Measurements of photoelectron angular distributions for
rotationally resolved transitions in para- H2+
A. M. Juarez* , E. Sokell***, P. Bolognesi** , D. Cubric* , G.C. King*
M. De Simone ** and M. Coreno**
*The Department of Physics and Astronomy, University of Manchester. Manchester, UK. M13 9PL
** Instituto di Metodologie Avanzate Inorganiche-CNR, Monterotondo, Italy.
*** Department of Experimental Physics, University College Dublin, Belfield, Dublin 4, Ireland
Abstract. Rotationally resolved measurements of photoelectron angular distributions for the X2 Σg+(ν+=0, N+=0) ground
state of para-H2+ are presented, over the photon energy range, 15.47 to 15.75 eV, that includes most of the dominant
autoionising resonances decaying into the ground ionic state. It is observed that the value of the asymmetry parameter in
this energy interval is close to 2, but sharp variations are observed at particular photon energies. The measurements were
performed using synchrotron radiation, a high-resolution hemispherical analyser and a magnetic angle changer.
β, that characterises the angular distributions, as a
function of photon energy across the region of the
autoionising resonances. At present, only a few
measurements of β-parameters in H2 have been
performed, and those with sufficient energy resolution
to separate rotational states have been made at the
fixed photon energies provided by discharge lamps
[e.g. 3]. Rotationally resolved measurments,
performed over a range of photon energies using
synchrotron radiation, have been limited to a single
observation angle [4]. Previous synchrotron-based
measurements, performed at different angles, have
been limited to integrated measurements over
rotational levels [5].
INTRODUCTION
The photoionisation spectrum of H2 presents a
wealth of rich structure above the first ionisation
threshold [1]. This structure is due to the presence of
autoionising states, 1sσ npσ 1Σ+u and 1sσ npπ 1Π+u,
which dominate the weak continuum of direct
ionisation. These states that correspond to
vibrationally excited Rydberg states may decay to a
lower ionic state by the transfer of energy and angular
momentum from the molecular core to the excited
electron. Measuring the energies of the photoelectrons
emitted during the autoionisation process provides a
means of studying the energy exchanges between
electrons and nuclei. Photoelectron angular
distributions, on the other hand, provide information
on the momentum transferred during the
photoionisation process [2]. In order to understand the
autoionisation process completely these angular
distributions have to be measured with sufficient
energy resolution to separate all the rotational
transitions involved. A complete picture is obtained by
measuring the variation of the asymmetry parameter,
Here,
we
present
rotationally
resolved
measurements of photoelectron angular distributions
for ionisation into the lowest vibrational level of paraH2+, over the photon energy range that includes the
most dominant autoionising resonances. In particular
we present variations, as a function of photon energy,
of the asymmetry, β-parameter in the photon energy
range from 15.47 eV to 15.75 eV. Para-H2 was
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© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
60
employed since it only has even rotational states, thus
making it easier to separate different rotational
transitions. The experimental results presented are
discussed in terms of the relative contributions of
different values of momentum transferred during the
photoionisation process [6].
The high photon flux and resolving power (E/∆E >
10000) provided by the GASPHASE beamline allowed
us to resolve individual autoionising states in para-H2,
which are typically separated by a few meV, whilst
maintaining sufficiently high counting rates.
EXPERIMENTAL ARRANGEMENT
45°
3-5
+
1-3
+
Counts (arb. units)
600
2-0
Para-H 2
+
400
0-2
2-2
0
15.34
15.36
15.38
15.40
+
0-0
15.42
+
+
2-4
15.44
+
15.46
15.48
15.50
15.52
Binding energy (eV)
FIGURE 2. Photoelectron spectra of normal („) and parahydrogen (ο). The dotted lines show the different rotational
transitions X1Σg+(ν’’=0, K’’) → X2Σg+(ν+=0, K) observed in
each species.
Figure 2 shows photoelectron spectra of normal
(black squares) and para-hydrogen (white circles),
respectively, recorded at the photon energy of 15.75
eV. The overall energy resolution in these spectra is 15
meV. For both spectra, the pressure in the chamber
was 5x10-5 mbar and the acquisition time was 1 second
per point. The binding energies of the different
transitions are represented as dotted lines, and were
calibrated against data obtained by high-resolution
threshold photoelectron spectroscopy [9]. The
rotational transitions are labelled according to the
initial (N) and final (N+) rotational states as N-N+.
Comparison of the normal and para-H2 spectra allowed
us to estimate the purity of the para-H2 to be greater
than 99%.
polarization axis
Magnetic anglechanger
(a)
+
200
Incoming synchrotron
radiation
HDA
1-1
800
Capillary array
(towards viewer)
Magnetic angle-changer
(cross sectional view)
+
Normal H 2
In the present work, the photon beam from the
GASPHASE beamline of the Elettra Synchrotron
Radiation Source was crossed with a gas beam of paraH2 effusing from a capillary array. The para-H2 used
was produced at the beamline using a conversion
technique based upon the circulation of normal-H2
through a paramagnetic catalyst maintained at a
temperature of ∼20K [7]. The paramagnetic compound
induces a change in the nuclear spins from the parallel
(ortho-H2) to the antiparallel (para-H2) configuration.
A photoelectron spectrometer of large mean radius
(165mm) was used to provide sufficient energy
resolution to resolve individual rotational transitions.
The spectrometer also allowed the angular
distributions of the photoelectrons to be measured. For
this a magnetic angle changer device [8] was used.
This device consists of three concentric solenoids that
produce a localised magnetic field. It can deflect the
electrons through a well defined angle, for a given
kinetic energy, by suitably adjusting the currents in the
solenoids. Thus it enables photoelecton angular
distributions to be measured without physically
moving the analyser. Figure 1 shows schematically the
relative positions of the hemispherical deflection
analyser (HDA), the magnetic angle changer and the
photon beam.
Capillary array
3-3
1000
By scanning the photon energy and simultaneously
scanning the collection energy of the electron
spectrometer, the excitation function, or constant ionic
state spectrum, of a particular rotational transition can
be determined. In addition, the magnetic angle changer
can be used to obtain the photoelectron angular
distribution of the photoelectrons at each value of
photon energy. The result of this is a measure of the
yield of photoelectrons as functions of both photon
energy and angle and this can be presented as a two-
HDA
(b)
FIGURE 1. The relative positions of the magnetic
angle-changer and the hemispherical deflection analyser.
(a) Front view. (b) Top view.
61
dimensional map. From this map the variation of the
asymmetry parameter, β, with photon energy can be
readily deduced for each rotational transition.
σ  β
dσ

=
1 + (3P cos(2θ ) + 1)
dΩ 4π  4

10p2
13p2
11p2
2.0
1.5
beta param eter
The angular distribution of photoelectrons can be
expressed, in terms of the degree of linear polarization,
P, the total cross section, σ, and an asymmetry
parameter, β, as [10]:
8p2
2.5
Fitting the angular distributions from the two
dimensional map, at each photon energy, to this
expression allows the values of the β parameter to be
obtained. The fitting procedure is performed after the
data points have been corrected for photon intensity
variations and the transmission function of the
spectrometer. The value of polarization of the
synchrotron radiation P was measured to be very close
to P=1 using a three-mirror polarimeter [11].
1.0
+
V =1 lim it
0.5
9p0
8p0
11p0
10p0
13p0 14p0
0.0
-0.5
-1.0
15.50
15.55
15.60
15.65
15.70
15.75
Photon energy
FIGURE 3. Variations of the β-parameter as a function of
photon energy for the 0-0+ transition in para-H2. The labels,
which follow the ‘nPN’ convention for Hund’s case (d),
correspond to neutral Rydberg states, converging to the v+=1
limit.
RESULTS AND DISCUSSION
Figure 3 shows a spectrum of the variation of the
asymmetry parameter with photon energy for the
transition X1Σg+(ν=0,N=0) → Σg+(ν+=0, N+=0), which
will be referred to as 0-0+. It can be observed that the
value of the β-parameter is very close to 2, but it has
sharp variations at particular photon energies. The
error bars correspond to 65% confidence limits of the
fitted parameter, and are presented for alternative
values of β to avoid overcrowding the figure. The
continuous line joining the data points is provided only
as a guide for the eye. Assignments of the resonances
close to these variations of the β-parameter are
included in figure 3. The assignments follow the ‘nPN’
notation of Hund’s case (d) for Rydberg states with
principal quantum number larger than n=8. In this
notation, n corresponds to the principal quantum
number of the state, P refers to the value of the
projection of angular momentum of the intermediate
state on the internuclear axis and N refers to the
rotational ionic limit to which the series converges.
The vibrational limit of these Rydberg series
corresponds to the v+=1 ionic state, which is
represented in figure 3 as a vertical line.
The asymmetry parameter is closely related to the
exchange of angular momentum during the
autoionisation process. The angular momentum
transferred during photoionisation, Jt, is defined as, Jt
= Jc-Jo, where Jc is the total angular momentum of the
ionic core and Jo is that of the neutral target. Each
value of momentum transfer has associated with it a
particular value of the asymmetry parameter, β(Jt) [2].
The observed asymmetry parameter is obtained as an
average over the asymmetry parameters, β(Jt),
weighted by their respective integrated cross sections,
σ(Jt),
β=
∑ σ ( Jt ) β ( Jt )
∑ σ ( Jt )
Jt
Jt
For the particular case of pure rotational
autoionisation and a transition between an initial N and
final N+ rotational state, this equation can be explicitly
expressed in terms of S-matrix elements as [6],
β
N →N +
2
2
2
2 S N → N + (0)  − 3 S N → N + (1)  +  S N → N + ( 2) 






=
2
2
2

 + 5 S
 + 3 S
 S
+ ( 0)
+ (1)
+ ( 2)

  N →N
  N →N
 N →N
where the S-matrix elements are a function of the
possible values of momentum transfer, Jt=0, 1 and 2. It
is straightforward to see that, if only one of the values
of transfer momentum is present, the asymmetry, βparameter has a constant value. For example, if only
62
Jt=0 were possible, a value β=2 would be obtained.
Similarly, values of β= -1 and β=1/5 are obtained if
only Jt=1 and Jt=2 are present, respectively. However,
if more than one value of angular momentum transfer
is present, the situation is not so simple and the
explicit calculation of the different S-matrix elements
is needed in order to obtain the value of the βparameter. This calculation have been done for the
case of pure rotational autoionisation [6], but the
extension to the case where vibrational transitions
occur in addition to rotational ones is not available.
REFERENCES
1. Dehmer P.M. and Chupka W.A., J. Chem. Phys. 65,
2243 (1976).
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Comer J. and Hammond P., J. Phys. B: At. Mol. Opt.
Phys. 35 1393 (2002).
The fact that the β-parameter presented in figure 3
is generally very close to a value β=2, suggests that the
predominant value of momentum transferred, over the
photon energy range considered is Jt=0. Departures
from this value are therefore attributed to contributions
from other values of transferred momentum, in
particular Jt=2. The value Jt=1, although possible from
conservation of angular momentum, is forbidden due
to considerations of parity conservation [6]. The
physical origin of contributions of Jt=2 is attributed to
anisotropic interactions between the escaping
photoelectron and the ionic core.
5. Dehmer J.L, Dehmer P.M. West J.B., Hayes M.A. and
Siggel R.F. J. Chem. Phys. 97, 7911 (1992).
6.
Dill D., Phys. Rev A 6, 160 (1972).
7.
Juarez A.M. Cubric D. and King G.C., Meas. Sci.
Technol., 13, N52 (2002).
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Cubric D., Thompson D.B., Cooper D.R., King G.C.
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9.
Peatman B. W. J., Chem. Phys., 64, 4093 (1976).
10. Manson S. T. and Starace A.F., Rev. Mod. Phys, Vol.
54, 3 (1982).
We hope that these first observations at the
individual rotational level will stimulate further
theoretical calculations of the β-parameter variations
in this fundamental molecular system. In particular, it
would be important to have explicit calculations of the
S-matrix elements for the case where vibrational
transitions are included.
Calculations based on
multichannel quantum defect theory have been
successful in the prediction of total photoionisation
features [12] but they are more challenged in their
ability to predict differential cross sections. State
selected measurements, such as those obtained in the
present work will provide, for the first time, a direct
test of these theories for rotationally resolved
transitions over a range of photon energies.
11. Cubric D., Cooper D.R., Lopes M.C.A., Bolognesi P.
and King G.C., Meas. Sci.Technol. 10, 554 (1999).
12. Raoult M. and Jungen Ch., J. Chem. Phys., 74, 3388
(1981).
ACKNOWLEDGMENTS
We would like to thank the great support provided
by Luca Romanzin, Sergio de Simone and the whole
GASPHASE staff and research team during the
realisation of this experiment.
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