Measurement of Br photofragment orientation and alignment from HBr photodissociation: Production of highly spin-polarized hydrogen atoms

Article abstract of DOI:10.1063/1.1794691

The use of slice imaging to measure the orientation and alignment of ²P_3/2 and ²P_1/2 photofragments at 193 nm in terms of polarization parameters, a_q^k(p) parameters, was described. The photofragments were obtained from the photodissociation of HBr. It was found that the photodissociation was a source of spin-polarized hydrogen. The spin-orbit branching ratio and the polarization parameters showed that the photodissociation proceeded predominantly via nonadiabatic transition to the a³π and 1³∑⁺ states. It was also found that the electrons of the nascent H atom cofragments were highly spin polarized.

Full text of DOI:10.1063/1.1794691

Measurement of Br photofragment orientation and alignment from HBr
photodissociation: Production of highly spin-polarized hydrogen atoms
T. Peter Rakitzis, P. C. Samartzis, R. L. Toomes, and Theofanis N. Kitsopoulos
Citation: The Journal of Chemical Physics 121, 7222 (2004); doi: 10.1063/1.1794691
View online: http://dx.doi.org/10.1063/1.1794691
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 15
15 OCTOBER 2004
Measurement of Br photofragment orientation and alignment from HBr
photodissociation: Production of highly spin-polarized hydrogen atoms
T. Peter Rakitzis
Department of Physics, University of Crete, P.O. 2208, 71003 Voutes-Heraklion, Greece
and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas,
711 10 Heraklion-Crete, Greece
P. C. Samartzis
Department of Chemistry, University of Crete, Leof. Knosou, 71409 Heraklion, Greece
and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas,
711 10 Heraklion-Crete, Greece
R. L. Toomes
Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas,
711 10 Heraklion-Crete, Greece
Theofanis N. Kitsopoulos
Department of Chemistry, University of Crete, Leof. Knosou, 71409 Heraklion, Greece
and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas,
711 10 Heraklion-Crete, Greece
͑Received 7 July 2004; accepted 27 July 2004͒
The orientation and alignment of the 2P3/2 and 2P1/2 Br photofragments from the photodissociation
of HBr is measured at 193 nm in terms of a(qk)(p) parameters, using slice imaging. The A 1⌸ state
is excited almost exclusively, and the measured a(qk)(p) parameters and the spin-orbit branching
ratio show that the dissociation proceeds predominantly via nonadiabatic transitions to the a 3⌸ and
1 3⌺ϩ states. Conservation of angular momentum shows that the electrons of the nascent H atom
cofragments ͑recoiling parallel to the photolysis polarization͒ are highly spin polarized: about 100%
for the Br(2P1/2) channel, and 86% for the Br(2P3/2) channel. A similar analysis is demonstrated for
the photodissociation of HCl. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1794691͔
I. INTRODUCTION
systems that yield highly polarized fragments. Strongly po-
larized atomic photofragments have been measured for O,8,9
S,10–12 Cl,13–16 Br,11,13 and H.12 The present study investi-
gates the potential of HBr as a source of highly polarized H
and Br photofragments.
The measurement of photofragment angular momentum
polarization, and the spatial decomposition of this polariza-
tion into coherent and incoherent contributions from multiple
dissociative states, has intensified in recent years since the
quantum mechanical treatment of Siebbeles et al.1–4 These
contributions to the photofragment angular distributions can
be expressed in terms of the a(qk)(p) parameters,5 where ͑p͒
denotes whether the contribution originates ͑incoherently͒
Recently, the alignment parameters a(02)(Ќ) and a2(2)
ϫ(Ќ) were measured for Br(2P3/2) from the photodissocia-
tion of HBr at 193 nm using slice imaging,17,18 a variant of
ion imaging,19 and velocity mapping.20 For HCl, it was
shown that the H atom cofragments were strongly spin po-
larized, demonstrating that photodissociation can provide an
intense source of spin-polarized hydrogen. The aim of this
paper is to determine the Br(2PJ) and H cofragment polar-
ization as well, and to include in the analysis the effects of
the polarization parameters a(qk)(p) with kр3 for the
Br(2P3/2) and Cl(2P3/2) photofragments from the photodis-
sociation of HBr and HCl at 193 nm. a(qk)(p) can then be
expressed in terms of dynamically significant variables such
as nonadiabatic transition probabilities and asymptotic phase
differences.6 From these expressions, we deduce the degree
of polarization of the photofragments, and the nonadiabatic
dissociation mechanisms.
ʈ
from a dissociative transition that is parallel ͑ ͒ or perpen-
dicular ͑Ќ͒, or ͑coherently͒ from the interference between
parallel and perpendicular transitions ͑ ,Ќ͒. The measure-
ʈ
ment of each a(qk)(p) parameter gives specific information
about the dissociation process. Recently, for hydrogen halide
photodissociation, Balint-Kurti et al. expressed a(qk)(p) in
terms of adiabatic and nonadiabatic-transfer probabilities,
and in terms of phase shifts between asymptotic wave func-
tions of dissociative states.6 Therefore, measurement of a(qk)
ϫ(p) allows the most complete understanding of the disso-
ciation process, and detailed comparison with theory.
Polarized atoms and nuclei are used to study spin-
dependent effects in atomic, molecular, nuclear, and surface
collisions. The possibility of the production of highly polar-
ized atoms from molecular photodissociation was suggested
by van Brunt and Zare.7 The measurement of atomic photo-
fragment polarization ͓such as the measurement of the com-
plete set of a(qk)(p) parameters͔ allows the identification of
II. THEORY
The spatial distribution of unpolarized photofragments
about the linearly polarized photolysis direction light is
given by the well-known expression.21
0021-9606/2004/121(15)/7222/6/$22.00
7222
© 2004 American Institute of Physics
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
HBr photodissociation
7223
The contributions from the kϭ2 and kϭ3 parameters
will be significantly less than the kϭ1 parameters, mainly
because these parameters are reduced more by hyperfine de-
polarization ͑the kϭ1, 2, and 3 parameters are reduced by
factors of 0.5, 0.27, and 0.2, respectively͒. Therefore, for a
first approximation, the data for the (2P3/2) photofragments
can be analyzed with the kϭ1 parameters only, using Eqs.
͑3͒ and ͑4͒, as for the (2P1/2) photofragments. It will be
interesting to compare this analysis to a more complete
analysis including higher order a(qk)(p) parameters.
I ␪͒ϭI 1ϩ␤P cos ␪͒ ,
͑1͒
͑
͓
͑
͔
0
2
where ␤ is the spatial anisotropy parameter, which, for
prompt photodissociation of a diatomic molecule, ranges
from Ϫ1 ͑for a pure perpendicular transition͒ to ϩ2 ͑for a
pure parallel transition͒, and I0 is a constant. However, a
more complicated expression is required for the description
of the angular distribution of photofragments which have
been detected in a fashion sensitive to angular momentum
polarization of the fragments ͓such as resonantly enhanced
multiphoton ionization or caser-induced fluorescence͔. When
the photolysis and probe polarization directions are parallel
͑for either linearly or circularly polarized light͒, and for J
р3/2, the photofragment angular distribution is given by:
We can express the (2P3/2) photofragment angular dis-
tributions in terms of the non-negligible ͑in this case͒ kϭ2
and kϭ3 a(qk)(p) parameters:
I ␪͒ϭI 1ϩ␤ P cos ␪͒ϩ␤ P cos ␪͒ ,
͑2͒
͑
͓
͑
͑
͔
0
2
2
4
4
s1
͑1͒
͑1͒
ʈ
Ќ͒ϩͱ2 Re a
͓
I0ϭ1ϩ
1Ϫ␤/2͒a
,Ќ͒
͑
͓͑
͑
͔͔
0
1
3
where I0 , ␤2 , and ␤4 are parameters that depend on ␤ and
a(qk)(p). The experiments reported in this paper deal with a
single laser geometry, that with counterpropagating photoly-
sis and probe lasers, which are both circularly polarized.
For the Br(2P1/2) and Cl(2P1/2) photofragments, k is
limited to 1 ͑as kр2J). In this case, ␤4ϭ0, and I0 and ␤2
1Ϫ␤/2͒s
͑
2
͑2͒
͑2͒
2
Ќ͒Ϫ2ͱ6a
͑
ϩ
a
Ќ͒ ,
͑5͒
͓
͑
͔
0
15
ͱ2 Re a
1 2s1
͑1͒
͑1͒
(1)
expressed in terms of ␤, a(01)(Ќ), and Re a ( ,Ќ) by:
22,23
ʈ
ʈ
␤2ϭ
1Ϫ␤/2͒a Ќ͒Ϫ
,Ќ͒
͔
͑
͑
͓
͑
͓
͔
ͫ
ͩ
ͪ
0
1
1
I0
3
2
s1
͑1͒
0
͑1͒
1
4 1Ϫ␤/2͒s
͑
ʈ
Ќ͒ϩͱ2 Re a
͑ ͓
2
I0ϭ1ϩ
1Ϫ␤/2͒a
,Ќ͒ ,
͔͔
͑3͒
͓͑
͑
͑2͒
0
͑2͒
Ќ͒ϩͱ6a
͑
ϩ
4a
Ќ͒͒
͑
͑
3
2
21
ͱ2 Re a
1 2s1
8ͱ3 Re a
͑1͒
͑1͒
s3
ʈ
͑3͒
͑3͒
␤2ϭ
1Ϫ␤/2͒a Ќ͒Ϫ
,Ќ͒
͑ ͔
͑
͑
͓
ͫ
ͩ
ͪ
0
1
ʈ
ϩ
3 1Ϫ␤/2͒a Ќ͒Ϫ
,Ќ͒
͑
͑
͑
͓
͔
ͩ
ͪ
I0
3
2
0
1
7
2
Ϫ␤/2 ,
͑4͒
ͬ
Ϫ␤/2 ,
͑6͒
͑7͒
ͬ
where s1 is the experimental sensitivity to the kϭ1 param-
eters, which depends on the details of the detection transition
͑given in the Experimental section͒. The value of ␤ for both
Br(2P1/2) and Cl(2P1/2) has been measured previously,
therefore there are only two unknowns, a(01)(Ќ) and
1
1Ϫ␤/2͒s
͑
2
͑2͒
0
͑2͒
2
Ќ͒Ϫ2ͱ6a
␤4ϭ
6a
Ќ͒͒
͑
͑
͑
ͭ
I0
35
4s3
͑3͒
0
͑3͒
1
(1)
1
ʈ
Ќ͒ϩͱ3 Re a
͓
ϩ
1Ϫ␤/2͒a
,Ќ͒
.
͓͑
͑
͑
͔͔
ʈ
ͮ
Re a ( ,Ќ) . It is convenient to measure I only as a relative
͓
͔
0
7
quantity, such as the ratio of I0 between the two polarization
geometries I0 RL /I RR ͑where the first R indicates that
͓
͔
͓
͔
0
The parameters a0(2)( ) and a(23)(Ќ) have been omitted from
Eqs. ͑5͒–͑7͒ because their contribution to the experimental
signals ͑for the experiments considered in this paper͒ can be
ʈ
the photolysis polarization is circularly polarized, and the
second R or L indicates that the probe polarization is either
right or left circularly polarized, respectively͒. This ratio is
given by the ratio of Eq. ͑3͒, measured for the two geom-
etries. Another equation can be generated by subtracted the
neglected. The contribution of the a(02)( ) parameter is
ʈ
weighted by ͑1ϩ␤͒; for both Cl and Br(2P3/2) photofrag-
ments, ␤ϭϪ1, so that ͑1ϩ␤͒Ϸ0 ͓the magnitude of the con-
␤
values
for
these
two
geometries:
⌬␤2
2
tribution of a(02)( ) parameter is a few times smaller than the
ʈ
ϭ␤2(RL)-␤2(RR), using Eq. ͑4͒. These two equations can
sensitivity of the experiment͔ and therefore a(02)( ) can be
(1)
1
be solved for the two unknowns a(01)(Ќ) and Re a ( ,Ќ) in
ʈ
ʈ
͓
͔
neglected. The a(23)(Ќ) parameter is proportional to
terms of the experimental observables I0 RL /I RR and
͓
͔
͓
͔
0
sin ⌬␸Aa ,6 where ⌬␸ is the asymptotic phase shift between
⌬␤2 .
Aa
the A 1⌸ state and a 3⌸ state ͑⍀ϭ0 component͒. The phase
shift was both measured11 and predicted24 to be approxi-
mately zero at this photodissociation wavelength; therefore,
the contribution from the a(23)(Ќ) parameter can also be ne-
glected in this case. Furthermore, both a(01)(Ќ) and a0(3)(Ќ)
can be expressed in terms of nonadiabatic transition prob-
abilities between the A 1⌸ and a 3⌸ states ͑see the Discus-
sion section͒; these expressions allow, in this case, a(03)(Ќ)
to be related in terms of a(01)(Ќ):
For the Br(2P3/2) and Cl(2P3/2) photofragments, k is
limited to 3, and now I0 , ␤2 , and ␤4 are expressed in terms
of kϭ2 and kϭ3 parameters as well. The complete inver-
sion of all the a(qk)(p) with kр3 would require more detec-
tion geometries or detection transitions ͑beyond the one used
here͒. However, in this particular case, the contribution of
several parameters are negligible, so that approximations can
be made to reduce the number of unknown parameters to be
equal to the set of experimental observables.
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7224
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Rakitzis et al.
4
2
͑3͒
͑1͒
a0 Ќ͒ϭ a0 Ќ͒Ϫ
.
͑8͒
͑
͑
ͫ
ͬ
5
ͱ
15
Using these approximations, we have reduced the number of
unknown parameters to 3 the a(01)(Ќ), Re a ( ,Ќ) , and
(1)
ʈ
͓
͔
1
(3)
2
ʈ
Re a ( ,Ќ) . As with Eqs. ͑3͒ and ͑4͒ for the ( P1/2) atoms,
͓
͔
1
Eqs. ͑5͒–͑7͒ can be used to generate three new equations:
I0 RL /I RR , ⌬␤ , and ⌬␤ . These three equations can
͓
͔
͓
͔
0
2
4
be solved for the three unknowns.
III. EXPERIMENT
The apparatus has been described in detail
elsewhere.14,25 Briefly, a 10 Hz pulsed molecular beam con-
taining 5% HBr or HCl in He is skimmed and collimated,
and is intersected at right angles by two counter propagating
laser beams. The photolysis laser beam is generated by an
ArF excimer laser ͑COMPEX, Lambda Physik͒; the linearly
polarized Brewster reflection from a suprasil window is then
circularly polarized with a quarter-wave plate, and is focused
onto the molecular beam (fϭ25 cm). The probe laser beam
is generated by MOPO-SL ͑Spectra Physics 730DT10͒, and
is also made circularly polarized using a quarter-wave plate.
The Br(2P3/2) and Br(2P1/2) photofragments are ionized us-
ing the two-photon resonant transitions 5p(2P1/2
4p5(2P3/2) at 250.41 nm and 5p(2P3/2 4p5(2P1/2) at
263.12 nm, whereas the Cl(2P3/2) and Cl(2P1/2) photofrag-
)
)
ments are ionized at 4p(2P1/2
)
3p5(2P3/2) at 234.62 nm
FIG. 1. ͑a͒ Br(2P1/2) and Br(2P3/2) photofragments slice images following
the photolysis of HBr at 193 nm. The photolysis laser is right ͑R͒ circularly
polarized, and the counterpropagating probe laser is right ͑R͒ or left ͑L͒
circularly polarized. These distinct polarization geometries are denoted RR
and RL, respectively. ͑b͒ The Br(2P1/2) and Br(2P3/2) photofragment angu-
lar distributions calculated from the images shown in ͑a͒ ͑and described in
the text͒.
and 4p(2P3/2
)
3p5(2P1/2) at 236.51 nm, respectively.26–28
2
For the ionization of the P3/2 photofragments, for right ͑up-
per sign͒ and left ͑lower sign͒ circularly polarized light, the
ͱ
sk are given by: s1ϭϯ3 3/5(1/2), s2ϭϩ(5/4)(10/37), and
ͱ
s3ϭϯ 15/4(1/5) ͑note that the long-time-limit hyperfine
depolarization coefficients are included in these factors; 1/2
for kϭ1, 10/37 for kϭ2, and 1/5 for kϭ3).29 For the P1/2
2
ͱ
atoms, s1ϭϯ 3(1/2) ͑which includes the depolarization co-
the photolysis and probe are linearly polarized parallel to the
time-of-flight axis͒ and are then fit to Eq. ͑2͒.13 The slice
efficient of 1/2͒. Using the slice-imaging technique, 400 ns
after the photofragment ionization, the extraction field is
pulsed ON, and the Brϩ or Clϩ ions are accelerated towards
the ion-imaging detector. Ions of different mass separate in
their time-of-flight during their field-free trajectory on route
to the detector. The detector gain is pulsed ON for ϳ20 ns at
the proper arrival time for slice-imaging velocity selection.14
Images appearing on the detector anode are recorded using a
charged-coupled device camera ͑Cohu 4910, using EYESPY
Software by k-Space Associates Inc.͒. Images are taken with-
out Doppler scanning. Effects of Doppler selection are re-
moved by normalizing the images with images taken with
both photolysis and probe polarizations linear and perpen-
dicular to the imaging plane.13
images and angular distributions for Cl(2P3/2) and Cl(2P1/2
)
are shown elsewhere.12 The variations in I0 , ␤2 , and ␤4
between the RL and RR geometries are given by
I0 RL /I RR , ⌬␤ , and ⌬␤ are shown in Table I for
͓
͔
͓
͔
0
2
4
both B(2PJ) and Cl(2PJ).
The polarization of the Br(2P1/2) photofragments is de-
scribed by the a(01)(Ќ) and Re a ( ,Ќ) parameters only ͑be-
(1)
1
ʈ
͓
͔
cause kр2J, and is limited to 1 in this case͒. The values for
the variations in intensity and angular distributions ͓given by
I0 RL /I RR and ⌬␤2 described in the Theory and Re-
͓
͔
͓
͔
0
TABLE I. The Br and Cl(2PJ) difference anisotropy parameters, ⌬␤2
ϭ␤2(RL)-␤2(RR), and ⌬␤4ϭ␤4(RL)-␤4(RR), and the intensity ratios
I0 RL /I RR ͓see Eqs. ͑1͒ and ͑2͔͒. The first R indicates that the photoly-
sis polarization is right circularly polarized, and the second R or L indicates
͓
͔
͓
͔
0
IV. RESULTS
The Br(2P3/2) and Br(2P1/2) photofragment slice images
are shown for the RR and RL polarization geometries in Fig.
1. The angular distributions ͑also shown in Fig. 1͒ are deter-
mined by integrating the signal within the full width at half
maximum of the Br-photofragment slice-image radius as a
function of ␪. The angular distributions are normalized with
the corresponding ZZ angular distribution ͑for which both
that the probe polarization is either right or left circularly polarized, respec-
tively. For the ⌬␤2 and ⌬␤4 , ␴ϭ0.05, and for I0 RL /I RR , ␴ϭ0.1.
͓
͔
͓
͔
0
Br(2P3/2
)
Br(2P1/2
)
Cl(2P3/2
)
Cl(2P1/2
)
0.63
Ϫ0.23
1.6
0.20
Ϫ0.03
1.75
0.97
Ϫ0.11
1.4
0.33
0.02
1.8
⌬␤2
⌬␤4
I0 RL /I RR
͓ ͔
͔
͓
0
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J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
HBr photodissociation
7225
TABLE II. Calculated polarization parameters for Br and Cl(2PJ), using the
experimental data from Table I and Eqs. ͑3͒–͑7͒. Measurements of ␤, a0(2)
ϫ(Ќ), and a(22)(Ќ) are given from Ref. 11. Error bars are 2␴.
⌬␤4 , are inserted into Eqs. ͑5͒–͑7͒. These three equations
(1)
(3)
are then solved for a0(1)(Ќ), Re a ( ,Ќ) , and Re a ( ,Ќ)
ʈ
ʈ
͓
͔
͓
͔
1
1
parameters, shown in Table II and Fig. 2.
It is worth noting that if the (2P3/2) data is analyzed
Br(2P3/2
)
Br(2P1/2
)
Cl(2P3/2
)
Cl(2P1/2
)
ignoring the kϭ2 and kϭ3 parameters, using Eqs. ͑3͒ and
␤
Ϫ0.88Ϯ0.10 Ϫ0.21Ϯ0.10 Ϫ0.97Ϯ0.06 Ϫ0.87Ϯ0.06
ϩ0.30Ϯ0.07 ϩ0.55Ϯ0.16 ϩ0.39Ϯ0.08 ϩ0.60Ϯ0.10
ϩ0.09Ϯ0.08 ϩ0.46Ϯ0.16 Ϫ0.06Ϯ0.10 ϩ0.32Ϯ0.12
(1)
͑4͒, then, for Br(2P3/2) a(1)(Ќ)ϭ0.38 and Re a ( ,Ќ)
ʈ
͓
͓
͔
͔
a(01)(Ќ)
0
1
ϭ0.04, and for Cl(2P3/2) a(1)(Ќ)ϭ0.42 and Re a ( ,Ќ)
(1)
Re a(1)( ,Ќ)
ʈ
ʈ
͓
͔
͔
0
I
1
a(02)(Ќ)
ϭϪ0.13. These numbers deviate less then 10% of the physi-
cal range of the parameters from the more complete analysis
using kϭ2 and kϭ3 parameters as well. Therefore, it seems
that the kϭ1 parameters can be measured fairly accurately to
a first approximation by ignoring the higher-order parameters
in this case. However, this approximation is unlikely to hold
in cases where the higher-order parameters are not reduced
by hyperfine depolarization, such as in O(1D) and S(1D).
Ϫ0.7Ϯ0.2
Ϫ0.3Ϯ0.2
Ϫ0.22Ϯ0.14
¯
¯
¯
Ϫ0.5Ϯ0.2
Ϫ0.45Ϯ0.2
Ϫ0.12Ϯ0.15
¯
¯
¯
a(22)(Ќ)
Re a(3)( ,Ќ)
ʈ
͓
1
sults sections, determined from fitting with Eq. ͑1͒ and given
in Table I, are inserted into Eqs. ͑3͒ and ͑4͒. These two
equations are then solved for a(01)(Ќ) and Re a ( ,Ќ) pa-
(1)
1
ʈ
͓
͔
rameters, shown in Table II and Fig. 2. Note that even though
V. DISCUSSION
⌬␤2 for the Br(2P1/2) photofragments is small, the values of
(1)
the a(01)(Ќ) and Re a ( ,Ќ) parameters are found to be near
ʈ
͓
͔
HBr is optically excited at 193 nm predominantly via the
perpendicular transition A 1⌸ X 1⌺ϩ, and at this photodis-
sociation wavelength the spatial anisotropy ␤ of the
Br(2P3/2) photofragments us close to the limiting value of
Ϫ1.11,30–33 Here we use the value of ␤ϭϪ0.88 we have re-
ported previously,11 which may indicate a small contribution
of an ⍀ϭ0 component to the excitation of about 4%. In
contrast, the a 3⌸ (⍀ϭ0 component) X 1⌺0ϩ transition to
the production of Br(2P1/2) photofragments is about 25%.
The phase difference between states i and j is denoted by
⌬␸i, j . In terms of the phase shift between the a 3⌸ ͑⍀ϭ0
1
maximal because of the large value of the I0 RL /I RR
͔
͓
͔
͓
0
(1)
ratio. In particular, a0(1)(Ќ) and Re a ( ,Ќ) parameters are
ʈ
͓
͔
1
both large and positive, so that they largely cancel in Eq. ͑4͒
to give a small value of ⌬␤2 , and add in Eq. ͑3͒ to give a
large value of I0 RL /I RR .
͓
͔
͓
͔
0
For the Br(2P3/2) photofragments, the angular momen-
tum distributions can be described by the perpendicular-
transition alignment parameters, a(01)(Ќ), a(02)(Ќ), and a(22)
(1)
(3)
ʈ
ʈ
ϫ(Ќ), as well as the Re a ( ,Ќ) and Re a ( ,Ќ) interfer-
͓
͔
͓
͔
1
1
ence parameters; the contribution from the a(02)( ), Re a
(2)
1
ʈ
͓
component͒ state and the 1 3⌺1ϩ state, a(qk)(p) for the (2P1/2
)
ϫ( ,Ќ) , and a(3)(Ќ) are neglected as the contributions to the
ʈ
͔
2
atoms are given by
experimental signals are too small to be measured in the
current experiments. The values of ␤, a(02)(Ќ), and a2(2)(Ќ)
used in Eqs. ͑5͒–͑7͒ ͑and shown in Table II͒ are from Ref.
11. Right and left circularly polarized probe light are equally
sensitive to the ␤, a0(2)(Ќ), and a(22)(Ќ) parameters, there-
fore they do not strongly affect the values of the orientation
parameters determined here; in particular, the relatively large
error bars of the a0(2)(Ќ) and a(22)(Ќ) parameters do not
strongly affect the error bars of the orientation parameters.
The values for the variations in intensity and angular distri-
1
͑1͒
Ќ͒ϭ ͱ3
a0
,
͑9͒
͑
2
͑1͒
1
ʈ
ͱ 1ϩ␤͒ 1Ϫ␤/2͒cos ⌬␸
͑
Re a
,Ќ͒ ϭ
.
a0,3⌺
͓
͑
͔
͑
3ͱ3
͑10͒
We see from Fig. 1͑a͒ that the measured values of the a0(1)
(1)
1
2
ʈ
ϫ(Ќ) and Re a ( ,Ќ) parameters, for the Br( P1/2) photo-
͓
͔
butions from Eq. ͑2͒, given by I0 RL /I RR , ⌬␤ and
͓
͔
͓
͔
0
2
fragments, correspond, approximately, to the maximal physi-
cal range of these parameters. Therefore, the measured a0(1)
ϫ(Ќ) is in agreement with Eq. ͑9͒, and the maximal value of
(1)
ʈ
Re a ( ,Ќ) implies that cos ⌬␸
is also approximately
͓
͔
a0,3⌺
1
maximal.
The ⍀ components of the A 1⌸ and a 3⌸ states that
participate in the dissociation, and yield (2P3/2) atoms, cor-
relate asymptotically to the atomic states ͉mA ,mB as
͘
R→ϱ
1
3
2
͉
͉
͉
Ϯ1 ——
ϯ ,Ϯ
,
͑11͒
͑12͒
͑13͒
→
͘
ͯ
ͯ
ʹ
ʹ
A
2
R→ϱ
1
1
2
Ϯ1 ——
Ϯ ,Ϯ
,
→
͘
a
2
R→ϱ
1
1
2
0
——
ϯ ,Ϯ
.
→
͘
FIG. 2. The measured a(qk)(p) polarization parameters for the nascent
Br(2P1/2) and Br(2P3/2) photofragments and the inferred nascent H-atom
electron polarization Pe from the photodissociation of HBr at 193 nm.
ͯ
ʹ
a
2
For the (2P3/2) atoms a(qk)(p) are given by
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7226
J. Chem. Phys., Vol. 121, No. 15, 15 October 2004
Rakitzis et al.
to be 86Ϯ27% ͑2␴͒. The theoretical electron polarization for
the H atoms corresponding to Br(2P1/2) atoms is 100%.
Therefore, the overall H-atom electron polarization is about
88%. The degree of this polarization may be confirmed both
directly35 and theoretically,36 and the polarization may in-
crease at different photodissociation wavelengths.21 This
work shows that HBr photodissociation can be used as an
intense source of spin-polarized hydrogen.
3Ϫ2p͒
͑
͑1͒
a0 Ќ͒ϭϩ
,
͑14͒
͑
ͱ15
͑1͒
1
ʈ
Re a
,Ќ͒ ϭcA,a0 cos ⌬␸A,a0ϩca1,a0 cos ⌬␸
,
͓
͑
͔
a1,a0
͑15͒
͑2͒
a0 Ќ͒ϭϩ 4/5͒ 1Ϫ2p͒,
͑16͒
͑
͑
͑
͑2͒
Ќ͒ϭϪ 4ͱ2/5͒ͱp 1Ϫp͒cos ⌬␸
͑
a2
,
͑17͒
͑18͒
͑
͑
A,a1
2 1Ϫ4p͒
͑
ACKNOWLEDGMENTS
͑3͒
a0 Ќ͒ϭ
,
͑
5ͱ15
This work is conducted at the Ultraviolet Laser Facility
operating at FORTH-IESL ͑Improving Human Potential-
Transnational Access to major Research Infrastructures,
Grant No. HPRI-CT-1999-00074͒ and is also supported by
Grant Nos. HPRN-CT-2002-00183 ͑PICNIC͒ and HPRN-
CT-2000-0006 ͑REACTIVES͒.
where p is equal to p1 /(1Ϫp2); p1 and p2 is the probability
of nonadiabatic transfer from the A 1⌸ to the a 3⌸ state and
1 3⌺1 state, respectively. Notice that Eq. ͑18͒ differs from
Eq. ͑21͒ in Ref. ͑6͒, due to a different convention.
Using either Eq. ͑14͒ or Eq. ͑16͒, we can solve for p, and
obtain 0.93Ϯ0.13. The probability p2 was measured to be
about 2͑0.14͒/3;33,34 hence we determine p1 to be 0.80Ϯ0.10.
Therefore, after excitation to the primary absorber, the A 1⌸
state, only 6% dissociates adiabatically ͓Eq. ͑11͔͒, whereas
80% transfers nonadiabatically to the a 3⌸ state ͓Eq. ͑12͔͒
and 14% to the 1 3⌺1 state, both of which involve an H spin
flip. Using pϭ0.93 and Eq. ͑17͒, we see that ⌬␸A,a1ϭ0. The
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ʈ
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