257
Journal of Electron Spectroscopy and Related Phenomena, 16 (1979)257267 0 ElsevlerSc~en~f~cPubllshlngCompany,AmateKlam~~dmTheNetherlands
VACUUM ULTRAVIOLET PHOTOELECTRON SPECTROSCOPY OF ATOMS AND MOLECIJ’LES
JAMES A.R. SAMSON Behlcn Laboratory of Physics, University of Nebraska, Lincoln, NE
68588 U.S.A.
ABSTRACT For a complete study of the photoionization of atoms and molecules it is essential to make use of the technique of Photoelectron Spectroscopy and the continuum characteristics of synchrotron radiation. A brief review is given of the application of the above techniques in measuring partial photoionization cross sections and the angular distribution assymetry parameter 8.
Selected results are given,
which are compared to theoretical values.
INTRODUCTION Photoelectron spectroscopy is now a well established branch of photon collision physics and photochemistry. been able to obtain a large
In past studies of photoionization of gases we have amount of information from the conventional techniques
of absorption spectroscopy, ionization yields, and mass analysis of the photoionized products.
However, a blank area has existed.
its state of excitation or internal energy? ejected'
When an ion was produced what was
From what orbital was the photoelectron
In a few cases these questions could be answered by the indirect approach
of studying any fluorescent radiation that was produced.
However, the direct ap
proach of studying the kinetic energy of the photoelectrons completely opened up this blank area.
Now there Is virtually no area in the field of photoionization
that cannot be studied, given a sufficient number of atoms. The technique of photoelectron spectroscopy is currently being used in two modes. In one case, undispersed radiation from resonance lamps provide electron energy spectra from which ionization potentials and vibrational spacings can be determined at two or three fixed photon energies.
The other approach has been to
use a many line spectral source or a continuum and disperse the radiation with a vacuum uv monochromator. of photon energy.
The motive here is to obtain information as a function
Although much valuable information can be obtained by the use
of undispersed resonance lamps the reason for their continued use is because of their simplicity and convenience, low cost, and in some cases because of the greater flux available within the resonance line.
However, more information can be obtained
JAR
258
SMSON
by the use of many discrete lines or especially from a continuum source of vacuum uv radiation. The most intense continuum and the one with the widest spectral range is, of course, the continuum obtained from synchrotron radiation The continuum allows measurements to be made within discrete structure and to study threshold phenomena as a function of the photoelectron energy
It is the purpose of this
review to show, briefly, how photoelectron spectroscopy has contributed to our understanding of the process of photoionization and of atomic and molecular structure.
DISCUSSION In the photoionization of an atom or molecule the photon energy can be absorbed by any of the various channels that are available. Theoretical analysis of the photoionization process must consider absorption by each of these channels then sum them to produce a total photoionization cross section. Clearly, it is desirable to measure these specific or partial cross sections to provide the most sensitive test of a particular theoretical model, and to do so as a function of photon energy. The partial cross sections are obtained by measuring the number of electrons within each energy group and comparing this to the total number of electrons produced.
This ratio is called the branching ratio.
That is, it is the fraction of
the total cross section that is involved in a specific photoionization process. Thus, the partial cross section o for ejecting an electron from the jth orbital j is given by,
?
= (N~/EN ) a(tota1) , Aj
where a(tota1) is the total photoionization cross section and Nj represents a fixed fraction of the electrons produced from the jth orbital. As long as this fraction remains constant as the photoelectron energy varies then the measured branchfng ratio is correct. This requires the collection efficiency of an electron energy analyzer to be calibrated as a function of electron energy. Figures 1 and 2 show two types of collecting efficiency curves, which depend upon whether the electron energies are analyzed at a fixed energy (by use of a retarding/accelerating lens system) or at variable energies by changing the voltage on the analyzer electrodes As can be seen from the Figures there is a large discrimination between low and high energy electrons in either case. Owing to the variation in the angular distribution of photoelectrons as a function of their energy the measured branching ratio will not, in general, be correct because electron energy analyzers sample only a certain small solid angle of the ejected electrons. In the vacuum uv region where dipole transitions dominate, the angular distribution of the photoelectrons ejected from atoms or molecules is given,
259
UPS OF ATOMS AND MOLECULES
ELECTRON
Fig. 1. Collecting efficiency curve of a cylindrical mirror electron energy analyzer with the use of a retarding/accelerating lens (pass energy = 3V).
for plane polarized
Nj =
9/47G
where
11 +
radiation,
and the direction P2(cos8)
Fig. 2. Collecting efficiency curve of a cylindrical mirror analyzer wlthout the use of a lens
by the relation,
(21
Bp2hJse)1,
0 is an asymmetry
can take on values
parameter
defining
to apply
the electron
angular distribution
ranging from 1 to +2, EJ is the angle between of the ejected
electron,
= 312 cos26  l/2 (refs. l2).
uv monochromators
WI
ENERGY
is partially
and the Legendre
Normally,
plane polarized.
to the case of partially
plane polarized
the electric vector
polynomial
the radiation
Thus, Eq.
and
emitted by vacuum
(2) has been generalized
or elliptically
polarized
radla
tion, namely,
a
N
~~~14~)
~1 + 3148
f (l+~) co~2ex
+
M~COS~~~

2131 I,
(3)
3 when
the photon
direction
is along
Ox and By refer to the direction axis, respectively Either
of the photoelectron
parallel
P is the degree of polarization
= 54' 44' the expression Y
as shown in Fig. 3, and the angles with respect
to the x and y
(refs. 34).
the x or y axis must be oriented
polarization. ex = 6
the zaxis,
containing
to the direction
of the incident
8 and P vanish.
of maximum
radiation.
When electrons
When are
JAR
260
SAMSON
Fig. 3. Coordinate system showing the direction of ejection of a photoelectron The photon beam is in the direction of the with respect to the x, y, and zaxis z*axis.
observed
in this direction
lax distribution
accepting
ratios.
effects become important,
range, then Eq. (2) is not strictly
(Uj/4")
with BC = 1.
T BnPn n=O
etc., are usually 1' B3, B4, the dipole approximation.
energies
continuum
in the keV angle.
(4)
are less than one or two hundred
small and Eq.
energies.
Figures
(refs. 6, 7).
as a function of photon
state into the ionization
the ion that are not accessible
However,
structure
of 02.
continuum
by
reveals the discrete
4(a,b) illustrate
the electronic
spectroscopy
For direct photoionization
energy.
electron
(4) tends to that obtained
there should be little difference
coincide with a discxete autoionizing tion of the excited
out that
radiation),
energy levels of 02 as revealed by photoelectron
584 and 736 i, respectively
distribution
as they do for photon
spectrum of a molecule most dramatically
nature of the electron binding
ionization
Tseng et al. (ref. 5) have pointed
(for unpolarized
When the photon energies
and vibrational
This Thus,
at this "magic angle" in order to measure
(~0~8s) ,
volts B
The photoelectron
radiation.
on 54' 44'.
correct and there would be no magic
They give the more general expression
Nj =
of the incident
of thefr angu
If angles other than 54' 44' are used then we must have a
of 8 and P and use Eq. (3).
if multipole
are independent
a conical shell centered
should observe electrons
true branching knowledge
measured
and the degree of polarization
is also true for analyzers all analyzers
the quantities
in the vibrational
intensity
the 736 i line happens When this happens populates
from the direct photoionization
at
into the
vibration
process
to
the relaxalevels of
Thus,
UPS OF ATOMS
J
AND
I
I
I
I
I
IS
I6
I7
I
13
12
II
261
MOLECULES
14
IONIZATION Fig.
4a.
584
photoelectron
i
spectrum
POTENTIAL of
I
16
I
I
20
21
WV)
02
73.6lnn
02’
I
I9
0 VT”
x %* “‘OrRi4rr$ 0
4 6 lIIIIIIIIlIIIIIII,ee
2 I
8
10
I2
H
l6la
4
ELEC
Fig.
736 i
4b.
measurements numbers of
by
of the
photoelectron
spectrum
vibrational use
of
suitable
autoionizing
When the
vibrational
obtain
the
photon
energy.
branching Then,
can be
obtained
as
spacing
the
tunable
of
can
02.
be
character
extended of
to
higher
synchrotron
vibrational
quantum
radiation
and
the
selection
state
integrated
states. intensities ratios by
use
a function
of
within
the
of of
various
Eq. the
(1)
each
electronic
states the
photon
partial energy.
that
are
are
accessible
photoionization Results
of
to
the
cross this
nature
we given
eection have
262
JAR
SAMSON
been obtained for at least the first three ionic states of 02, N2, and CO2 (refs. 810).
Figure 5 illustrates
theoretical
the partial
results of Davenport
(ref
cross sections
11).
been made of the partial photoionization most of the calculations
a broad resonance
show two overlapping
theoretical
agreement with experiment.
peaking at 31 eV in the X*Z
resonances.
Davenport
suggests
the
calculations
cross section of N2 (ref. 1214).
show poor agreement with experiment.
for the B State are in excellent predict
Several
for N2, including
Davenport's
have
However, results
His calculations
also
state. The experimental data g that the higher energy resonance
(about 28 eV) is related to the theoretical "finalstate" resonance, whereas the lower energy state, at approximately 23.6 eV, is caused by twoelectron excitations, which were not included in his calculations. section
The peak observed
in the total cross
curve (refs. 1516) at 23 6 eV is clearly caused by the resonances + 2'
in both
the X and A states of N
14l
’ 4
‘1.’
’
’
’
’
’
’
’
’
’
’ 
Illlll”‘ll”~“l 014
18
22
26
30
34
38
42
46
PHOTON ENERGY(&) Fig. 5. Partial photoionization cross sections for the X, A, and B states of N+ (uncorrected for electron angular distribution). The solfd curves are the cal2 culated values from Davenport (ref. 11). (from Plummer et al. ref. 9).
In the case of atoms, the experimental of the asymmetry in illustrating
parameter
values of the partial
$ have been extremely
the importance
of including
correlation
of cross sections.
This effect is particularly
of the 5selectrons
in Xe.
correlations
correlations between
tance of interchannel
being considered.
the selectrons coupling
and
theory, especially
effects in the calculation
noticeable
Figure 6 shows various
imental data (ref. 17), of the 5s Xe photoionization and without
cross sections
useful in gufding
in the photoionization
calculations,
with some exper
cross sections
(ref. 18) with
The results clearly show the need for
and both the 5p and 4delectrons.
is also illustrated
in measurements
The impor
of 6, the photo
263
UPS OF ATOMS AND MOLECULES
1.2 (mb)
photon
energy
(Ry)
Partial photoionization cross section for the 5s electrons in Xe as a funcFig. 6. tion of photon energy. The dashed curve represents the RPAE calculation taking into account correlations between the 5s and 4d shells, whereas, the solid curve represents correlations between the 5s and (4d t 5p) shells. The dotted curve does not take correlations into account. The experimental points are from Samson and Gardner, ref. 17 (from Amusia, ref. 18).
electron
angular distribution
theory and experiment the theoretical and 4d electrons correlations
parameter.
Figure 7 shows the comparison
for fl for the 5pelectrons
in Xe.
results obtained when the interchannel are neglected,
are included
whereas,
(ref. 19).
between
The dashed curve represents correlations
between
the 5p
the solid line curve is obtained when these
The experimental
and Torop et al. (ref. 21) are in excellent
agreement
data of Dehmer et al (ref. 20 with the calculations that
include full correlations.
Fig. 7. Angular distrfbutfon pararaeter f3 for the 5p electrons in Xe as a function of photon energy (1Ry = 13.6 eV). Theoretic81 data: Iresults obtained when interchannel correlations between 5p and 4d electrons are neglected. results obtained when these correlations are Included (from Amusia and Ivanov, ref. 19). Experimental data:l , D&met et al., ref. 20; 0, Torop et al., ref. 21.
264
JAR
SAMSON
The expected Bvalue (in the dipole approximation) for electrons with zero angular momentum, that is, sshell electrons, is g = 2.
Measurements at 584 i of the
f3parameterfor the 6selectrons in Hg by Niehaus and Ruf (ref. 22) gave the result g = 1.68. 304 ;.
Dehmer and Dill (ref. 23) found B = 1.4 for the 5selectrons in Xe at
The deviation from f3= 2 can be explained when spinorbit interactions are
considered that allow s + up
and s t ~~~~~ transitions to take place (ref 24). l/2 In fact, Starace et al. (ref. 25) have predicted that even in the nonrelativistic case the photoelectron angular distribution of selectrons in openshell atoms (other than those with R = 0 for the outer shell) will fluctuate with the energy of the incident radiation because the various possible couplings of the continuum pwaves to the ion core give rise to several distinct final states. An example of the calculated variation in the value of B for the 6selectrons in Cs is shown in Fig. 8 (ref. 26).
The vertical arrows indicate the photoelectron energies where the radial
matrix elements R1,2,3,2 for the a + ~112,312 transitions go to zero. Also shown in the Figure (dashed curve) are the results calculated by Marr (ref. 27) using the experimental results of the degree of spin polarization of electrons produced in the photoionization process (ref. 28)
There is excellent agreement in the shape
of the two curves. However, there is considerable displacement in their relative positions.
PHOTOELECTRON
ENERGY CV)
Angular distribution parameter 6 for the 6s electrons in Cs as a function Fig. 8. of photon energy. The solid line represents the theoretical results of Ong and Manson, ref. 26. The dashed curve represents the semiemperical results of Marr, ref. 27.
Some of the earliest studies that utilized photoelectron spectroscopy were concerned with measuring the ratio for producing the rare gas ions in their 2P l/2,3/2 states From their statistical weights a ratio of 2 was expected. However, most measurements have shown the ratio to be nonstatistical (refs. 2932). This effect has also been observed in Cd, Hg, and Cs (refs. 3335).
Although these ratios
UPSOFATOMSANDMOLECULES appeared
266
to be nearly
constant
aa a function
of photon energy it has recently been
shown for Cs and Xe that if the ratios are studied over a sufficiently
extended
photon
(ref. 32, 34).
energy
range the ratios will tend toward the statistical
The experimental
values
to 110 eV, are shown in Fig. 9 (refs. 30, 32, 36). in the data between the presence
autoionizing
a pressure
effect occurs
40.81 eV.
Their data, plotted
pressure
measurements.
energies
to indicate
("10%) at photon
and 60 eV
energies
solid line curve in Fig
et al
energies
(shown by the
(ref. 32) have shown that
at these two photon energies,
represent
their lowest
circle data at the above
These error bars are typical of all
The rise in the ratio to the statistical
They used a DiracFock
9
coupling between
scatter
of 21 2 and 30 55 eV but not at
results of Ong and Manson
coupling
range 13.4
caused by
occurs just in the region of the Cooper minimum,
The theoretical
interchannel
in this region
the spread to be expected.
effect of spinorbit
This is possibly
Error bars are placed on the closed
the closed circle data points. higher photon
resonances
In fact, Wuilleumier
ref. 37).
energy
There is considerable
(13.436 eV) and 33 eV.
threshold
of numerous
shaded rectangle,
values
of the ratios found in Xe, for the photon
and treats exchange
(ref
value for between
40
38) are shown by the
formulation
exactly.
that includes
However,
the
the effects
the 5p and 4d channels were not included
of
in the cal
culation.
SENERGY 0
I
l20
20
I
I
1
60
T’
80
I
T’
I
p’ f f{
__________

too ‘T
 
I
Ii
$J
bX
(eV)
40
15
+ Lm
T
i7i
Xe
I
20
I 40
I
I
I
I 80
60 PHOTON
ENERGY
I
I
I
100
(eV)
2 2 Pl,2 branching ratios for Xe as a function of photon energy The '312  statistical weight value; theoretical values, Ong and Manson, ref 38 Experimental pointso, Wuilleumier et al., ref. 32, l , Samson et al., refo. 29, 30, A , Dehmer, ref. 36. Shaded area represents region of numerous autoionizing line* Fig. 9.
ratio is found to vary dramatically within autoionizing resonances The 2p1,2,3,2 (ref. 30, 39). For example, in the vicinity of the Xe 5~5p~6p(~l?~) window resonance at 20.95 eV the ratio is observed
to change from 1.54 to 3.0.
The calculations
of
266
J A R SAMSON
Starace predict that the ratio will increase to about 9.0 at the minimum of the resonance and, in fact, variations in the ratio within resonances are sxpected as This may explain the very low ratio for the a general phenomenon (ref. 40) 2 cross section ratio for Hg at 584 i as observed by Hotop (ref. 41) 2P He P3/2 l/2 observed a ratio of 0.28 (see Fig. 10) rather than the statistical weight value of 2.0.
From Mansfield's absorption spectrum of Hg (ref. 42) the 584 i line appears
to coincide with a broad absorption feature and this may perturb the ratio. More data in the vicinity of the 584 i line will be necessary to clarify this result.
584A  Hg _______
mr,s
I’, 40
40
‘P%
1
I1I JS
Electron Enerov IeV) Fig.
10.
A portion of the 584 i photoelectric spectrum of Hg as a function of elec
tron energy illustrating the relative strengths of the 2P and 2P3,2 lines. l/2 data are not corrected for the analyzer transmission. (from Hotop, ref 41).
The
There are many interesting effects in photonatom interactions and it is clear that such effects as spinorbit coupling and correlation effects between electrons within the same orbit and between neighboring orbits are very important in explaining these interactions
It is also clear that the use of synchrotron radiation and the
technique of photoelectron spectroscopy will be required to study many of the details of photoionization in atoms and molecules
ACKNOWLEDGEMENT It is a pleasure to acknowledge the US Department of Energy, the National Aeronautics and Space Administration (under Grant #NGR28004021), and the Atmospheric Sciences Section of the National Science Foundation for their support of our program on Photoionization of atoms and molecules.
I would also like to express my appre
ciation to Professor Hotop for making available his unpublished results on Hg and to Professor Manson for his revised figure showing the Cs asymmetry parameter.
UPSOFATOMSANDMOLECULES
267
REFERENCES
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
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