted in Fig. 3 show that AlŽ P
.
r2
3
2
reacts ;3–4 times less than AlŽ P . with O at
1
r2
2
the lowest kinetic energy sampled, ´ s12 meV,
tr
were acquired at 16 angles between 3pr4 and pr8
for beams 1 and A on, then 2 and A on; Ž4. sequence
Ž3. was repeated 4 times to increase the sample size;
Ž5. sequence Ž1. was repeated to check that no drift
had occurred and to validate the whole series of
measurements.
and that the gap in reactivity tends to reduce with
increasing kinetic energy. This is different from the
results of Chen et al. obtained at kinetic energies
y1
above 74 meV Žz s640, 1720, 3000 m s , z s
Al
O
2
y1
750 m s , and uspr2. who concluded that
2
AlŽ P . is the only reactive spin–orbit component
1
r2
Uncertainties in the determined ratio s3r2rs
w3x. Theoretical work w4x based on the ACCSA
method shows that the difference in reactivity arises
from the different contributions of the long range
1r2
were evaluated using two different methods. The
first one consisted of a direct resolution of the
two-equation system for all experimental data
2
potential. For AlŽ P ., the reaction is controlled by
1
r2
1
, 2
recorded Ži.e., two samples of 400 shots for I
and
the dispersion forces at any kinetic energy whereas
AlO
1
, 2
2
two samples of 500 shots for I1 .. The least-squares
for AlŽ P . the reaction is governed by electro-
r2
3r2
procedure used yielded a direct estimate of the vari-
ance on the ratio. The alternate method was based on
a simple resolution of the two-equation system for
static quadrupole–quadrupole interactions at low en-
ergy, but again by dispersion forces at high energy.
The theoretical low and high energy limits w18x, also
given in Fig. 3, are in agreement with the present
determination.
1
, 2
1, 2
the I
and I
sample means, and a subsequent
AlO
1r2
analysis of the variance. Both methods yielded simi-
lar results. An uncertainty of "10% on the spin–orbit
population ratio PŽ3r2.rPŽ1r2. was introduced into
the calculations Žboth methods.. The covariance be-
2
3.3. Excitation function for Al( P )qO reactiÕe
1
r 2
2
collisions
tween AlO and Al intensities, which could not be
measured, was neglected. However, since both these
terms are likely to be strongly correlated Žwith a
positive covariance. this results in an overestimate of
the uncertainty on the final result, s3r2rs1r2. The
uncertainties, given at 95% confidence interval, are
displayed in Fig. 3.
Cross-section measurements, performed with al-
2
most pure AlŽ P . beams, were based on the acqui-
1
r2
sition of batches of 50 shots of the AlO LIF intensity
at the Ž1–0. bandhead, at 46 angles between 3pr4
and pr8 with beams 1 and A Ž255–12 meV., at 10
angles between pr2 and pr8 with beams 1 and B

C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
237
Ž122–15 meV., and at 28 angles between pr2 and
pr8 with beams 3 and B Ž82–6 meV..
The former excitation function normalised in the
same way and obtained between 420 and 41 meV w1x
is also displayed in Fig. 4. The agreement in the
The total reaction cross-section, s1
,
for
r2
2
AlŽ P .qO reactive collisions, can be derived
common energy domain Ž255–41 meV. is excellent.
1
r2
2
from the following expression:
The sharp decrease of the cross-section above ´ s
tr
2
300 meV revealed in the former experiments could
not be verified due to lower signal-to-noise in the
LIF AlO signal at high energies. Indeed the nozzles
are at larger distances in the present experiment to
allow for a beam intersection angle of uspr8, and
the new atom-beam source is less efficient than the
former one when high velocity beams have to be
generated.
dwAlOxrdtss1r2zr Al P
wO x ,
4
Ž .
ž
1r2
/
2
where the total flux of production, dwAlOxrdt, is
related to the relative LIF intensity measured at the
AlOŽ1–0. bandhead, through the knowledge of the
Y
Y
rovibrational populations PŽÕ , N . determined from
2
the LIF excitation spectra. The relative wAlŽ P .x
1
r2
densities of beams 1 and 3 were measured. The
relative densities of A and B O beams could not be
2
determined. Two sets of data where thus obtained
3
.4. Thermal rate coefficient
yielding two distinct plots of ln
tion of ln
w1x. However, these two plots are
almost linear in their common energy domain Ž12–
22 meV., exhibiting
typical functionality
Äs1 wO x4
as a func-
r2 2
Ä
´tr
4
The thermal rate coefficient, kŽT., is related to
the excitation functions as follows:
1
a
a
s1 Ž´ . A
Ä
´tr
4
, with the same slope Ža f
k
Ž
T
.
s ÝP
Ž
T
.
²si
Ž
´tr
.
zr :
T
,
5
Ž .
r2
tr
i
i
y0.82.. This allowed the data to be normalised
Žnormalisation to s s1 was done for ´ s<D´ <
where the symbol ² . . . : stands for averaging over
a Maxwell distribution of relative velocities at tem-
perature T, and s Ž´ . the excitation function for
any combination, indexed i, of reactant internal
states; the sum extends over a normalised, Boltz-
mann distribution, P ŽT., of reactant internal ener-
gies. If the influence of O -reactant internal energy is
neglected, the sum is then restricted to spin–orbit
1
r2
tr
0
T
s155 meV., and then plotted as a function of
relative translational energy at the same scale. This
yielded the excitation function displayed in Fig. 4.
The fact that the three runs give exactly the same
result in their common energy domain is clear proof
that the dynamical result, the excitation function, is
not sensitive to the laboratory conditions Žkine-
matics..
i
tr
i
2
2
states of AlŽ P ., Js1r2 and 3r2:
J
k
Ž
T
.
s ÝP
Ž
T
.
kJ
Ž
T
.
,
Ž
6
.
J
J
with
kJ
Ž
T
.
s²sJ
Ž
´tr
.
zr :
T
`
1
r2
sJ ueyu du ,
s
Ž
8kTrpm
.
H
Ž
7
.
0
where us´ rkT. The integral normally extends
tr
from zero to infinity.
The rate coefficient has been computed using Eqs.
Ž6. and Ž7. for thermal distributions of aluminium
atoms. This calculation requires analytical expres-
sions of the experimental excitation functions. The
following functions have been used: s Ž´ . A
1
r2
tr
Fig. 4. Excitation function Žs1r2 in arbitrary units.. Symbols and
a
Ä
´tr
4
, with a f y0.82, and
Ž´ . s y =
Ž´ .; the ratio yss rs
has been taken
1r2
s
3r2
tr
beam conditions: open down-triangles, 3 collided with B; open
up-triangles, 1 collided with A; open diamonds, 1 collided with B;
filled circles, former results ŽRef. w1x..
s
1r2
tr
3r2
b
yb
as: ysB
Ä 4
´ , with the parameters Bs1.22 eV
tr

2
38
C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
and bs0.41 Žfor ´ in eV. chosen to give the best
tr
fit to the experimental values of this ratio. In fact,
the functional form of this ratio has almost no influ-
ence on the result: at energies below the energy
2
domain sampled, AlŽ P . is not significantly popu-
3
r2
lated; at energies beyond that domain, collisions are
highly improbable since the Maxwell distribution
function becomes negligible at any temperature
within the domain sampled.
With these functions, the rate coefficient can also
be analytically calculated, which allows testing of
the influence of truncation on the numerical integra-
tion. On the one hand, when the upper bound of
integration is set at the highest energy sampled in
this experiment instead of infinity, i.e. 255 meV, the
truncation error remains negligible even at the high-
est temperature sampled Ž1083 K.. On the other
Fig. 5. Thermal rate constant. Symbols: filled circles, experimen-
tal kinetic data ŽRef. w5x.; triangles, experimental kinetic data ŽRef.
w2x.; solid line, calculated curve Žthis Letter.; dashed line, ACCSA
rate constants ŽRef. w4x..
hand, setting the lower bound to the lowest energy
sampled in the experiment, instead of 0, i.e. 6 meV,
strongly affects the result of the computation, and
would prevent computing of the rate coefficient for
temperatures lower than 50 K Žat 20 K, 95% of the
collisions occur with a relative translational energy
lower than 6 meV.. It is thus essential to extrapolate
the excitation function down to low energy Žusing its
functional form. to recover the rate coefficient at low
one hand, an unsuspected experimental error can
affect the determination of the present excitation
function and a slight change in the exponent, i.e.
afy0.7, instead of the y0.82 fitted value, is
sufficient to give a close match between kinetic and
dynamic results over the whole temperature range.
On the other hand, the kinetic measurements at very
low temperature ŽT-50 K. were performed at buffer
gas pressures which might have been insufficient to
maintain the equilibrium of the Al spin–orbit states
w19x during the reactive process. The stronger reactiv-
temperature. A lower bound truncation should never-
theless be introduced to reflect the presence of an
energy barrier. However, computations show that the
presence of such a threshold, even low, would cause
the rate coefficient to exhibit a maximum within the
temperature range of a CRESU experiment Žat TG40
K for threshold energyG2 meV., which is not ob-
2
ity of AlŽ P . towards O indeed induces a dise-
1
r2
2
quilibrium which might have yielded slightly under-
estimated rate coefficients in measurements based
2
solely on the AlŽ P . disappearance. To conclude,
1
r2
we also note that our calculated values are in excel-
lent agreement with the theoretical ACCSA rate
constants.
served experimentally. It is thus very unlikely that
this reaction might have a significant energy barrier
ŽG2 meV.. The results displayed in Fig. 5 were
obtained by assuming the absence of any barrier, and
extrapolating the excitation function down to ´ s0.
Acknowledgements
tr
Computed values are normalised to the experimental
data at 295 K w4x. The normalisation yields the value
The authors wish to thank Professor W.R. Gentry
for his help in the design of the apparatus, the
Conseil R e´ gional d’Aquitaine for financial support,
and the S.E.I.V. Aquitaine for the perfect machining
of the scattering chamber. The authors also thank
Professor D. Liotard for his help in the statistical
treatment of errors. This work was supported by
European Union TMR contract FRMX-CT97-0132
ŽDG12-MIHT..
2
of the absolute cross-section: s1r2 f0.12 nm at
´tr s155 meV. Very high cross-sections are thus
2
reached at low kinetic energy, e.g. 1.2 nm at ´ s6
tr
meV.
There is a good agreement between the present
computed values and the two sets of kinetic data.
The agreement is, however, not perfect. The differ-
ence observed might be due to several causes. On the

C. Naulin, M. CostesrChemical Physics Letters 310 (1999) 231–239
239
w10x W.R. Gentry, in: G. Scoles ŽEd.., Atomic and Molecular
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