J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 2225–2238. Printed in the UK
PII: S0953-4075(98)89932-X
A high-resolution study of the threshold photoelectron
spectrum of helium
D B Thompson†, P Bolognesi†, M Coreno‡, R Camilloni‡, L Avaldi‡,
K C Prince§, M de Simonek, J Karvonen§¶ and G C King†
† Department of Physics and Astronomy, University of Manchester, Manchester, UK
‡ IMAI del CNR, Monterotondo Scolo, Italy
§ Sincrotrone Trieste, Padriciano, Trieste, Italy
k Dipartimento di Fisica, III Universita’ di Roma, Rome, Italy
Received 11 December 1997
Abstract. Measurements of the threshold photoelectron spectrum of helium have been made
at the Gas Phase beamline at Elettra Synchrotron, Trieste. The energy region studied spans the
thresholds of the He+ (N) satellite states, beginning with N = 2, up to the He2+ threshold. The
energy resolution in the new spectrum is five times better than that of previous measurements
and has enabled us to resolve satellite states with N = 13–19 for the first time. The part of
the spectrum in the region of the double-ionization threshold exhibits a cusp-like feature in
accordance with predictions of the Wannier model for threshold photo-double ionization. This
region has been used to examine the role of doubly excited neutral states in single-ion formation
and also to compare with previous experiments the ratio of the discrete and continuum amplitudes
of the cusp. The use of the threshold photoelectron technique as an accurate and convenient
method to calibrate the energy scales of optical monochromators for synchrotron radiation is
noted.
1. Introduction
The last few years have witnessed the development of beam lines at synchrotron light
sources with resolving powers of greater than 10 000 at photon energies above 50 eV. This
has led to great improvements in photoion measurements of the helium total ionization
cross section (Domke et al 1996 and references therein, Schulz et al 1996), providing
experimental identification of several new Rydberg series of resonances due to doubly
excited neutral states. Benefitting from the high resolving power of the incident radiation
high-resolution partial cross sections of helium satellite states up to n = 5 have also been
reported (Menzel et al 1995, 1996). In contrast, photoelectron spectra of helium with
comparable resolution do not yet exist. The spectrum of helium satellite states has been
studied extensively by both conventional photoelectron (Carlson 1967, Samson 1969, Krause
and Wuilleumier 1972, Wuilleumier et al 1980, Lindle et al 1985, 1987, Svensson et al
1988, 1995, Wehlitz et al 1991, 1993) and threshold photoelectron (Heimann et al 1986,
King et al 1988, Hall et al 1991, Cvejanovic et al 1995) spectroscopies. The most recent
conventional photoelectron spectrum, by Svensson et al (1995) using 96.5 eV radiation,
achieved a resolution of 88 meV in the energy region of the satellite states, while the
latest three threshold photoelectron spectra have photon-limited resolutions between 60 and
¶ Permanent address: Department of Physical Sciences, Oulu University, Oulu, Finland.
c 1998 IOP Publishing Ltd
0953-4075/98/102225+14$19.50 2225
2226
D B Thompson et al
70 meV. Here we report the results of recent measurements of the threshold photoelectron
spectrum of helium, performed with a resolving power five times greater than previous
measurements.
A threshold photoelectron (TPE) measurement involves the detection of nearly zeroenergy electrons, ejected each time the photon energy is scanned across the threshold of
an ion state. The TPE technique is characterized by high collection efficiency and highenergy resolution. For atomic species, TPE spectroscopy is used to probe photoionization
leading to the creation of excited ion states close to their threshold energies, i.e. the shape
of the ionization cross section close to threshold. With only two electrons, helium is the
fundamental system to study, since simultaneous excitation and ionization of this atom by the
absorption of a single photon can only occur as a result of electron–electron correlation. The
TPE spectrum of helium contains, along with the main line corresponding to formation of the
ion in its ground state, a hydrogenic series of discrete satellite lines converging to the doubleionization potential. Each satellite line corresponds to an ionization process in which the
ion is left in an excited state, denoted as He+ (N ), where N is the principal quantum number
of the remaining electron. Helium ion states with the same principal quantum number, but
different angular momentum quantum numbers, are nearly energetically degenerate, with the
largest fine-structure splitting calculated to be only 0.7 meV (see Moore 1971), so that it is
not yet possible to resolve these states energetically. Above the double-ionization threshold,
the TPE spectrum consists of a continuous signal of nearly zero-energy electrons due to the
fact that the excess energy can be continuously shared by the two escaping electrons: the
excess energy, E, is equal to E = hν − IP2+ , where IP2+ is the helium double-ionization
potential. The process leading to the double-electron escape in helium by absorption of a
single photon is one of the fundamental phenomena in atomic physics because it involves the
understanding of the three-body Coulomb problem as well as the role of electron–electron
correlations. Thus the study of the processes occurring near the helium double-ionization
threshold has attracted a lot of attention since the pioneering work of Wannier (1953).
The TPE spectra of helium that have appeared in the literature over the last ten years
mirror the advances made in the TPE technique. The first one by Heimann et al (1986),
had an instrumental resolution of 150 meV and clearly distinguished satellites up to N = 8.
Analysis of this spectrum concentrated on extracting the relative magnitudes of the partial
cross sections of the ion states at threshold. These authors also observed that the yield
of threshold electrons was continuous above the double-ionization potential and that this
yield increased with photon energy. This work was followed by a measurement by King
et al (1988), with a photon-limited resolution of 60 meV, that resolved satellites up to
N = 12. Here again, the emphasis was on extracting relative ion state intensities, but also
the first attempt was made to analyse the cusp-like feature occurring at the double-ionization
threshold. Subsequent measurements (Hall et al 1991, Cvejanovic et al 1995) exploited
increased detection efficiencies to study in detail the energy region containing the doubleionization threshold, where the cross sections are extremely small. Further investigations
on the dynamics of the process close to threshold have been made by the photoelectron–
photoion coincidence experiments of Lablanquie et al (1990) and Hall et al (1992) and
the measurement of the double-photoionization cross section in time-of-flight experiments
by Kossmann et al (1988). Hall et al (1991, 1992) found that the rise in the wing of the
cusp above the double-ionization threshold is consistent with Wannier threshold predictions.
Cvejanovic et al (1995) focused their attention on the regions both just above and below
the double-ionization threshold. Their analysis showed that both wings of the cusp may
be characterized by the same threshold power law, although the two wings have different
relative amplitudes, the ratio of these amplitudes being dependent on the target pressure.
Threshold photoelectron spectrum of helium
2227
They also modelled the pressure dependence of the second-order processes that can lead to
different amplitude ratios between the two wings in experimental observations.
The helium TPE spectrum presented here encompasses satellite states from N = 2
through to the double-ionization potential. Satellites up to N = 19 have been resolved.
At the same time as these TPE spectra were being collected, helium photoion spectra were
collected in parallel. The helium photoion spectrum provides an independent measurement
with which the photon energy scale of the TPE spectrum can be calibrated. With this
calibration, we have determined TPE peak energy positions precisely. These results
demonstrate the possibility of using TPE spectroscopy itself as a tool for energy calibration.
We have accurately determined the TPE lineshape, so that we are able to extract the relative
intensities of satellite states for N = 3–19. Furthermore, the statistical accuracy of the
measurements in the double-ionization region of the spectrum is adequate for comparing
the data with the predictions of the Wannier threshold law.
2. Experimental set-up and procedures
2.1. Experimental set-up
The experiment was conducted at the Elettra Synchrotron Light Source in Trieste, Italy. A
schematic of the full experimental set-up, including both TPE and photoion spectrometers,
is shown in figure 1. The main elements of the TPE spectrometer are the photon beam, an
effusive gas beam and a threshold photoelectron energy analyser. The photoion spectrometer
consists of an ionization gas cell through which the same photon beam passes.
Figure 1. Schematic of the experimental set-up which includes the threshold electron analyser,
the photoionization cell and the photodiode.
The photon beam was provided by the Gas Phase beam line at Elettra Synchrotron
(Prince et al 1997). The beam line is designed for atomic and molecular science experiments
using high-resolution, high-flux synchrotron radiation. It consists of an undulator source,
a variable-angle spherical grating monochromator and two experimental stations. The
2228
D B Thompson et al
undulator source is of the type U12.5, with a 12.5 cm period (Diviacco et al 1992),
which provides radiation from 20 to well above 900 eV. The monochromator is composed
of a plane mirror and five interchangeable spherical gratings (Melpignano et al 1995),
with pre-focusing and post-focusing optics placed before and after the entrance and exit
slits, respectively. This design provides the considerable advantage of a fixed focus in
the experimental chamber, and the post-focusing optics results in a beam spot of about
200 µm × 200 µm at the target position. Both of these technical features are particularly
useful for gas-phase experiments.
For the TPE measurements the spectrometer was housed inside one of the beam line
end-stations, with the electron energy analyser fitted onto a 200 mm flange. Helium entered
the experimental chamber via a 0.3 mm bore stainless steel hollow needle extending from
the top of the chamber. The arrangement of these elements was such that the photon beam,
gas beam and analyser optical axis were mutually orthogonal. Both the analyser and the
gas needle were mounted on x–y–z translators, enabling precise alignment of these two
elements with respect to the incident photon beam and to each other.
The threshold analyser was developed from the photoelectron energy analyser described
by King et al (1987) and consists of an electrostatic lens system and 127◦ cylindrical
deflector analyser (CDA). This analyser is tuned to collect nearly zero-energy electrons using
the penetrating field technique, first described by Cvejanovic and Read (1974) and more
recently by King et al (1987). Briefly, a potential well is formed in the interaction region by
field penetration of an extracting electrode through a 5 mm aperture in a screening electrode.
This provides a very large collection angle and, furthermore, forms a crossover point in the
particle trajectories that ensures efficient transmission of electrons through the subsequent
optics. The optics consists of two triple-aperture lenses which image the crossover onto the
entrance plane of the 127◦ CDA. This lens combination provides very good spatial definition
of the electron beam so that unwanted electrons are strongly suppressed and therefore the
noise discrimination of the analyser is very high. The purpose of the CDA is to remove the
high-energy tail in the analyser transmission function due to those energetic photoelectrons
that are emitted in the direction of the extraction electrode. Electrons transmitted by the
analyser are detected using a channel electron multiplier (Philips model X919).
The ionization gas cell for the photoion measurements was attached to the rear of the
main experimental chamber. These measurements provided a continuous calibration of
the energy of the incident radiation, as discussed in the following section. The windowless
ionization cell houses two electrodes (100 mm long and 20 mm wide). One electrode is used
as a repeller electrode and is biased usually at +30 V, while the photoionization current is
read via a current amplifier and digital voltmeter at the second electrode. An x–y translator
enabled alignment of the cell with the beam direction, while a 2 mm diameter, 5 mm
long pipe operated as a differential pumping section resulting in a pressure drop of about a
factor of 100 between the cell and the main chamber. Finally, a photodiode (International
Radiation Detectors Ltd type AXUV-100), located at the exit of the gas cell, monitored the
beam current and was used to normalize the photoion and threshold photoelectron signals
to the incident flux. It was also used to measure the absolute photon intensity and to ensure
that the photoion spectra were collected in the linear absorption regime. A Macintosh
Centris computer with a Labview code was used to set the photon energy and to record
synchronously the TPE signal, ionization current and beam monitor signal.
We conducted the TPE measurements at a relatively low target gas density, with a
residual helium gas pressure in the experimental chamber of 9.0 × 10−6 mbar. The helium
double-ionization cross section at 80 eV is very low being 1.02 × 10−21 cm2 (Kossmann
et al 1988), and so we chose to operate the monochromator with a moderate resolving
Threshold photoelectron spectrum of helium
2229
Figure 2. Typical energy calibration spectra in the region of He+ N = 2 ion state threshold.
The bottom spectrum is a photo-ion spectrum of the helium ‘2, 0n ’ Rydberg series. The top
spectrum shows the N = 2 ion state TPE peak. The dwell time is 1 s per step.
power of 10 000, i.e. 7 meV at 70 eV. The tuning of the threshold analyser was optimized
by collecting, at periodic intervals, TPE spectra encompassing the He+ (2) satellite line.
This line was chosen for tuning because it could be reached using the same monochromator
grating with which spectra of the other satellite lines were collected and because it is
energetically well isolated from neutral excited states converging to higher-lying ion states.
A typical He+ (2) TPE spectrum, along with the simultaneously acquired photoion
spectrum, is shown in figure 2. In the TPE spectrum, the satellite line has a slightly
asymmetric line profile. This asymmetry is characteristic of TPE energy profiles, with
the high-energy tail arising from incomplete discrimination of non-zero-energy electrons.
The resulting convolution of photon and analyser energy profiles leads to an observed line
that, when fitted with an asymmetric Lorentzian lineshape, has a 10.5 meV full-width halfmaximum (FWHM). We note that the final resolution achieved is not the limit of either the
photon beam or the analyser, but is a necessary compromise in order to obtain effective
counting rates in the region of the double-ionization threshold. This resolution is, however,
a factor of five better than that achieved in previous TPE spectra of the helium satellite
states.
In the TPE spectrum of figure 2, the satellite peak appears superimposed upon a
statistically flat background equivalent to 7 counts/s. This background signal arises from two
sources. The first source, present when both the photon beam and gas beam are switched
off, is channeltron ‘dark’ counts and contributes 3 counts/s. The second source, appearing
2230
D B Thompson et al
Figure 3. He+ TPE spectrum covering the energy region from the N = 3 ion state threshold
through the He2+ threshold. The dwell time is 6 s per point.
only when both gas and light are present, contributes the remaining 4 counts/s. The second
source results from two contributions. The first arises from energetic electrons, ejected in
ionization events that create helium ground state ions, entering and striking surfaces in the
analyser optics. The second arises from near-zero-energy electrons ejected in photo-doubleionization events produced by second-order light. The relative contributions from these two
mechanisms is unknown since we did not measure the relative contribution of second- and
higher-order light to the total light intensity. This flat background appears over the entire
range of the scanned energy in the TPE measurements and has been taken into account in
all fitting procedures.
The TPE measurements presented in figure 3 span the energy region between 72.3
and 79.6 eV, extending from below the He+ (3) satellite threshold through to just above
the double-ionization threshold. These measurements have been made by scanning four
separate energy regions, each with a different setting of the undulator gap. For the first
three energy regions, the data presented correspond to single scans with a dwell time of 6 s
at each energy interval. For the fourth energy region, extending from below the He+ (8)
satellite line to above the double-ionization potential, the spectrum represents a collection
time of 78 s per energy step. Overlapping features and the measured photon flux have been
used to scale the four sets of measurements.
2.2. Energy scale calibration
For the TPE spectra presented here, a precise calibration of the incident photon energy
is critical both for comparing the position of an individual satellite peak with the ion
state’s known spectroscopic energy and for assigning features near the double-ionization
Threshold photoelectron spectrum of helium
2231
threshold. Our energy scale calibration has been achieved by using the photoion spectrum
measured simultaneously with the TPE spectrum. For example, the photoion spectrum in
figure 2 shows resonance features belonging to the 1s2 → 2, 0n Rydberg series of doubly
excited states converging to the He+ (2) threshold. Here and in figure 2 the simplified
nomenclature, N, Kn , has been adopted to describe the resonances (Herrick and Sinanoglu
1975, Zubek et al 1989) where N and n are the principal quantum numbers of the inner
and outer electrons, respectively, and K is the collective quantum number. Comparison
of the photoion spectrum in figure 2 with the recent measurements of Schulz et al (1996)
and Domke et al (1996) enabled us to calibrate the photon energy scale with a relative
uncertainty of ±2 meV. We note that for an absolute energy calibration, we must add
the ±4 meV quoted by Domke et al (1996) as the absolute uncertainty in their energy
scale. Once the photon energy is calibrated, the experimentally observed position of the
He+ (2) peak in the TPE spectrum can be compared with the value of 65.401 eV for the
He+ (2) ionization threshold used by Schulz et al (1996) as the limit of the 2, 0n and 2, 1n
Rydberg series of doubly excited neutral states. In the TPE spectrum, the maximum of
the threshold photoelectron peak occurs at 65.400 ± 0.002 eV. This shows that neither the
extraction field nor any space-charge effects, at least at the pressure of this work, perturb
the threshold measurement. This demonstrates that peaks in threshold spectra can be used
as an alternative to photoion measurements to calibrate the photon energy scale. The
same calibration procedure has been used for all satellite lines up to He+ (9), the highest
satellite state below which doubly excited state resonances have been measured (Shulz
et al 1996). Peak positions for satellites with N > 9 were located by extrapolating the
energy scale determined from the He+ (8) and He+ (9) satellite energy calibrations. The
peak energies of all the observed satellite states were used in a fit of the Rydberg formula
IPN = IP2+ − 4RHe /(N − δ)2 , where RHe = 13.603 83 eV, δ is the quantum defect and
IP2+ is the double-ionization potential. In the fit, both the double-ionization potential and
the quantum defect were left as free parameters. As expected, the best fit is obtained with a
value of δ that is zero within the uncertainty. The value of IP2+ determined by the best fit,
is equal to 79.004 ± 0.003 eV. With this value the measured peak positions of all satellites
agree to within ±3 meV with values calculated using the Rydberg formula. Thus, along
with giving a value for the double-ionization potential, this fit confirms the consistency of
our energy calibration up to the region of the double-ionization threshold.
3. Results
In figure 3 the complete TPE of helium from 72.3 to 79.6 eV is shown, while the region
above the He+ (9) satellite threshold is displayed in figure 4 on an expanded scale. The
superior energy resolution of the present experimental set-up has enabled us to discern
satellite states up to N = 19.
As was the case for the He+ (2) satellite states in figure 2, the satellite states in figures 3
and 4 appear as asymmetric lineshapes. While the low-energy side contains only the photon
beam width, the high-energy side is affected by both the photon beam and analyser profiles.
The intensities of the different satellite states have been obtained by fitting an asymmetric
Lorentzian lineshape to the individual peaks. In order to extract relative intensities of the
satellites, the width of the fitted lineshape has been kept fixed for all the satellite states,
although some broadening of the high-energy tail was observed for higher N satellite lines.
The use of a fixed lineshape has been made because we are interested in comparing the
relative intensities of the satellite states, and therefore their relative cross section, at the
same excess energy above their respective thresholds. Using lineshapes with different
2232
D B Thompson et al
Figure 4. He+ TPE spectrum covering the energy region from the N = 9 ion state threshold
through the He2+ threshold. This spectrum is the interpolated sum of eight separate scans, using
a 2.9 meV step size (the average step size in each scan) with a total dwell time of 78 s per step.
The full curve is a fit to the data of a convolution with the instrument function of a differential
form of the Wannier power law: σ (E − E0 ) = g± |E − E0 |α−1 , where α = 1.056, E0 is the
double-ionization threshold and g± are ionization/excitation amplitudes.
widths would have implied a comparison of cross sections integrated over different energy
ranges.
The energy positions of the satellite states measured in the present work are compared
with previous data in table 1, while their relative intensities are reported and compared
with previous measurements in table 2. Unlike some of the earlier experimental studies,
our measured energy positions are in good agreement with the calculated values given by
Moore (1971). The observed relative intensities are discussed below.
4. Discussion of results
In the region near the double-ionization threshold two types of processes occur that can
lead to the ejection of a nearly zero-energy electron:
hν + He → He+ (N) + e−
hν + He → He2+ + e− + e− .
Below the double-ionization threshold only the former process, in which one electron is
ejected and the second one is promoted to an excited state, can occur. The resulting
ionic states produce discrete lines in the TPE spectrum, although for high-N satellites the
Threshold photoelectron spectrum of helium
2233
Table 1.
Binding energy (eV)
N
This work
Moorea
Martinb
Heiman
et al c
Svensson
et al d
Kossmann
et al e
Svensson
et al f
IP
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
—
65.400
72.955
75.606
76.829
77.492
77.893
78.153
78.330
78.460
78.552
78.624
78.682
78.723
78.760
78.786
78.812
78.832
78.850
—
65.399
72.960
75.605
76.829
77.494
77.895
78.155
78.333
78.461
78.555
78.627
78.683
78.727
78.763
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
65.44
72.95
75.57
76.80
77.46
77.86
78.12
78.30
78.46
—
—
—
—
—
—
—
—
—
—
65.407
72.967
75.557
76.697
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
24.59
65.42
72.95
75.60
76.82
77.49
77.89
78.15
78.33
78.46
78.56
—
—
—
—
—
—
—
—
IP2+
79.004
79.005
79.006
—
79.013
—
cm−1
Moore (1971). Use eV
= 8065.540 961 842 and IP = 24.5874 eV.
Martin (1973).
c Heimann et al (1986).
d Svensson et al (1988). Use IP = 24.5874 eV.
e Kossmann et al (1988).
f Svensson et al (1995).
a
b
separation between the states becomes too small to be resolved by our spectrometer, leading
to the observation of a quasi-continuum. This continuum yield then decreases to a minimum
at the double-ionization threshold, where both the electrons can escape. This latter process
can be considered the limit of the previous one with N → ∞. Furthermore, in the energy
region of the satellite states, helium doubly excited states can be formed. Several types of
doubly excited states may exist (Read 1992). They are the Wannier ridge resonances, with a
configuration (r1 = r2 , θ12 = π) similar to that of the continuum electron pair near-threshold
double ionization, the Langmuir states (θ12 6= π) and the planetary states (r1 6= r2 ). These
resonances may then decay to the ionic states. When a resonance is almost degenerate
with an ionic peak, its decay to that ion state, involving a near-zero-energy electron, will
contribute to the observed TPE intensity of the satellite state. This is particularly true
for high-N satellites where a high density of doubly excited states exists and where the
selection rules for resonance decay strongly favour the closest energy channel (Rost and
Briggs 1991). Therefore the observed relative intensities of the high-N satellite states may
not follow the predicted N −3 (Fano and Cooper 1968) or N −3.11 (King et al 1988) power
laws. The model that predicts an N −3 dependence does not include the effect of electron
correlations, while the model that predicts N −3.11 does. However, neither model includes
the effect of resonance excitation.
2234
D B Thompson et al
Table 2.
Relative intensities × N 3
N
This work
Heimann
et al a
King
et al b
Svensson
et al c
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0.69
1.00
0.48
0.68
0.69
0.75
0.38
0.54
0.60
0.71
0.58
0.60
0.62
0.60
0.55
0.54
0.84
1.00
0.54
0.63
0.61
0.77
0.61
0.72
—
—
—
—
—
—
—
—
0.80
1.00
0.45
0.54
0.50
0.55
0.30
0.35
0.43
—
—
—
—
—
—
—
1.14
1.00
0.92
0.89
0.89
0.90
0.90
0.90
0.82
—
—
—
—
—
—
—
a
b
c
Heimann et al (1986).
King et al (1988).
Svensson et al (1995).
In figure 5 the relative intensities of the present work are compared with previous TPE
measurements (Heimann et al 1986, King et al 1988) and the conventional photoelectron
results of Svensson et al (1995). Only the conventional photoelectron data are consistent
with a N −3 behaviour; the results from all three TPE measurements do not present a
smooth behaviour. The observed fluctuations can be ascribed to the decay of doubly excited
resonances to ion states that are nearly energetically degenerate. Such resonance states can
enhance or suppress (King et al 1988) the formation of He+ (N ) ions, as well as distort
the high-energy tail of the observed lineshape. The extent to which a degenerate resonance
affects a measured threshold peak intensity is expected to depend strongly on the resolution
of the experiment. This may account for the observed differences in figure 5 between the
three threshold measurements. However, despite quantitative differences, it is important to
note that the relative intensities extracted from Heimann et al (1986), King et al (1988)
and the present data follow the same qualitative trend. It is interesting to observe that for
N > 12 the value of the relative intensity multiplied by N 3 seems to level off at a value of
about 0.6. This latter observation may be interpreted as follows. Due to the high density
of doubly excited states in this energy region which get closer and closer together, the
contribution of the resonance decay to the threshold electron yield becomes constant. Thus
the trend of the measured yield is determined by the power law for the other contribution,
i.e. direct satellite ionization.
The total (Domke et al 1996) and partial (Zubek et al 1989, Sockell et al 1996)
ionization cross section measurements may provide some evidence of doubly excited
resonances that can produce the general trend of the observed intensities. The photoion
spectra show that the He+ (3) satellite appears well isolated from resonances converging
to higher thresholds. For higher satellite lines (N > 4) resonances in which the principal
quantum number n of the ‘outer’ electron equals the ‘inner’ electron principal quantum
Threshold photoelectron spectrum of helium
2235
Figure 5. A plot of experimentally measured N ion states’ relative intensities (multiplied by
N 3 ), normalized at the N = 4 peak. The present data ( ) are compared with the measurements
of Heimann et al (1982) (4) conducted with 150 meV resolution, the measurements by King
et al (1988) () conducted with 60 meV resolution and those from Svensson et al (1995)
(O).
•
number N , appear at energies below N − 1 ion state thresholds. For example, Domke
et al (1996) locate the 5, 35 resonance state at 75.56 eV, about 40 meV below the N = 4
satellite state threshold. Extensive interference effects among the different series converging
to these thresholds have been observed (Domke et al 1991, 1995, 1996). The decay of these
resonances when close to the ion thresholds, affects the threshold electron yield and alters
the N −3 trend.
As the double-ionization threshold is approached, the ion peaks merge together and the
characteristic cusp-like feature predicted by the Wannier model (Wannier 1953, Read 1985)
is observed (figure 4). The differential cross section, according to the threshold model, can
be written as
σ (E1 , E) = E α−1 g(E1 /E)
(1)
where E1 is the energy of the detected electron, E is the excess energy shared by the two
electrons and g(E1 /E) is the energy partitioning function between the electrons. In the
case of double photoionization of helium, for which α = 1.056 (Wannier 1953), Read and
Cvejanovic (1988) have calculated the g function using classical trajectories in small energy
ranges on both sides of the threshold. The results predict that both single ionization with
simultaneous excitation and double ionization near threshold can be represented by energy
partitioning functions g± with a small asymmetry between their respective amplitudes: the
amplitude of the partition function below the threshold, g− , is predicted to be approximately
2236
D B Thompson et al
5% lower than that above. Below threshold, however, a second contribution to the yield
may arise from the decay of the resonances as noted above. This contribution may alter the
ratio observed in the experiments between the two wings of the cusp. Moreover, Cvejanovic
et al (1995) recently suggested that second-order collisional processes may also alter this
ratio. These authors modelled the dependence of this ratio on the pressure in the interaction
region.
As a first step in the analysis of the present data we have verified the consistency of the
measured data with the prediction of the Wannier threshold law above the double-ionization
threshold. For this purpose the experimental data were fitted to a form of equation (1)
in which a constant background term had been added and the resulting expression was
convolved with the same instrumental function used to fit the satellite peaks. This fitting
was performed over the range of excess energy 0.03 6 E 6 0.3 eV. In this first procedure
only the g+ value was used as a free parameter: α was fixed equal at 1.056, the value of the
double ionization used was that obtained by the Rydberg formula fit to the satellite positions
and the value of the constant background term was deduced from the observed value near
the N = 8 satellite. The resulting fitted curve, displayed in the inset of figure 4, gives
a satisfactory representation of the data. By extending this fit to the energy region below
the double-ionization potential a g− /g+ value of 1.24 ± 0.05 was obtained. As a second
step, a similar fitting procedure was performed using the double-ionization potential, the
ratio g+ /g− and α as free parameters and using the energy range from 0.15 eV below the
double-ionization potential up to 0.3 eV above. The best fit was obtained with the doubleionization potential equal to 79.004 ± 0.003 eV, α equal to 1.062 ± 0.007 and g+ /g−
equal to 1.26 ± 0.02. This value of α is in agreement with the prediction of the Wannier
model within the experimental uncertainties. It is interesting to observe, however, that the
weighted average of all the recent measurements of α (Van der Wiel 1972, King et al 1988,
Kossmann et al 1988, Hall et al 1991, 1992) is 1.061 ± 0.004, a value slightly higher than
the expected one although the uncertainty on the value is too large to allow a definitive
statement on the breakdown of the classical model.
The measured ratio, g− /g+ , is in reasonable agreement with the previous determination
of 1.43 by Hall et al (1991, 1992) in both a TPE (Hall et al 1991) and TPEPICO (Hall et al
1992) measurement. This observed asymmetry of the cusp is definitely larger than the one
predicted by models which assume that the Wannier law describes the energy dependence of
the threshold yield produced by the decay of resonances. In their recent study Cvejanovic
et al (1995) measured the threshold photoelectron spectrum of helium in the region of the
cusp as a function of the pressure in the target region. The observed variation of the cusp
asymmetry with pressure was interpreted in terms of second-order collisional processes.
According to these authors the g− /g+ ratio displays a negative pressure effect, i.e. the
asymmetry increases as the pressure decreases. The present data, obtained at a pressure of
9 × 10−6 mbar, and the data of Hall et al (1991), obtained at 5.5 × 10−5 mbar, where both
the values have not been corrected for the ion gauge efficiency, occur in a region where an
almost symmetric cusp is expected by the model of Cvejanovic et al (1995). Thus these
two sets of data do not support the proposed model for second-order collisional processes in
the target region. Recently, non-Wannier resonances have been studied theoretically. These
‘Langmuir’ and planetary states (Read 1991, Rau 1992, Burgers and Wintgen 1994, Heim
1993) are predicted to be more stable against autoionization than the Wannier resonances.
However, in an energy range characterized by a vanishing cross section, even a small
contribution from these resonances might change the measured yield and its slope below
the double-ionization potential.
Threshold photoelectron spectrum of helium
2237
5. Conclusions
We have used the high performance of the Gas Phase photoemission beam line at Elettra
(Trieste) together with the high efficiency of a threshold photoelectron to measure the TPE
spectrum of helium at much improved energy resolution. This has enabled us to determine
precisely satellite positions and intensities and to obtain an accurate determination of the
helium double-ionization potential via photoemission experiments. The results have also
demonstrated that TPE spectroscopy offers a valuable and alternative method to calibrate
the energy scale of VUV beam lines.
A detailed study of the double-ionization region has shown that the cross section for
double ionization is consistent with the classical Wannier model. However, despite all
attempts, a definite statement on the value of the exponent could not be extracted from the
analysis of all the existing data. Whether this is an intrinsic limit of this type of measurement
or whether it can be overcome by improvements to the experimental set-up is still a matter
of investigation.
The measured asymmetry between the two branches of the spectrum near the doubleionization threshold shows that further work is needed in order to understand the role of
resonances in the energy region below the double-ionization potential and does not support
the proposed model for second-order collisional effects.
Acknowledgments
The authors thank L Romanzin for his technical support during the measurements and
acknowledge financial support from European Union (contract ERBFMGECT950022), from
the Research Council for Natural Sciences of the Academy of Finland and from NATO (CRG
96014).
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