INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 2927–2948
PII: S0953-4075(02)35466-X
High-resolution threshold photoelectron
measurements of the Ne+ 2p4 n satellite states
P Bolognesi1 , L Avaldi1 , D R Cooper2 , M Coreno1 , R Camilloni1 and
G C King2
1
2
CNR-IMIP, Area della Ricerca di Roma 1, Rome, Italy
Department of Physics and Astronomy, Manchester University, Manchester, UK
Received 3 April 2002, in final form 7 May 2002
Published 18 June 2002
Online at stacks.iop.org/JPhysB/35/2927
Abstract
The Ne+ 2p4 n satellite states lying between the Ne+ 2s main line and the
Ne2+ 2p4 (3 P, 1 D, 1 S) doubly charged ion states have been studied. The study
combined the high-energy resolution of the threshold photoelectron technique
and of the gas phase photoemission beamline at the Elettra synchrotron radiation
source. The threshold photoelectron (TPE) measurements show many more
states than observed in previous photoemission or optical measurements. The
TPE spectrum in the region of the Ne2+ 2p4 (1 D) ionization potential shows a
clear cusp-like shape, the typical signature of threshold photodouble ionization.
This feature is found to be well represented by an asymmetric power law as in
the He2+ (1 S) case.
1. Introduction
The absorption of a single photon, of sufficient energy, may induce the ejection of one electron
and the simultaneous excitation of another to an unoccupied orbital. These excited states of
the ion appear in the photoelectron spectrum as ‘satellite lines’ lying at higher energies than
the ‘main lines’, which correspond to single-electron processes. In LS notation, the excited
electron is labelled by the principal quantum number n and the angular momentum of the
excited orbital. In this picture, the satellite states form series that can be built up by adding a
Rydberg electron, n, onto a doubly charged ion core. As the excitation energy is increased, the
electron is promoted to higher Rydberg states until it is eventually removed and photodouble
ionization (PDI) occurs. In the case of Ne the processes are represented by
hν + Ne → Ne+ 2p4 (3 P, 1 D, 1 S)n + e−
(1)
hν + Ne → Ne2+ 2p4 (3 P, 1 D, 1 S) + e− + e− .
(2)
and
0953-4075/02/132927+22$30.00
© 2002 IOP Publishing Ltd
Printed in the UK
2927
2928
P Bolognesi et al
In process (2), the two photoelectrons share the available excess energy, Eexc , in a continuous
manner, where Eexc = hν − IP2+ , and IP2+ is the double-ionization potential. In reality,
the excitation of a satellite state is more complicated than this schematic picture. Being a
two-electron process, it is not allowed in the ‘single-particle’ approximation. The excitation
of satellite states is in fact dominated by electron–electron correlations, as is manifested in the
strong mixing of configurations, so that the purity of the LS states is lost [1]. This results in
the low cross sections for the excitation of satellite states whose intensities are typically of the
order of a few per cent of the corresponding main line [2].
The main goals in the experimental study of satellite states are the determination of their
binding energies and the understanding of the dynamics of their formation. A further point of
interest is the comparison of their energies and intensities with the theoretical predictions, which
differ depending on the type of electron correlation taken into account. Various experimental
approaches have been adopted to study the satellite states in Ne. The most complete and
well-resolved set of spectroscopic data has been obtained from optical measurements [1].
Photoemission measurements have been carried out for different values of photon energy. The
results obtained from x-ray photoemission spectroscopy [2] show the lowest members of the
ns, np and nd series (n 6), corresponding to the 2 P, 2 S final state symmetries. At lower
excitation energies, the photoelectron spectroscopy (PES) measurements [3,4] also display the
lowest members of the nf and ng series (n 8). These PES measurements also show more
final state symmetries, such as 2 D and 2 F that contribute to the spectrum via the conjugate
shake-up mechanism [2], and some quadruplet final states. In the near-threshold region [5–7],
the threshold photoelectron (TPE) spectroscopy measurements show extended satellite series
(n 13) [6] and a large variety of peaks corresponding to all possible final state symmetries
and to both doublet and quadruplet states. These observations were possible because of the
high energy resolution that characterizes the threshold technique, but also because some of the
states are only excited at threshold. The differences in the intensity distributions of the satellite
states with respect to photon energy reflect the appearance and then the dominance of ‘dynamic
correlations’ as the threshold region is approached. In the high-energy regime, the ejected
photoelectron is considered fast enough to have no significant interaction with the residual
ion. In this limit, known as the ‘sudden approximation’, a satellite transition is successfully
described as a shake-up process [8] due to the response of the passive electrons to the ionization
process. Within this approximation, the shake-up intensity distribution arises from the initial
state configuration interactions (ISCI) and final ionic state configuration interactions (FISCI),
where the latter appear to be dominant (see [9, 10] and references therein). These types of
correlation are, to a first approximation, independent of the photoelectron kinetic energy so that
they are sometimes referred to as ‘intrinsic correlations’ [9]. As the near-threshold region is
approached and the kinetic energy of the ejected electron decreases the sudden approximation
no longer holds. This introduces an energy dependency in the shake-up model, leading to a
decrease in the intensities of the shake-up satellites in the near-threshold region. The electron–
electron interactions introduced by the slowly escaping photoelectron also become important
towards threshold [9]. These include continuum state configuration interactions (CSCI), and
mechanisms of ‘inelastic internal collisions’, where the photoelectron collides with another
electron on its way out. Two-step ionization, via the autoionization of excited neutral states,
is also possible, i.e.,
hν + Ne → Ne∗∗ 2p4 n n → Ne+ 2p4 n + e− .
(3)
Indeed, the partial ionization cross sections of specific satellite states, measured in constant
ionic state (CIS) measurements, have shown that indirect ionization can be the dominant
mechanism for the formation of the satellite states [11–13], especially in the near-threshold
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2929
region [14]. As a consequence, new spectral features that only exist in the vicinity of their
respective thresholds can be observed. So, the complexity of a TPE spectrum is due to the fact
that many types of electron correlation and indirect processes are active at threshold.
From the experimental point of view, the high sensitivity and energy resolution of TPE
spectroscopy make it an ideal tool to study the processes characterized by a low cross section
and a high density of states, e.g. [15–17]. With the advent of third-generation synchrotron
radiation sources further improvements, in terms of energy resolution and sensitivity, have
been achieved. Now the quality of the photoemission experiments is comparable to that of the
optical data. In TPE spectroscopy particular care has to be taken to distinguish ionic features
from features due to neutral, autoionizing states that decay into ion states. This is well known
in TPE spectroscopy [16], but it becomes more apparent when a high-resolution photon source
is employed. Comparison between the photoemission spectra and photoabsorption spectra
provides a very useful way to distinguish between the two processes.
As the satellite series approach their limit, for n → ∞, the energy spacing
between adjacent peaks and among the different series is reduced until the peaks become
indistinguishable, merging together in a continuum just below the double-ionization threshold.
Above this threshold (process 2) a finite yield of low-energy electrons is always present, due to
the continuous energy sharing between the two ejected electrons. The PDI process has been the
subject of extensive theoretical and experimental study. It is one of the fundamental phenomena
in atomic physics, because it involves the understanding of the three-body Coulomb interaction.
Particularly in the vicinity of the double-ionization threshold, the very slow photoelectrons
moving away from the residual doubly charged ion have long interaction times and their
motion is strongly correlated. For the He double-differential cross section, for example, a
typical cusp-like shape has been predicted [18] and observed in TPE measurements at the
double-ionization threshold (see, for example, [19] and references therein). This feature is
attributed to electron–electron correlations, producing a vanishingly small yield of low-energy
electrons. Although He is the archetypal target to investigate the PDI process, similar studies
have also been undertaken in the heavier rare gases, where different initial and final state
configurations are possible. Similar observations as for the He case have been reported for
specific doubly charged ion state symmetries in Ne2+ [6, 7] and Ar 2+ [16]. However, because
the doubly charged ion continua can be distorted by excited neutral states or satellite states
converging to higher-lying doubly charged ion states, a quantitative analysis of these features
becomes more difficult. For example, in Kr and Xe [17] the high density of states has prevented
any conclusions being made in those systems.
Following our studies of He [19] and Ne, below the Ne+ 2s main line [20], we present a
high-resolution study of the full Ne+ 2p4 n satellite spectrum in the energy region between the
Ne+ 2s and the Ne2+ 2p4 (3 P, 1 D, 1 S) doubly charged ion states. This work shows many new
satellite features and also allows the cusp-like feature at the Ne2+ 2p4 (1 D) state to be studied
quantitatively.
2. Experimental details
2.1. The experimental apparatus and procedures
The experimental set-up consisted essentially of a TPE spectrometer connected to the gas
phase photoemission beamline at the third-generation synchrotron radiation source Elettra.
This beamline consists of a 4.5 m undulator source [21] and a variable-angle spherical grating
monochromator with pre- and post-focusing optics placed before and after the entrance and
2930
P Bolognesi et al
exit slits, respectively [22, 23]. Five interchangeable gratings cover the energy range from 20
to about 1000 eV. The resolving power E/E is about 10 000 over the full range. This results
in an expected energy spread of the incident radiation of about 4 meV in the region of interest
of this work.
The threshold spectrometer and its modes of operation have been described in detail
elsewhere [24]. The collection of threshold electrons is based on the penetrating field
technique [25, 26]. The electron analyser is made of an electrostatic lens system and a
127◦ cylindrical deflector analyser (CDA) [26] where the electrostatic lens uses an extracting
electrode as its first stage. The electrostatic lens system was designed for the efficient
transmission of low kinetic energy electrons and is a combination of two three-aperture lenses
with two 1 mm defining apertures. The field penetration of this electrode through a 5 mm
grounded aperture forms a potential well at the interaction region which provides a large
collection angle (∼4π Sr) for almost-zero energy electrons. This results in a combination of
high detection efficiency and high energy resolution in the collection of threshold electrons. The
purpose of the 127◦ CDA is to discriminate against energetic photoelectrons that are emitted
in the direction of the analyser. Electrons transmitted by the analyser are detected using a
channel electron multiplier (Philips X919). The typical lineshape of a TPE peak results from
a combination of the transmission efficiency of the extraction field, the profile of the photon
source and the transmission of the 127◦ CDA. The transmission function of the extraction stage
has a sharp rise at zero-kinetic energy, a half width of a few meV, and then a rapid decrease
to higher energy. The low-energy side of the transmission function is a direct measure of the
photon resolution while the high-energy side is dominated by the transmission function of the
CDA. The threshold analyser was housed inside the multicoincidence end-station [23] of the
beam line and placed at 0◦ with respect to the direction of polarization of the light. The gas
source was an effusive gas jet produced by a 0.3 mm bore stainless steel needle which was
mounted on a x–y–z translator for precise alignment with the spectrometer. The experiment
was conducted at a gas pressure of Ne at the interaction region of typically 3 × 10−4 mbar with
a base pressure in the chamber of 10−7 mbar. An empirically determined voltage was applied
to the needle to optimize the detection efficiency for threshold electrons.
A windowless gas ionization cell was attached to the rear of the main experimental
chamber for calibration of the incident photon energy [23]. A photodiode (International
Radiation Detectors Ltd type AXUV-100) was located at the exit of the gas cell to monitor the
light intensity and to normalize both the photoion and photoelectron signals to the incident
photon flux. A computer running a Labview program set the photon energy and recorded
the threshold electron signal, the photoion current and the light intensity. A TPE spectrum is
obtained by scanning the photon energy over the region of interest and measuring the threshold
electron signal. Tuning of the threshold spectrometer was optimized at periodic intervals by
observing the peak corresponding to the Ne+ 2s main line. The overall energy resolution of
the measurements was approximately 9 meV, full width at half maximum (FWHM).
The TPE spectrum of Ne spans the energy region from 48.36 to 69.80 eV. It was recorded
over several different regions, with an average step size of 1.1 meV. This was done to optimize
the intensity of the light output from the undulator, which has a FWHM of about 4% of the
selected photon energy. Within each region, the spectrum was normalized to the variation of the
photon intensity as measured by the photodiode. Overlapping peaks in adjacent regions were
then used to match the measured intensities from one region to another. The photon energy
was calibrated using the known structures in the photoabsorption spectra of the Ne∗∗ and He∗∗
doubly excited states in the regions 48–53 eV [14] and at about 65.2 eV [27], respectively. In
the region between 53 and 65 eV, a comparison with the optical data [1] was used to check the
validity of this calibration and, where needed, corrections were applied to the TPE data.
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2931
2.2. Observation of neutral states in a TPE spectrum
It is well known in TPE spectroscopy that the spectra can be strongly influenced by the presence
of neutral, autoionizing states lying at or just above the ion states [16, 28]. If the resonance is
degenerate with the ion state then the threshold feature will be enhanced. If the autoionizing
electron has a finite energy that lies within the transmission function of the threshold analyser,
it will show up as a structure superimposed on the lineshape of the ion peak or as a separate peak
lying just above it. This assumes that the energy spread in the photon beam is comparable to or
smaller than the threshold resolution of the analyser, as is the case here. This effect has become
increasingly apparent with the improved energy resolution and higher fluxes of third-generation
synchrotron radiation sources, as clearly demonstrated in figures 1(a) and (b). In figure 1(a),
the TPE spectrum in the region of the Ne+ 2p4 (3 P)3s(2 P3/2,1/2 ) states shows the two main TPE
peaks corresponding to the 2 P3/2 , 2 P1/2 components. It also displays structures on the 2 P3/2
peak corresponding to Ne∗∗ 2p4 (3 P)3s(2 P1/2 )np autoionizing resonances. The lineshapes of
the ionic states have been approximated by asymmetric Lorentzian functions with a rising edge
of 4 meV (FWHM) and a falling tail of 14 meV (FWHM). This lineshape was extracted from
the peak shape of the 2p4 (3 P)3s(2 P1/2 ) component that is free from autoionizing structure.
The structure in the region of the 2p4 (3 P)3s(2 P3/2 ) state is well reproduced by a superposition
of two contributions:
(i) the asymmetric Lorentzian function corresponding to the 2p4 (3 P)3s(2 P3/2 ) ion state (the
thick line presented in figure 1(a)); and
(ii) a series of symmetric Lorentzian functions with a FWHM of ≈4 meV, that corresponds
to the photon energy resolution.
The energy positions of these peaks have been fitted by a modified Rydberg formula [29]
representing the Ne∗∗ 2p4 (3 P)3s(2 P1/2 )np (n = 15–22) series of autoionizing resonances,
converging to the Ne+ 2p4 (3 P)3s(2 P1/2 ) ion.
Previous high-resolution absorption
measurements [14] only resolved up to n = 18.
A second example of the influence of autoionizing states is illustrated in figure 1(b).
This shows the TPE and the absorption spectra collected simultaneously in the regions of the
Ne+ 2p4 (3 P)3s(4 P5/2,3/2,1/2 ) ion states and the Ne∗∗ 2p4 (3 P)3s(2 P)6p autoionizing states. It
can be noted that the peaks in the TPE spectrum labelled as 1 and 2 do not match any known
ionic state (indicated by the vertical bars at the bottom of the spectrum), while peak 3 appears
to be far more intense than would be expected from the statistical ratio of 6:4:2 for the three
J components, 4 P5/2 :4 P3/2 :4 P1/2 . However, by comparison with the absorption spectrum, it
is possible to understand these features in terms of Ne∗∗ autoionizing states: TPE peaks 1
and 2 correspond to excited neutral states rather than ionic states, and peak 3 corresponds
to the Ne+ 2p4 (3 P)3s(4 P1/2 ) state, whose intensity is dominated by the autoionization of the
Ne∗∗ 2p4 (3 P)3s(2 P1/2 )6p1/2 resonance. The widths of the observed autoionizing features
depend only on the photon resolution. Consequently, the better the photon resolution the
more dominant the contribution of the indirect process is with respect to the direct one. This
situation has some analogy with photoabsorption measurements, where a poor photon energy
resolution reduces the intensity of the excited neutral states with respect to the direct ionization
continuum. To aid the correct interpretation of the TPE data we have used, whenever possible,
the support of photoabsorption measurements carried out simultaneously as for the case in
figure 1(b). This identifies unambiguously any doubly excited states that give features in the
TPE spectrum and helps to distinguish between the two processes.
2932
P Bolognesi et al
1500
a
Ne
yield (arb. units)
1200
900
**
4 3
2
Ne 2p ( P)3s( P1/2)np
n=15
600
+
4 3
2
Ne 2p ( P)3s( PJ)
300
TPES
0
J=3/2
49.30
J=1/2
49.35
49.40
49.45
49.50
photon energy (eV)
1200
b
3
yield (arb. units)
900
**
600
4 3
2
Ne 2p ( P)3s( P)6p
Absorption
spectrum
1
300
+
4 3
4
Ne 2p ( P)3s( PJ)
2
0
48.70
J=5/2
48.75
TPES
J=3/2
J=1/2
48.80
48.85
48.90
photon energy (eV)
Figure 1. TPE spectrum of the Ne+ 2p4 3s states. Excited neutral states lying within the threshold
analyser resolution appear in the spectrum as: (a) sharp peaks superimposed on the lineshape of
an ionic state or (b) distinctly separate structures. In both cases the TPE data have been fitted by
a combination of asymmetric (for the ion states) or symmetric (for the autoionizing resonances)
Lorentzian shapes (see text).
3. Results and discussion
The full TPE spectrum of the Ne+ 2p4 n satellite states extends from just below the Ne+ 2s
main line to above the Ne2+ 2p4 (1 S) double-ionization potential. For the sake of clarity the
full spectrum has been divided into six energy regions which are presented in figures 2(a)–(f)
together with the suggested assignments of the different features. These assignments have been
deduced from optical measurements [1] (full lines) or from our own fitting procedures (dashed
lines) where previous data were not available. The main features that remain unassigned
are indicated by the small squares. All data in figures 2(a)–(f) are on a common scale
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
1800
6
D
3p
3s
2000
4
2
P
P
P
1000
2
D
2,4
4
4 1
2
4 1
2s 2p ( D)nl
2
S
D
2
4 3
2s 2p ( P)nl
1200
P
2
4
2
2s 2p ( S)nl
b
1500
2
F
2
P
4s
4 3
3d
2
2s 2p ( P)nl
yield (arb. units)
4 1
3s
2
2s 2p ( D)nl
2
3p
2s2p
yield (arb. units)
a
3s
3000
2933
S
2
900
4
2
D
4
600
F
2
4
P
D
4
P
P
2
P
F
300
0
0
49
50
51
52
53
55.4
55.6
55.8
56.0
photon energy (eV)
1800
56.6
56.8
57.0
2
D
P
2
4
4
4
D
2,4
P
D
2
P
P 2P
D
2,4
D
2
S
D
2
4
F
S
4,2
F
8f-8g
4f
2
D
9f-9g
7f-7g
6f-6g
2
G F
11f-11g
2+ 3
12f-12g
10f-10g
P
9p
P
2
5s
4d
4p
4
4,2
2
D P
7s
200
2
4
2
8p
4f
4d
2
2
600
2
F
6p
P S D
D
6s
2
4 3
2s 2p ( P)nl
2
F
5f-5g
2
5s
4p
4
2
4s
G
2s 2p ( P)nl
2
5d
1200
4 3
5p
2
d
4 1
7p
2
2s 2p ( D)nl
6d
P
4 1
2s 2p ( D)nl
4 1
yield (arb. units)
3p
2
3d
2
yield (arb. units)
56.4
300
2
2s 2p ( S)nl
c
·
Ne ( PJ)
·
·
100
F
2
P
4,2
·
D
0
0
57.6
58.0
58.4
58.8
59.2
59.6
60.0
60.5
61.0
61.5
62.0
62.5
photon energy (eV)
photon energy (eV)
200
56.2
photon energy (eV)
30
e
f
2
4 1
2
4 1
2s 2p ( S)nl
3d
yield (arb. units)
ns
100
4s
4p
2
5s
4d-f-g
np
4 1
2s 2p ( S)nl
2s 2p ( D)nl
ns
n=6
n=18
n=6
n=5
nd-nf-ng
n=5
2+ 1
Ne ( D)
50
n=26
yield (arb. units)
150
20
np
n=5
nd - nf
n=5
2+ 1
Ne ( S)
10
0
63
64
65
photon energy (eV)
66
66
67
68
69
70
photon energy (eV)
Figure 2. The full TPE spectrum of the Ne+ 2p4 n satellite states has been split into six different
energy regions (a)–(f). The vertical bars connected by the full line are the assignments according
to the optical measurements of Persson [1]. The vertical bars connected by the dashed line are
assignments based on the predictions of a Rydberg formula.
of intensity. In the low-energy range (figures 2(a)–(c)) the spectra display well isolated
structures corresponding to the lowest members of the various Ne+ 2p4 (3 PJ , 1 D, 1 S)n satellite
series, with J = 2, 1, 0. As the Ne2+ 2p4 (3 PJ ) double-ionization thresholds are approached
(figure 2(d)) the density of states increases and there is overlapping of the different series.
Above the region of the Ne2+ 2p4 (3 PJ ) thresholds (figures 2(e), (f)) regular series appear,
converging to the Ne2+ 2p4 (1 D, 1 S) states.
2934
P Bolognesi et al
Table 1. A comparison of the peaks in the TPE spectra presented in figure 2 with previous
optical [1] and TPE [6] measurements. The Ne∗∗ states lying, according to photoabsorption [14]
and CIS [12, 13] measurements, within 50 meV of the measured ion states and used for their
assignment are also reported.
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energy (eV)
This work
[6]
Energya (eV)
Assignment
48.48
2s2p6
48.739
(3 P)3s(4 P5/2 )
N
(3 P)3s(4 P3/2 )
(3 P)3s(4 P1/2 )
48.742
48.764
48.801
48.844
(3 P)3s(2 P3/2 )
N
N
N
N
N
49.354
49.36
49.368
49.376
49.383
49.387
49.429
(3 P)3s(2 P1/2 )
49.43
52.094
52.119–52.144
(3 P)3p(4 P5/2 )
(1 D)3s(2 D5/2,3/2 )
(3 P)3p(4 P3/2,1/2 )
52.10
52.455
52.463
52.476
52.482
52.501
52.533
52.537
52.47
52.497
52.528
52.546
(3 P)3p(4 D7/2 )
N
N
(3 P)3p(4 D5/2 )
(3 P)3p(4 D3/2 )
(3 P)3p(4 D1/2 )
52.691
(3 P)3p(2 D3/2 )
52.693
52.75
52.755
(3 P)3p(2 D1/2 )
N
52.756
52.782
52.913
52.932
(3 P)3p(2 S1/2 )
(3 P)3p(4 S3/2 )
52.913
52.939
52.92
53.082
53.098
(3 P)3p(2 P3/2 )
(3 P)3p(2 P1/2 )
53.081
53.096
53.08
55.587
55.592
(1 D)3p(2 F5/2 )
(1 D)3p(2 F7/2 )
55.591
55.601
55.58
55.824
55.853
55.874
(1 D)3p(2 P3/2 )
N
(1 D)3p(2 P1/2 )
(1 S)3s(2 S1/2 )
55.826
55.831
55.853
55.874
55.83
55.954–55.956
(1 D)3p(2 D3/2,5/2 )
55.956
55.95
48.803
48.84
49.353
52.126
48.74
49.35
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
48.764b
2p4 (3 P)3s(2 P)6p
49.363b
49.370b
49.377b
2p4 (3 P)3s(2 P)16p
2p4 (3 P)3s(2 P)17p
2p4 (3 P)3s(2 P)18p
52.474b
52.48c
2p4 (3 P)3p(2 P)5d
52.792b
2p4 (3 P)3p(2 P)7d
52.10
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2935
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
Energy (eV)
This work
[6]
56.179
56.189
56.202
56.214
(3 P)3d(4 D7/2 )
(3 P)3d(4 D5/2 )
(3 P)3d(4 D3/2 )
(3 P)3d(4 D1/2 )
N
56.178
56.188
56.203
56.214
56.221
56.307
56.318–56.319
56.344
56.372
56.381
56.403–56.413
56.431
(3 P)3d(4 F9/2 )
(3 P)3d(4 F7/2 , 2 D5/2 )
(3 P)3d(2 D3/2 )
(3 P)3d(2 F7/2 )
(3 P)3d(4 P1/2 , 4 F5/2 )
(3 P)3d(4 F3/2 , 4 P3/2 , 2 F5/2 )
(3 P)3d(4 P5/2 )
56.320
56.344
56.371
56.384
56.412
56.43
56.451
(3 P)3d(2 P1/2 )
N
56.45
56.463
56.499
(3 P)3d(2 P3/2 )
N
(3 P)4s(4 P5/2 )
N
(3 P)4s(4 P3/2 )
(3 P)4s(4 P1/2 )
N
56.50
56.511
56.533
56.543
56.58
56.617
56.629
56.52
56.697
56.768
(3 P)4s(2 P3/2 )
(3 P)4s(2 P1/2 )
56.696
56.766
56.69
57.572
(3 P)4p(4 P5/2 )
57.598
(3 P)4p(4 P3/2 )
57.625
(3 P)4p(4 P1/2 )
57.674
57.711
(3 P)4p(4 D7/2 )
N
N
(3 P)4p(4 D5/2 )
57.674
57.677
57.679
57.71
57.749
(3 P)4p(4 D3/2 )
57.75
57.769
57.778
57.829
57.841
57.854
(3 P)4p(4 D1/2 )
(3 P)4p(2 D5/2 )
N
(3 P)4p(2 D3/2 )
(3 P)4p(2 S1/2 )
(3 P)4p(4 S3/2 )
58.032
58.063
(3 P)4p(2 P3/2 )
(3 P)4p(2 P1/2 )
56.533
56.58
56.618
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
56.680d
(1 D)3d(2 D)4f
57.70
57.697d
(3 P)4p(2 P)8s
57.77
57.776
57.787
57.828
57.839
57.853
57.81
57.777d
(3 P)4p(2 P)9s
58.029
58.059
58.02
56.17
56.35
2936
P Bolognesi et al
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
Energy (eV)
This work [6]
58.989
58.995
(3 P)4d(4 D7/2 )
(3 P)4d(4 D5/2 )
58.987
58.993
N
58.999
(3 P)4d(4 D3/2 )
(3 P)4d(4 D1/2 )
(3 P)4d(4 F9/2 )
(3 P)4d(4 F7/2 )
(3 P)4d(2 D5/2 )
N
(3 P)4d(2 D3/2 )
59.005
59.019
59.039
59.044
59.051
59.056
59.065
(3 P)4d(4 P1/2 )
(3 P)4d(2 F7/2 )
(3 P)4d(4 P3/2 ), (3 P2 )4f,
(3 P)4d(2 P1/2 ), (3 P)4d(4 F5/2 )
(3 P)4d(2 F5/2 )
(3 P2 )4f
(3 P2 )4f
(3 P)4d(4 F3/2 )
(3 P2 )4f
(3 P2 )4f
(3 P)4d(4 P5/2 )
(3 P)4d(2 P3/2 )
(3 P)5s(4 P5/2 )
(3 P1 )4f
(3 P)5s(4 P3/2 )(3 P1 )4f
(3 P1 )4f
N
59.076
59.106
59.122
59.126
59.129
59.133
59.137
59.141
59.145
59.163
59.170
59.200
59.203
59.21
59.222
59.239
59.252
59.258
59.316
(3 P0 )4f
(3 P)5s(4 P1/2 )
(3 P)5s(2 P3/2 )
(3 P)5s(2 P1/2 )
N
59.237
59.254
59.264
59.312
59.318
59.43
(1 D)3d(2 G9/2,7/2 )
59.43
59.435
59.436
59.456
59.511
59.539
59.542
59.594
59.621
59.642
(1 S)3p(2 P3/2 )
(1 S)3p(2 P1/2 )
(1 D)3d(2 P3/2,1/2 )
(1 D)3d(2 S1/2 )
59.436
59.440
59.456
59.512
(1 D)3d(2 D5/2,3/2 )
59.541
(1 D)3d(2 F
59.595
59.621
59.007
59.02
59.037
59.044
59.051
59.066
59.072
59.106
59.115–59.118
59.124
59.125
59.129
59.132
59.136
59.136
59.146
59.167
59.172
59.2
59.202–59.203
59.212
5/2,7/2 )
(3 P)5p(4 P5/2 )
(3 P)5p(4 P3/2 )
59.116
59.06
59.17
59.42
59.51
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
59.01c
59.04c
(1 D)3d(2 S)5p
(1 S)3p(2 P)6d
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2937
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energy (eV)
This work
[6]
Energya (eV)
Assignment
59.663
59.672
59.685
(3 P)5p(4 D7/2 )
(3 P)5p(4 P1/2 )
(3 P)5p(4 D5/2 )
59.729
59.744
(3 P)5p(4 D3/2 )
(3 P)5p(2 D5/2 )
(3 P)5p(2 S1/2 )
(3 P)5p(4 D1/2 )
59.729
59.743
(1 D)4s(2 D5/2,3/2 )
(3 P)5p(4 S3/2 )
(3 P)5p(2 D3/2 )
(3 P)5p(2 P3/2 )
(3 P)5p(2 P1/2 )
59.769
59.775
59.778
59.847
59.87
(3 P)5d(4,2 D)
60.281
60.290
60.302
60.307
60.313
60.323
60.346
60.352
59.758
59.77
59.774
59.779
59.849
59.878
60.304
60.308
(3 P)5d(4 F9/2 )
(3 P)5d(4 F7/2 )
60.348
60.353–60.356
(3 P2 )5f
(3 P2 )5f, (3 P2 )5g
(3 P2 )5g
(3 P2)5f
(3 P)6s(4 P5/2 )
(3 P)5d(2 F7/2 )
60.358
60.365
60.376
60.399
60.430
60.434
60.435
60.437
60.458
60.466
60.469
60.503
59.74
59.76
59.84
60.361
(3 P)6s(4 P3/2 )
N
(3 P1 )5f
(3 P1 )5g
(3 P1 )5f
(3 P1 )5g
(3 P)6s(2 P3/2 )
(3 P0 )5f
(3 P0 )5g
(3 P)6s(2 P1/2 )
60.365
60.377
60.383
60.390
60.395
60.418
60.429
60.432
60.435
60.438
60.458
60.463
60.466
60.505
unassigned
unassigned
60.653
60.698
60.84
(3 P)6p
60.716
60.723
60.730
60.747
60.96
60.33
60.40
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
2938
P Bolognesi et al
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
60.858
60.86
60.955
(1 D)4p(2 F5/2 )
(1 D)4p(2 F7/2 )
(1 D)4p(2 P3/2 )
60.97
60.976
(1 D)4p(2 D5/2,3/2 )
(1 D)4p(2 P1/2 )
(3 P)6d(4,2 P)
61.029
(3 P2 )6f
(3 P2 )6g
(3 P)7s(4 P5/2 )
61.053
(3 P)7s(4 P3/2 )
61.016–61.022
(3 P)6d(4,2 F)
61.097–61.101
61.114
61.134
(3 P1 )6f, (3 P1 )6g
(3 P)7s(2 P3/2 )
(3 P0 )6f
(3 P0 )6g
unassigned
unassigned
unassigned
61.064
61.070
61.072
61.09
61.127
(3 P2 )7f
(3 P2 )7g
61.40
61.415
61.39
(3 P1 )7f
(3 P1 )7g
(3 P0 )7f
(3 P0 )7g
61.476
61.493
61.511
61.529
61.546
61.47
(3 P)8p
61.610
61.681
(3 P
2 )8f
61.691
61.761
61.796
(3 P1 )8f
(3 P0 )8f
(3 P)9p
(3 P2 )9f
(3 P1 )9f
61.767
61.788
61.820
61.886
61.955
61.860
61.94
61.07
61.29
61.499–61.502
61.535
61.536
60.752
60.859
60.877
60.950
60.958
60.966
60.971
60.992
60.998
61.012
61.016
61.191
61.20
61.224
61.279
61.288
61.310
61.331
(3 P)7p
61.419–61.423
Energy (eV)
This work
[6]
61.65
61.94
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2939
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
Energy (eV)
This work
[6]
61.974
(3 P0 )9f
61.972
(3 P2 )10f
(3 P1 )10f
62.026
62.071
62.113
62.131
62.151
62.170
62.213
62.21
62.209
(3 P0 )10f
(3 P2 )11f
(3 P2 )12f
(3 P1 )11f
(1 D)4d(2 G9/2,7/2 )
62.276
(1 D)4d(2 F5/2,7/2 )
62.307
62.319
62.323
62.338
62.342
(1 D)4f
(1 D)4f
(1 D)4f
(1 D)4f
(1 D)4f
62.271
62.293
62.303
62.313
62.328
62.333
62.350
62.366
62.31
62.379
(1 D)5s(2 D5/2,3/2 )
62.378
62.397
62.437
62.60
62.64
63.545–63.575
(1 D)5p
62.86
62.911
62.84
(1 S)3d
63.16
63.22
63.25
63.27
63.20
(1 S)4s(2 S1/2 )
63.40
63.48
(1 D)5f–5d–5g
(1 D)6s
63.542
63.572
63.54
(1 D)6p
63.817
63.848
63.908
63.83
(1 D)6f
64.206
64.223
64.244
64.260
64.19
64.410
64.427
64.37
64.220–62.227
(1 D)7s
(1 D)6d
(1 D)7p
63.40
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
2940
P Bolognesi et al
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
64.623
(1 D)8s
(1 D)7d
(1 D)7f
64.884
Energy (eV)
This work
[6]
64.63
(1 D)8p
(1 S)4p
64.60
64.638
64.653
64.689
64.724
64.745
(1 D)9s–8d–8f
(1 D)9p
64.89
64.967
64.87
(1 D)10s–9d–9f
(1 D)10p
65.066
65.120
65.04
(1 D)11s–10d–10f
(1 D)11p
65.190
65.220
65.17
(1 D)12s–11d–11f
(1 D)12p
65.282
65.513
65.27
(1 D)13s–12d–12f
(1 D)13p
65.353
65.375
65.34
(1 D)14s–13d–13f
(1 D)14p
(1 D)15s–14d–14f
(1 D)15p
(1 D)16s–15d–15f
(1 D)17s–16d–16f
(1 D)18s–17d–17f
(1 D)19s–18d–18f
(1 D)20s–19d–19f
(1 D)21s–20d–20f
(1 D)22s–21d–21f
(1 D)23s–22d–22f
(1 D)24s–23d–23f
(1 D)25s–24d–24f
(1 D)26s–25d–25f
65.408
65.426
65.452
65.463
65.485
65.515
65.539
65.558
65.574
65.589
65.602
65.612
65.621
65.629
65.636
(1 S)4d
(1 S)5s
66.031
66.092
66.174
66.240
(1 S)5p
66.598
66.652
66.700
66.782
65.96
66.10
66.63
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2941
Table 1. (Continued.)
Ne∗∗ states
Ne+ (2p4 )n states
TPE measurements
Optical measurements [1]
Energya (eV)
Assignment
Energy (eV)
This work
[6]
(1 S)5d
(1 S)6s
67.269
67.28
67.336
Photoabsorption and CIS
measurements
Energy (eV)
Assignment
67.23
67.31
67.536
(1 S)6p
67.598
67.651
67.57
(1 S)6d
(1 S)7s
67.938
67.977
67.92
(1 S)7p
68.059
68.128
68.08
(1 S)8s
(1 S)8p
68.332
68.456
68.32
(1 S)9s
(1 S)9p
68.585
68.672
68.60
(1 S)10s
(1 S)10p
68.758
68.826
68.74
(1 S)11s
(1 S)11p
68.882
68.938
68.91
(1 S)12s
(1 S)13s
(1 S)14s
(1 S)15s
(1 S)16s
(1 S)17s
(1 S)18s
68.975
69.050
69.100
69.142
69.180
69.208
69.233
68.99
a Ne+
2p state at 21.565 eV.
Taken from [14].
c Taken from [12].
d Taken from [13].
b
The results are summarized in table 1, where they are compared with previous TPE
and optical data. The doubly excited neutral states known to lie within 50–60 meV of the
measured TPE peaks and used to assign some of the features in the TPE spectrum are also listed.
Following the classification already adopted in previous work on Ne+ satellites [1–7, 11–13],
we have labelled the lower-energy states in the LS scheme and the higher-energy ones in the
j k coupling scheme. In the LS scheme, levels are built on the Ne2+ 2p4 (3 P, 1 D, 1 S) cores. In
the j k coupling, the core hole is described in the jj scheme, so that levels are built on the five
distinct groups of Ne2+ 2p4 (3 P2 , 3 P1 , 3 P0 , 1 D2 , 1 S0 ), whereas the excited electron couples its
spin and angular momentum to this state following LS coupling rules. The j k scheme is known
to be more appropriate for increasing and n [1], where all the electrostatic interactions between
the outer electron and the core are smaller than the magnetic interactions within the core.
2942
P Bolognesi et al
The discussion of the results is organized in two sections. In the first, the satellite states
are analysed while in the second the features in the regions of the Ne2+ 2p4 (3 PJ , 1 D, 1 S)
double-ionization thresholds are discussed.
3.1. The N e+ 2p 4 n satellite states
Almost 300 peaks are observed in the full TPE spectrum presented in figures 2(a)–(f). The
features in the region just below the Ne+ 2s main line have already been presented in a previous
work [20] and so will not be discussed here. For most of the states very good agreement is
observed, with the optical data [1] and the present photoemission results generally matching
within a few meV. Some differences, however, may be noted. Some states identified by
the optical data do not appear in the TPE spectrum while there are peaks observed in the
TPE spectrum that do not find a correspondence in the optical measurements. For the first
case, the most relevant examples are the 2p4 (3 P)4p(4 P) and the 2p4 (3 P)5p(4 P3/2,1/2 ) states
at 57.6, 59.64 and 59.67 eV, respectively. These states do not appear in previous PES spectra,
suggesting that the series are ‘unfavoured’ for direct excitation. They also do not appear
in previous TPE spectra, possibly because of the absence of degenerate neutral states that
could enhance their low cross section. A similar observation is valid for the 2p4 (3 P)7s state.
Many more examples of the second case can be seen in table 1. For most of these states,
we suggest that they can be assigned either as (a) excited neutral states that autoionize to
nearby ionic states or (b) higher members of known Ne+ satellite series. For possibility (a), we
were aided by the photoabsorption measurements taken simultaneously, by previous absorption
measurements [14] and by CIS measurements of selected satellite states [12,13]. From table 1,
it can be noticed that excited neutral states, Ne∗∗ , preferentially decay to Ne+ states with the
same Ne2+ core where the Rydberg electron acts as a spectator. However, a rearrangement of
the core is also possible, probably due to the mixing of configurations and loss of the LS purity
for the ionic states [12]. Examples of this behaviour are given by the Ne∗∗ 2p4 (1 D)3d4f, 3d5p
and 2p4 (1 S)3p6d states that couple with the satellite states built on the Ne2+ 2p4 (3 P) core. This
is a clear manifestation of the role of electron correlations at all steps of the excitation process.
They result in the modification of the two-electron orbitals in the transition from the initial to
the intermediate states (excitation of a doubly excited state) and the coupling to different cores
in the final ionic state.
Above 60 eV the TPE spectrum becomes more complicated due to the higher density of
states. Furthermore, the uncertainties in the optical measurements become larger because the
spectral features become weaker. Thus, some peaks could not be assigned unambiguously as
either excited neutral states or different J components of the satellite states. In particular, there
is a lack of information for the Ne+ satellites of high n and and satellites converging to the
Ne2+ 2p4 (1 D, 1 S) states. To predict the positions of these states we used a Rydberg formula
that was fitted to the observed states, averaged over the J components. In this procedure, the
limits of the series and the quantum defects were left as free parameters but were assumed to
be constant within each series. Their deduced values are reported in table 2. This procedure
gave double-ionization potentials that are in agreement with the values obtained from threshold
photoelectron—threshold photoelectron coincidence (TPEsCO) experiments [28]. In addition,
the deduced quantum defects are consistent with the type of orbital to which they refer. The
quantum defects for d, f and g orbitals are expected to be very similar and close to zero.
Furthermore, because the expected quantum defect for an s orbital is ∼1, it follows that ns
and (n − 1)d, f or g states overlap, at n larger than 5. Because of this, it was not possible to
distinguish unambiguously the s, d, f and g series at high n.
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2943
Table 2. Parameters of the Rydberg formula fitted to each Ne+ satellite series (averaged over the
J components) together with their uncertainties deduced from the fitting procedure.
Fit
Ne+ state
(3 P)ns(2,4 P)
(3 P)np(4 P)
(3 P)np(2 P)
(3 P)np(4 D)
(3 P)np(2 D)
(3 P)np(2,4 S)
(3 P)nd(2,4 D)
(3 P)nd(2,4 P)
(3 P)nd(2,4 F)
(3 P2 )nf–ng
(3 P1 )nf–ng
(3 P0 )nf–ng
IP2+ (eV)a
Quantum
defecta
62.63 ± 0.05b
—
—
0.60 ± 0.02
0.68 ± 0.02
0.66 ± 0.02
0.63 ± 0.02
0.06 ± 0.02
0.05 ± 0.02
IP2+ (eV)
[28]
62.527 ± 0.002
62.604 ± 0.004
62.664 ± 0.006
0.02 ± 0.02
0.01 ± 0.02
0.003 ± 0.020
(1 D)ns(2 D)
(1 D)np(2 F)
(1 D)np(2 P)
(1 D)np(2 D)
(1 D)nd
(1 D)nf
65.72 ± 0.02
(1 S)ns
(1 S)np
(1 S)nd–nf
69.43 ± 0.01
0.99 ± 0.02
0.68 ± 0.02
0.65 ± 0.02
0.63 ± 0.02
0.004 ± 0.020
0.04 ± 0.02
65.740 ± 0.006
0.99 ± 0.02
0.55 ± 0.02
0.04 ± 0.02
69.430 ± 0.002
[1]
Highest n
observed
This work
7
5
6
3
5
10
4
4
5
7
9
12
5
26c
4
13
4
8
26c
4
3
—
18c
11
a Uncertainty
from the fitting procedure.
over the Ne2+ (3 P2,1,0 ) components.
c Ambiguity between s–d–f.
b Averaged
Based on the general trend of the observed intensity distributions, the ns series seems to
be the dominant one converging to the Ne2+ 2p4 (1 S) threshold, while the nf–ng series seem to
dominate the region approaching the 2p4 (3 PJ ) thresholds. As for the region in the vicinity of
the Ne2+ 2p4 (1 D) threshold, it is difficult to distinguish between ns, nd and nf series, so they
have all been included in table 1. These observations are only partially consistent with the
general trend of the calculated photoionization cross sections of the Ne+ satellite states [30].
In these calculations the Ne+ 2p4 (3 P, 1 D, 1 S)np (n = 3, 4) and Ne+ 2p4 (3 P)3d cross sections
display a broad maximum at about 20 eV above their respective ionization thresholds, and
decrease towards threshold. For the Ne+ 2p4 (3 P, 1 S)3s states, the calculated cross sections
continuously increase towards threshold, while the Ne+ 2p4 (1 D)3s state has a negligible cross
section. Unfortunately, no calculation is available for nf and ng states. In comparison with
these theoretical predictions, the dominance of the Ne+ 2p4 (1 S)ns series in the TPE spectrum
is consistent with the expected behaviour of the conjugate shake-up transition of a 2p electron
to ns orbitals. There is, however, disagreement between theory and experiment with respect to
the intensity of the Ne+ 2p4 (1 D)ns series, that in the present experiment, as in previous TPE
measurements [6], is definitely not negligible.
The dominance of the nf and ng series among those converging to the Ne2+ 2p4 (3 PJ )
thresholds is similar to the Ar case where series with high angular momentum , i.e. nf and ng
series, dominate the TPE spectrum in the proximity of the Ar 2+ 2p4 (3 P, 1 D) thresholds [31].
2944
P Bolognesi et al
The efficient population of states of high n and near the threshold for double ionization was
predicted by Fano [32], within the framework of Wannier theory [18]. This was attributed to
the strong angular correlation between the two slow-moving electrons which enables them to
exchange angular momentum by an amount sufficient to attain high n and values. According
to this model one may tentatively attribute the dominant features in the series converging to the
Ne2+ 2p4 (1 D) threshold to high states. However, the dominance on the ns series among those
converging to the Ne2+ 2p4 (1 S) threshold does not fit in this picture and remains unexplained.
The other prediction of this model,
distribution of intensities between the states
√ where the √
with the same n should peak at n/2 [33] or n/2 [34], cannot be directly verified in the
threshold spectra. This is because of the presence of autoionizing resonances, which alter the
intensities of the satellite states. Again, the most evident difference would be in the region of
the Ne2+ 2p4 (1 S) threshold where, according to the present assignment, the ns series dominates
the spectrum.
In order to explain the other states above 60 eV in table 1 that remain unassigned we have
also considered the possible contribution of the Ne+ 2s0 2p6 n satellites excited by higher-order
radiation. However, this contribution has been ruled out, because not even the lower and more
intense members, as for example the Ne+ 2s0 2p6 (1 S)3s(2 S) state at 108.91 eV [4], are observed
in the present measurements.
It is interesting to note the appearance of both sharp and broad structures above the
Ne2+ 2p4 (3 PJ ) threshold at 62.527 eV (figures 2(e) and (f)). Among the sharp structures is
the series of high-n members converging to the Ne2+ 2p4 (1 D, 1 S) thresholds. Most of the
broad structures are probably due to the overlapping of unresolved J levels. However, the
broadening of the Ne+ 2p4 (1 S)5p state and other members of this np series is notable, since
each n satellite series built on the Ne2+ 2p4 (1 S0 ) core has only one possible L final symmetry,
with two J levels. However, in figure 2(f), more features than expected are observed, and their
assignment is still undetermined.
All the ionic states located above the Ne2+ 2p4 (3 P) threshold may decay via multipletchanging Auger transitions [35, 36] to the Ne2+ 2p4 (3 P) continuum. These low-energy Auger
electrons have been observed [12, 36] with kinetic energies from a few meV to about 6 eV,
the energy difference between the Ne2+ 2p4 (1 S) and (3 P) ionization potentials. In the present
experiment the occurrence of this process results in the production of two electrons: the
threshold electron from the initial photoionization and the Auger electron from the decay of
the Ne+ satellite state. Both the electrons have low kinetic energy, and thus post-collision
interaction (PCI) may occur. This would result in a shift of the photoelectron/Auger peaks
as well as an asymmetric broadening of the lineshapes. A previous study [12] of the states
between the Ne2+ 2p4 (3 P) and (1 D) did not show any appreciable PCI effect down to photon
energies 100 meV above the threshold of the satellite states. This result is consistent with the
observations shown in figure 2(e), where the positions of the ionic peaks are well matched
with the ones calculated with the Rydberg formula and the lineshapes do not display any
broadening. This implies that the lifetimes of these satellite states are long enough to prevent
any observable PCI effect in the experiment.
The ionic states above the Ne2+ 2p4 (1 D) ionization potential may decay to two different
continua. Some information on their decay has been provided by time-of-flight (TOF)
measurements [36]. In that work, the observed features were attributed to the decay of the
Ne+ 2p4 (1 S)ns(2 S), np(2 P) and nd(2 D) states to the Ne2+ 2p4 (3 P) and (1 D) continua. The
experiments were performed a few eV above the respective thresholds of the different satellite
states and the energy resolution of the TOF measurements was insufficient to observe any PCI
effects, which would be expected to be small. In figure 2(f) we do observe small differences
between the positions of the observed peaks (especially for the states with > 0) and the ones
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2945
calculated with the Rydberg formula. Some peaks are also broader than the others. These
effects may be due to PCI, implying a shorter lifetime of these satellite states with respect to
those states at lower energies. Unfortunately the high density of states and the uncertainty
of their assignment prevent a fit of a PCI lineshape to the spectral features to make these
observations more quantitative.
3.2. The regions of the double-ionization thresholds
The measured TPE spectra of He (see [19] and references therein) display a cusp-like feature
in the vicinity of the double-ionization threshold. This feature occurs because the correlations
between the two outgoing electrons of low energy lead to the frustration of double ionization.
In the work on He, the cusp was fitted by a generalized form of the Wannier threshold law [37].
This is an asymmetric function represented by
σ 2+ (E) ∝ g± |hν − IP2+ |α−1
(4)
and includes contributions from both below and above the double-ionization threshold, with
amplitudes g− and g+ respectively. α is the Wannier exponent. A weighted average of
all the recent experimental determinations of α in He gives a value of 1.061 ± 0.004 [19]
that is consistent with the theoretically predicted value of 1.056 [18]. The experiments also
determined the ratio between the below- and above-threshold amplitudes, g− /g+ , with values
varying from 0.95 ± 0.04 [38] through 1.26 ± 0.02 [19] to 1.43 [15]. This compares to the
theoretical prediction of 0.85 [37]. These differences in the ratio have been attributed [39] to
second-order collisional processes. For the case of the heavier rare gases extensions of the
Wannier theory to the case of the np4 (3 P, 1 D, 1 S) doubly charged ion states again predict a cusplike feature with the same α parameter value [40]. The observation and quantitative analysis
of such features in the heavier rare gases is, however, not straightforward. This is because the
presence of satellite states converging to higher-lying doubly charged states and autoionizing
neutral states can distort the double-ionization continua. Previous TPE measurements of the
Ne+ 2p4 n satellites do display a clear cusp-like shape at the Ne2+ 2p4 (1 D) threshold but not at
the Ne2+ 2p4 (3 PJ ) thresholds [6,7]. More controversial are the observations in the region of the
Ne2+ 2p4 (1 S) state. In one study [6], a small dip seems to be just visible but in another [7] it is
not present. The present TPE work gives support to the observations of [6]. The Ne2+ 2p4 (3 PJ )
thresholds do not show any feature while a clear cusp-like shape is observed at the Ne2+ 2p4 (1 D)
threshold and a dip is just barely visible at the Ne2+ 2p4 (1 S) threshold.
The reduced energy spread of the incident photon beam presented in this work, compared
to previous studies, has resulted in a larger energy range above the Ne2+ 2p4 (1 D) threshold
that is free of structures due to satellite peaks. This has facilitated fitting the TPE spectrum
in the Ne2+ 2p4 (1 D) region to expression (4). For this fit the expression has been convoluted
with a Lorentzian lineshape representing the overall energy resolution of 9 meV. As the region
of the double-ionization potential is approached, the satellite states become closer and then
overlap, so that a direct evaluation of the underlying background is not possible. In the fitting
procedure the background has been assumed to be flat. The extracted value of the α parameter
is very sensitive to any possible slope of the background and so the quoted uncertainty from
the fitting procedure may be an underestimate. The best fit is shown in figure 3, and gives
α = 1.074 ± 0.010 and g− /g+ = 1.23 ± 0.05. It is interesting to note the strong similarities
in cusp shape and parameter values for the Ne2+ 2p4 (1 D) and He2+ (1 S) cases. The original
development of the Wannier threshold law was concerned only with the above-threshold wing
of the cusp and formula (4) is a later derivation for the He case [37]. The present results
demonstrate a wider applicability of the expression. The numerical values of the extracted α
2946
P Bolognesi et al
30
14
25
+
4
Ne 2p nl
1
( S)5s-4d-4f
2p ( D)26s
4 1
2p ( D)25d,f
yield (arb. units)
12
yield (arb. units)
20
4 1
1
( D)ns
2+
4 1
Ne 2p ( D)
15
10
5
10
0
65.4
65.6
65.8
66.0
66.2
66.4
photon energy (eV)
8
6
65.6
65.7
65.8
65.9
photon energy (eV)
Figure 3. The TPE spectrum of Ne in the region of the Ne2+ 2p4 (1 D) double-ionization threshold.
The full line represents a fit using an asymmetric cusp shape (see text). The inset shows an extended
energy range.
and g− /g+ parameters for the two cases are consistent within the uncertainties, and the value for
α is consistent with that predicted by Wannier theory. At least for the cases of the Ne2+ 2p4 (1 D)
and He2+ (1 S) states, this suggests that there is no dependency on the different initial and final
state configurations. This is in contrast to the more complete (γ , 2e) experiments. These
measure the angular correlation between the two ejected electrons in the continuum, i.e. the
triple-differential cross section, and have shown clear evidence of the strong dependency of
the PDI process on the initial [41] and final states of the target [42]. No attempt has been made
in this work to investigate any pressure-dependent effect in the value of the g− /g+ ratio. It is
possible, therefore, that the similar values for the Ne2+ 2p4 (1 D) and He2+ (1 s) [19] states may
be fortuitous.
The region of the Ne2+ 2p4 (1 S) state is free from overlapping satellite peaks which should
increase the visibility of any cusp-like feature. However, the present data display only a weak
dip in that region, which makes any attempt to fit the power law (4) to the data unrealistic.
The absence of any discernible structure at the Ne2+ 2p4 (3 PJ ) thresholds could be attributed
to a lower threshold ionization cross section for the Ne2+ 2p4 (3 PJ ) states with respect to that
of the Ne2+ 2p4 (1 D) state. This is surprising, considering that the (3 PJ ) state corresponds to a
parity-favoured transition. This result is, however, supported by the observations in TPEsCO
experiments [28] which show that the (1 D) state is the dominant one at threshold.
4. Conclusions
We have measured the TPE spectrum of Ne from 48.36 to 69.80 eV with high resolution.
This region includes all the Ne+ 2p4 n satellite states, and the three lowest double-ionization
thresholds, corresponding to the Ne2+ 2p4 (3 P, 1 D, 1 S) states. Taking advantage of the improved
High-resolution threshold photoelectron measurements of the Ne+ 2p4 n satellite states
2947
photon resolution of third-generation synchrotron radiation sources and the high sensitivity of
the TPE technique, the present spectrum of the satellite states displays many more features than
previously observed by photoemission and optical measurements. We suggest that most of
them can be assigned as higher members of the known satellite series. Resonance coupling or
enhanced electron correlations in the near-threshold region have been considered as the possible
dominant excitation mechanisms. Generally speaking, it is difficult to discern between these
two possibilities. However, for the series converging to the Ne2+ 2p4 (1 S) states, the regularity
in the decreasing intensities suggests enhanced threshold ionization cross section at high n
rather than occasional resonant enhancement. For the case of the series converging to the
Ne2+ 2p4 (3 P, 1 D) thresholds, the distribution of intensity of the states is consistent with the
theoretical expectations of an enhanced cross section for high n and states in the vicinity of
the double-ionization thresholds.
For the regions of the three double-ionization potentials, only the Ne2+ 2p4 (1 D) region
shows clear evidence of a cusp-like feature: the signature of threshold PDI. This feature is
well described by an asymmetric power law. The extracted Wannier exponent α and the ratio
of amplitudes between the below- and above-threshold wings of the cusp have similar values
to the He case. As for the other double-ionization thresholds, a weak dip is just visible at
the Ne2+ 2p4 (1 S) threshold, while no dip is detectable at the Ne2+ 2p4 (3 P) threshold. This
finding has been attributed to a lower cross section of the Ne2+ 2p4 (3 P) states at threshold.
This observation, although consistent with previous TPEsCO data [28], conflicts with the
expected larger cross section at threshold for the symmetry-favoured states. This anomalous
trend of the intensity at the double-ionization thresholds of the three Ne2+ states requires further
investigation.
Acknowledgment
The authors acknowledge financial support from the European Union (contract
ERBFMGECT950022).
References
[1] Persson W 1971 Phys. Scr. 3 133
[2] Svensson S, Eriksson B, Martensson N, Wendin G and Gelius U 1988 J. Electron Spectrosc. Relat. Phenom. 47
327
[3] Heimann P A, Truesdale C M, Kerkhoff H G, Lindle D W, Ferrett T A, Bahr C C, Brewer W D, Becker U and
Shirley D A 1985 Phys. Rev. A 31 2260
[4] Kikas A, Osborne S J, Ausmees A, Svensson S, Sairanen O-P and Aksela S 1996 J. Electron Spectrosc. Relat.
Phenom. 77 241
[5] Heimann P A, Becker U, Kerkhoff H G, Langer B, Szostak D, Wehlitz R, Lindle W D, Ferrett T A and Shirley D A
1986 Phys. Rev. A 34 3782
[6] Hall R I, Dawber G, Ellis K, Zubek M, Avaldi L and King G C 1991 J. Phys. B: At. Mol. Opt. Phys. 24 4133
[7] Heiser F, Hergenhahn U, Viefhaus J, Wieliezek K and Becker U 1992 J. Electron Spectrosc. Relat. Phenom. 60
337
[8] Åberg T 1970 Phys. Rev. A 2 1726
[9] Becker U and Shirley D A 1990 Phys. Scr. T 31 56
[10] Schmidt V 1992 Rep. Prog. Phys. 55 1483
[11] Becker U, Hölzel R, Kerkhoff H G, Langer B, Szostak D and Wehlitz R 1982 Phys. Rev. Lett. 56 1120
[12] Wills A A, Cafolla A A, Svensson A and Comer J 1990 J. Phys. B: At. Mol. Opt. Phys. 23 2013
[13] Samson J A R, Chung Y and Lee E M 1992 Phys. Rev. A 45 259
[14] Schulz K, Domke M, Püttner R, Gutiérrez A, Kaindl G, Miecznik G and Greene K C H 1996 Phys. Rev. A 54
3095
[15] Hall R I, Avaldi L, Dawber G, Zubek M, Ellis K and King G C 1991 J. Phys. B: At. Mol. Opt. Phys. 24 115
2948
[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]
P Bolognesi et al
Cvejanovic S, Bagley G W and Reddish T J 1994 J. Phys. B: At. Mol. Opt. Phys. 27 5661
Hall R I, Avaldi L, Dawber G, Zubek M and King G C 1990 J. Phys. B: At. Mol. Opt. Phys. 23 4469
Wannier G H 1953 Phys. Rev. 90 817
Thompson D B, Bolognesi P, Coreno M, Camilloni R, Avaldi L, Prince K C, de Simone M, Karvonen J and
King G C 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2225
Lablanquie P et al 2000 Phys. Rev. Lett. 84 431
Diviacco B, Bracco R, Poloni C, Walker R P and Zangardo D 1992 Rev. Sci. Instrum. 63 388
Melpignano P, DiFonzo S, Bianco A and Jark W 1995 Rev. Sci. Instrum. 66 2125
Blyth R R et al 1999 J. Electron Spectrosc. Relat. Phenom. 101–3 959
Hall R I, McConkey A G, Ellis K, Dawber G, Avaldi L, MacDonald M A and King G C 1992 Meas. Sci. Technol.
3 316
Cvejanovic S and Read F H 1974 J. Phys. B: At. Mol. Phys. 7 118
King G C, Zubek M, Rutter P M and Read F H 1987 J. Phys. E: Sci. Instrum. 20 440
Domke M, Schulz K, Remmers G, Kaindl G and Wintgen D 1996 Phys. Rev. A 53 1424
Avaldi L, Dawber G, Gulley N, Rojas H, King G C, Hall R, Stuhec M and Zitnik M 1997 J. Phys. B: At. Mol.
Opt. Phys. 30 5197
Domke M, Xue C, Puschmann A, Mandel T, Hudson E, Shirley D A and Kaindl G 1991 Phys. Rev. Lett. 66 1306
Luke T M, Talman J D, Aksela H and Leväsalmi M 1990 Phys. Rev. A 41 1350
Krässig B, Hansen J E, Persson W and Schmidt V 1996 J. Phys. B: At. Mol. Opt. Phys. 29 L449
Fano U 1974 J. Phys. B: At. Mol. Phys. 7 L401
Drukarev G F 1982 Zh. Eksp. Teor. Fiz. 83 946 (Engl. transl. 1983 Sov. Phys.–JETP 56 532)
Rau A R P 1984 J. Phys. B: At. Mol. Phys. 17 L75
Becker U, Hemmers O, Langer B, Lee I, Menzel A, Wehlitz R and Amusia M Ya 1993 Phys. Rev. A 47 R767
Becker U and Wehlitz R 1994 J. Electron Spectrosc. Relat. Phenom. 67 341
Read F H and Cvejanovic S 1988 J. Phys. B: At. Mol. Opt. Phys. 21 L371
King G C, Zubek M, Rutter P M, Read F H, MacDowell A A, West J B and Holland D M P 1988 J. Phys. B: At.
Mol. Opt. Phys. 21 L403
Cvejanovic S, Shiell R C and Reddish T J 1995 J. Phys. B: At. Mol. Opt. Phys. 28 L707
Schmidt V 1997 Electron Spectroscopy of Atoms using Synchrotron Radiation (Cambridge Monographs on
Atomic, Molecular and Chemical Physics)
Scherer N, Krässig B and Schmidt V 2000 Phys. Essay 13 458
Krässig B and Schmidt V 1992 J. Phys. B: At. Mol. Opt. Phys. 25 L327
Schaphorst S J, Krässig B, Schwarzkopf O, Scherer N and Schmidt V 1995 J. Phys. B: At. Mol. Opt. Phys. 28
L233
Krässig B, Schaphorst S J, Schwarzkopf O, Scherer N and Schmidt V 1996 J. Phys. B: At. Mol. Opt. Phys. 29
4255