THE JOURNAL OF CHEMICAL PHYSICS 127, 124314 共2007兲
Localized versus delocalized excitations just above the 3d threshold
in krypton clusters studied by Auger electron spectroscopy
M. Tchaplyguinea兲
MAX-lab, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
A. Kivimäki
CNR-INFM, TASC Laboratory, 34012 Trieste, Italy
S. Peredkov and S. L. Sorensen
Department of Synchrotron Radiation Research, Institute of Physics, Lund University,
P.O. Box 118, SE-223 62 Lund, Sweden
G. Öhrwall, J. Schulz,b兲 M. Lundwall, T. Rander, A. Lindblad, A. Rosso, S. Svensson,
N. Mårtensson, and O. Björneholm
Department of Physics, Uppsala University, P.O. Box 530, SE-751 21 Uppsala, Sweden
共Received 27 April 2007; accepted 17 July 2007; published online 27 September 2007兲
We present Auger spectroscopy studies of large krypton clusters excited by soft x-ray photons with
energies on and just above the 3d5/2 ionization threshold. The deexcitation spectra contain new
features as compared to the spectra measured both below and far above threshold. Possible origins
of these extra features, which stay at constant kinetic energies, are discussed: 共1兲 normal Auger
process with a postcollision interaction induced energy shift, 共2兲 recapture of photoelectrons into
high Rydberg orbitals after Auger decay, and 共3兲 excitation into the conduction band 共or “internal”
ionization兲 followed by Auger decay. The first two schemes are ruled out, hence internal ionization
remains the most probable explanation. © 2007 American Institute of Physics.
关DOI: 10.1063/1.2770460兴
I. INTRODUCTION
The solid state allows relaxation and decay processes of
excited states not present for an isolated atom. Inert gas clusters are suitable model systems to study these processes, as
the solid state can be studied at advantageous conditions by
using large free clusters, and the case of the isolated atom is
well known. Recent studies of inert gas clusters excited in
the vicinity of the core-ionization thresholds have revealed
several interesting phenomena, such as the possible involvement of the conduction band electrons in the decay1 and the
ioniclike character of the core-excited neutral states.2,3 The
excitation regime studied in Ref. 2 corresponded to the photon energies within 2 eV below the 3d5/2 ionization threshold
of krypton clusters 共Fig. 1兲. In that work2 devoted to large
krypton clusters, the electron densities of the core-excited
states were shown to be mostly outside the closest coordination shell of the ionized atom. Due to this electron density
spatial distribution, the part of the excited atom remaining
inside the closest shell has a positive charge and is then
exposed to the polarization screening by the neighbors—as
in an ionic state. At the same time the cluster remains neutral
as a whole. The screening degree approaches the values typical for the cluster ionic state, in the sense that the excited
states are redshifted almost as much as the ionic state. In
consonance with this experimental finding, recent theoretical
a兲
Author to whom the correspondence should be addressed. Electronic mail:
[email protected]
b兲
Present address: Department of Physical Sciences, University of Oulu, Box
3000, 90014 Oulu, Finland.
0021-9606/2007/127共12兲/124314/8/$23.00
studies report a large degree of delocalization of the excited
electron density 共spread兲 over an inert gas cluster.3 Thus energetically and spatially the border between the excited and
the ionized states in inert gas solids becomes less and less
pronounced with the increase of the core-excitation degree.
The next logical question in such excitation studies is
what happens when the photon energy finally reaches the
cluster ionization threshold and then slightly exceeds it. If
one limits the excitation energy to the range within 1 – 2 eV
above the threshold, what type of energy relaxation channels
will be present or dominating in solidlike clusters?
This problem is not trivial to address by photoelectron
spectroscopy since the kinetic energy of the electrons directly emitted due to the ionization is close to zero in this
case. Such electrons are difficult to detect due to low and
varying instrumental transmission of the electron spectrometers in this energy region. Besides, the spectral features due
to photoelectron emission and normal Auger 共NA兲 processes
appearing at above-threshold photon energies are inherently
strongly distorted by the postcollision interaction 共PCI兲
effect4 when the kinetic energy of the photoelectron is low.
Moreover, a recapture of slow photoelectrons into Rydberg
orbitals after the Auger decay can contribute to the decay
pathways also in Kr clusters. The recapture phenomenon has
been observed earlier in free inert gas atoms 共for example,
Refs. 5–7兲 and possible indications of it—for free argon
clusters.8 Last but not the least, the close-to-threshold photon
energies that ionize clusters can at the same time populate
the cluster/solid conduction band,1,9 creating a delocalized
electronic excitation. Then the localized and delocalized de-
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124314-2
Tchaplyguine et al.
FIG. 1. 共Color online兲 The x-ray absorption 共XA兲 spectra of Kr normalized
to the photon flux: a: atoms; b: from the gas jet containing both uncondensed
atoms and clusters of the average size 具N典 ⬇ 4700. The XA spectra give the
energies of the core-excited states below and above the cluster ionization
thresholds. The latter are obtained from the photoelectron spectrum 共c兲 recorded at h␯ = 120 eV. The assignment of the XA features: A1, A2, A3, A4
−1
denote the 3d−1
5/25p, 6p, 7p, 8p states and A⬘
1, A⬘
2, A⬘
3 the 3d3/25p, 6p, 7p
states in free Kr atoms; S1, B1, B2, S2 the 5 / 2 related cluster features; S⬘1, B⬘1,
B⬘2, and S⬘2 the corresponding 3 / 2 cluster features.
cays compete on a femtosecond time scale. Such a deexcitation pathway followed by “internal” ionization has been observed in inert gas solids.10
As in the previous study,2 the knowledge of the final
states populated after the relaxation allows shedding additional light on the decay channels realized in large krypton
clusters when the ionization threshold is slightly exceeded.
In this work the above-threshold core-excited states are created by resonant excitations, the energies of which are obtained from the x-ray absorption spectrum 共Fig. 1兲. In the
resulting final state spectra, also known as resonant Auger
spectra, new features not present in the below-threshold
spectra2 are observed. The structure of these new features as
a whole resembles that of the normal Auger spectrum of
large Kr clusters,2 although the absolute energy positions and
the relative intensities are somewhat different. The present
work contains a detailed analysis of the deexcitation spectra
and a discussion of the origin of these new features, thus
addressing the role of various possible decay channels.
II. EXPERIMENT
The experiments have been performed at the undulator
beamline I411 共Ref. 11兲 of the third-generation electron storage ring MAX-II at MAX-lab, the National Swedish Synchrotron Radiation Facility. The beamline is equipped with a
modified Zeiss SX-700 monochromator and a Scienta R4000
electrostatic electron energy analyzer. During the measurements the analyzer was set to the so-called magic angle
共54.7°兲 with respect to the horizontal polarization plane of
the radiation in order to reduce the angular effects in the
cross sections of the processes under investigation.12
The cluster source is based on the adiabatic gas expansion into vacuum through a submillimeter size nozzle. The
J. Chem. Phys. 127, 124314 共2007兲
source chamber has been fixed in a way that the gas jet
propagation was at the right angle to the analyzer acceptance
axis and to the synchrotron-light direction.
It is necessary to underline that the near-3d-edge x-ray
absorption spectrum 共XAS兲 in the present work has been
obtained by collecting Auger electrons ejected after the core
excitation and ionization while scanning the photon energy
across the threshold. The 3d core-level excitation to various
neutral Rydberg states initiates the resonant Auger decay,
creating singly ionized valence-excited states. The 40– 75 eV
kinetic energy interval used in this work contains many resonant Auger lines for free Kr atoms15 and for Kr cluster
atoms.2
The monochromator contributions to the total instrumental spectral broadening were ⬇10 meV in the x-ray absorption and ⬇40 meV in the resonant Auger measurements. The
contribution of the electron spectrometer has been about
35 meV in the resonant and normal Auger spectra. In the
cluster x-ray absorption, resonant, and normal Auger measurements, the energy calibration has been made using
atomic Kr lines13–15 that appear in all three types of spectra
due to the presence of the uncondensed atoms in the clustercontaining gas jet.
In the present studies the same mean cluster size as in
the previous work2 共具N典 ⬇ 4700兲 was set by choosing the
stagnation pressure of the Kr gas and the temperature of the
nozzle. The conical nozzle with a 20° total opening angle
and a 150 ␮m throat diameter was kept at ⬇−140 ° C by a
cooling system incorporating Peltier elements for heating
and liquid nitrogen cooling. The mean size of clusters has
been estimated using the scaling parameter ⌫* formalism.16
The adiabatic expansion method creates a broad cluster size
distribution with the width of about 具N典 / 2. When the cluster
size reaches several thousand atoms, the spectral peak positions and their relative intensities change insignificantly and
vary slowly with the size.2,17
III. RESULTS AND DATA ANALYSIS
A. Prerequisites of the study
In free Kr atoms the excitation of the 3d core electrons
populates two spin-orbit split series of Rydberg levels, with
the 5 / 2 and 3 / 2 total angular momentum of the ionic core,
for briefness referred as the “5 / 2” and “3 / 2” components
later in the text. Each series converges, respectively, to the
−1
−1
and 3d3/2
core-ionized states.18 In free atoms the lowest
3d5/2
−1
dipole-allowed core excitation creates the 3d5/2
5p state de−1
noted as A1 in Fig. 1. 共Its spin-orbit twin 3d3/2
5p state is
1.2 eV higher: A1⬘ in Fig. 1.兲 The next 5 / 2 atomic transitions
−1
produce the 3d5/2
6p , 7p , 8p states 共A2, A3, A4 in Fig. 1兲,
−1
np
while the corresponding 3 / 2 atomic lines due to the 3d3/2
states have 1.2 eV higher excitation energies 共A2⬘, and A3⬘
denote 6p and 7p states in Fig. 1兲.
In each spin-orbit series the lowest excited cluster 5p
state is shifted up in energy 共a blueshift兲 relative to the parent
atomic levels2 共Fig. 1兲, and all the higher energy np states
with n ⬎ 5 are shifted down 共a redshift兲.
In the case of free Kr atoms the spectator Auger decay of
−1
the 3d5/2
np state populates the 4p4np singly ionized excited
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124314-3
J. Chem. Phys. 127, 124314 共2007兲
Excitations above 3d threshold in Krn
−1
TABLE I. Excitation energies in eV of the 3d−1
5/2 np and 3d3/2 np core-excited states for free Kr atoms 共Ref. 13兲 and clusters 共present work兲. See the text for
the explanation of the energies for 8p, 9p, and 10p for the cluster surface and bulk.
State
3d−1
5/25p
3d−1
5/26p
3d−1
5/27p
3d−1
5/28p
3d−1
5/29p
3d−1
5/210p
Ion 3d−1
5/2
3d−1
3/25p
3d−1
5/26p
3d−1
3/27p
3d−1
3/28p
3d−1
3/29p
3d−1
3/210p
Ion 3d−1
3/2
Atom
Bulk
Surface
b-a
s-a
共s-a兲/共b-a兲 共%兲
91.20 共A1兲
92.55 共A2兲
93.06 共A3兲
93.31 共A4兲
93.44
93.52
93.83
92.43 共A⬘1兲
93.80 共A⬘2兲
94.31 共A⬘3兲
94.57
94.68
94.76
95.04
91.60 共B1兲
91.90 共B2兲
92.10 共B3兲
92.31
92.44
92.53
92.73
92.83 共B⬘1兲
93.15 共B⬘2兲
93.35 共B⬘3兲
93.57
93.68
93.76
93.94
91.33 共S1兲
92.10 共S2兲
92.42
92.61
92.74
92.82
93.03
92.56 共S⬘1兲
93.35 共S⬘2兲
93.68
93.87
93.98
94.06
94.24
+0.40
−0.65
−0.94
−1.0
−1.0
−1.0
−1.10
+0.40
−0.65
−0.96
−1.0
−1.0
−1.0
−1.10
+0.13
−0.45
−0.64
−0.7
−0.7
−0.7
−0.8
+0.13
−0.45
−0.63
−0.7
−0.7
−0.7
−0.8
33
69
69
70
70
70
73
33
69
66
70
70
70
73
final states.15 The same states are also occupied after the
−1
3d3/2
np decay. In analogy, one can expect that the decay of
both 5 / 2 and 3 / 2 core-excited states populates the same
4p4np final states also in the case of clusters. The energies of
several 4p4np states in clusters have been obtained in Ref. 2.
It should be kept in mind for the discussion below that in
Kr clusters the probability is high that the final states have an
electron in an excited state with the main quantum number
larger than in the initial core-excited state.2 This additional
excitation is known as a shake-up process. In Kr clusters the
intensity of the shake-up states in most cases is more than
50% of the total final state intensity.
In the previous study2 of the core-excitation decay in Kr
clusters, all final singly ionized excited states were found to
be shifted toward lower binding energies relative to the
atomic parent states. The higher the degree of excitation was,
the larger were the energy shifts. Already for the 4p48p singly ionized cluster states, populated as the result of the resonant core excitation, the shift was more than 90% of the shift
value for the asymptotic doubly ionized 4p4 cluster states,
reached after the core ionization and subsequent normal Auger decay, and also shifted down in binding energy relative
to their parent atomic states.
−1
B. X-ray absorption spectroscopy above the 3d5/2
cluster threshold
Figure 1 presents the x-ray absorption spectrum and the
x-ray photoelectron spectrum17 共XPS兲 of the 3d levels in Kr
clusters on the same energy scale. The figure gives the relative positions of the core-excited neutral 3d−1np states and
core-ionized 3d states in clusters and atoms. The close-tothreshold excitation conditions described in the Introduction
apply to the spin-orbit partners of the 5 / 2 states: all but one
−1
np core-excited states are
excitation energies of the 3d3/2
−1
above the cluster 3d5/2 ionic bulk state at 92.73 eV. The first
−1
member in the 3d3/2
np series, the blueshifted 5p state, has its
surface component 共S1⬘兲 at 92.56 eV and the bulk 共B1⬘兲 at
92.83 eV.2,19 The peaks at 93.15 eV 共B2⬘兲 and 93.35 eV
−1
6p
共S2⬘ / B3⬘兲, assigned in Ref. 2 are due to the redshifted 3d3/2
bulk and surface core-excited states, respectively. The reader
is referred to Table I for the summarized energies of these
and higher states.
The 3d core ionization starts contributing to the XAS
spectrum when, first, the 3d5/2 and, later, the 3d3/2 thresholds
are passed while scanning the photon energy. The 3d ionization leads to normal Auger electron emission which contributes to the XAS spectrum. Indeed, the M 4.5N2.3N2.3 normal
Auger lines 共3d−14p6 → 3d104p4 transition兲 for atoms and
clusters lie within the 45– 65 eV kinetic energy region,11,2 in
which the electrons were collected in the XAS. The increase
in the cluster response is seen as a rising continuous background in the region where the XAS of free Kr atoms has no
background. Such a stepwise increase of the electron or ion
yield in an x-ray absorption spectrum is an established indication of the exceeded threshold.20
The lowest neutral core-excited state which is above the
−1
5p bulk state: B1⬘ in Fig. 1. It is,
3d5/2 threshold is the 3d3/2
however, possible to reach the above-threshold situation for
clusters at even lower photon energies than those indicated
by XPS. The spread of IPs due to different cluster sizes and
sites, reflected in the peak widths of the XPS 共Refs. 21 and
22兲 spectra, should be taken into account. Larger clusters and
krypton atoms at higher-coordination sites23 have thresholds
at lower binding energies. For example, the full width at half
maximum of the bulk core-ionized state in Fig. 1 is about
200 meV,17 so the lower energy tail of the corresponding
“vertical” ionization potential 共IP兲 is within the excitation
region of the surface resonance S1⬘.
The absorption spectrum analysis creates certain expectations for the final states that can be reached in the relaxation process. As shown above, resonant and normal Auger
electrons should contribute to the electron yield spectrum in
the excitation energy region under discussion. With this energy increasing further above the 3d5/2 threshold, the electron
yield due to the resonant Auger electrons has to decrease
since the oscillator strengths of the 3d3/2 → np transitions are
lower than those of 3d5/2 → np as a consequence of the larger
multiplicity of the 5 / 2 states. 共This decrease in the transition
probability is reflected in the shape of the atomic XA spectrum.兲 The latter consideration means that the increase in the
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124314-4
J. Chem. Phys. 127, 124314 共2007兲
Tchaplyguine et al.
FIG. 2. 共Color online兲 Dark-colored final state spectra excited at the x-ray
absorption resonances: S⬘1, h␯ = 92.53 eV; B⬘1, h␯ = 92.85 eV, B⬘2, h␯
= 93.13 eV; and S⬘2, h␯ = 93.33 eV. Bulk and surface 4p45p, 4p46p, 4p47p,
4p48p states with different ionic cores are shown with brackets. Lightercolored final state spectra are excited at the 5 / 2 resonances S1, B1, B2, S2.
All spectra have been calibrated on the binding energy scale using the
atomic 4s4p6 line at 27.51 eV. Intensity is normalized to the nonresonant
4s4p6 cluster feature 共not shown兲. Doubly ionized final states are also shown
in the upper spectrum.
electron yield with excitation energy should mainly be attributed to the opening of the normal Auger channel as a consequence of the core ionization. In other words, at the excitation energies above at least B1⬘ one should expect the
presence of both resonant and nonresonant decay channels of
a comparable intensity, leading to the population of singly
and doubly ionized final states.
affect the 4s intensity at resonant photon energies, is known
to be weak in rare gases.25兲 Such a normalization justifies the
comparison of the final state relative intensities. The similarity of the final states reached after the 5 / 2 and 3 / 2 excitation
decays is easily observable. 共The additional sharp narrow
peaks present in abundance in the 3 / 2 spectra, especially in
the S1⬘ one, are due to the atomic final states.14兲 Thus the
assignments for the spectral features obtained as the result of
the 3 / 2 excitations are made in the same way as for the
5 / 2-excited resonant Auger spectra in Ref. 2.
Apart from to the features which are similar in the 3 / 2
and 5 / 2 spectra, there is significant extra intensity in the 3 / 2
final state spectra S1⬘, B1⬘, B2⬘ and S2⬘. The extra features are,
for example, above 37 eV in the S1⬘ and B1⬘ spectra. A certain
part of this extra intensity is due to the close excitation en−1
np
ergies for different states: the energies of the lower 3d3/2
共n = 5 , 6兲 core-excited states overlap with those of the higher
−1
3d5/2
np 共n = 7 – 10兲 states. The estimated positions of the
higher 共n ⬎ 7兲 5 / 2 states have been obtained by supposing a
−1.0 eV bulk shift and a −0.7 eV surface shift 共Table I兲. The
accuracy in the estimation of these shifts is ⬇10%: they
cannot be smaller than those found experimentally for the
−1
7p states 共⬇−0.95 eV for the bulk and ⬇−0.64 eV for
3d5/2
the surface兲 or larger than the shifts for the core-ionized
states 共⬇−1.1 eV for the bulk and ⬇−0.8 eV for the surface兲. The decay of the higher excited 5 / 2 states should lead
to the final states with a higher binding energy than the states
with a smaller n, which can then indeed explain some of the
extra intensity. However, as already mentioned above, the
cross sections of the core-to-Rydberg transitions decrease
significantly with the principal quantum number n of the
−1
Rydberg levels.13 So the resulting 3d5/2
np 共n = 7 – 10兲 coreexcited states are not expected to contribute significantly to
the final state intensity distribution. And the extra higher
binding energy spectral features in the final state spectra
have intensities comparable to the peaks assigned to 5p-8p
final states. An attempt to explain the origin of these peaks
constitutes the main contents of the following discussion.
IV. DISCUSSION
A. Normal Auger features in the final state spectra?
C. Spectroscopy of the final states
As discussed in the Introduction, detailed information on
the relaxation channels in a core-excited system can be extracted from the spectra of the final states populated after the
relaxation. Figure 2 shows the binding energies of the final
−1
5p surface
states reached after the excitations to the 3d3/2
共S1⬘兲, 5p bulk 共B1⬘兲, 6p bulk 共B2⬘兲, and 6p surface 共S2⬘兲 resonances. For comparison, the assigned spectra2 of the final
states populated after the corresponding 5 / 2 state decay are
also presented. The latter spectra were recorded at photon
energies matching the 5 / 2 resonances S1, B1, B2, and S2 in
the x-ray absorption spectrum. All spectra are normalized to
the nonresonant 4s−1 Kr total cluster signal 共not shown in
Fig. 2兲 centered at ⬇26.5 eV.24 This normalization is justified since a small 共艋2 eV兲 variation of the photon energy of
60 eV above the 4s ionization threshold does not change the
4s−1 intensity much. 共The participator channel, which could
As mentioned above, in the strongest nonresonant
channel—the M 4,5N2,3N2,3 normal Auger decay—the electrons ejected by the cluster atoms have 45– 65 eV kinetic
energy.2 To identify constant kinetic energy features, such as
normal Auger peaks, one should plot the final state spectra
on the kinetic energy scale.
In Fig. 3 the same S1⬘, B1⬘, B2⬘, and S2⬘ final state spectra as
in Fig. 2 are presented, but on a kinetic energy scale. To
emphasize the extra intensity in these spectra 共relative to the
5 / 2 resonant decay spectra兲 the corresponding 5 / 2 spectra
共S1, B1, B2, and S2兲 are also shown—aligned according to the
state assignments. The far-above-threshold normal Auger
spectrum2 共with no resonantly populated states兲 is also included 关Fig. 3共e兲兴. The M 4,5N2,3N2,3 normal Auger spectrum
contains ten features for both bulk and surface cluster atoms2
关Fig. 3共e兲兴. When the photon energy is below the 3d3/2 IP, as
for the S1⬘, B1⬘, B2⬘, and S2⬘ resonances, instead of ten, only five
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124314-5
Excitations above 3d threshold in Krn
J. Chem. Phys. 127, 124314 共2007兲
FIG. 4. 共Color online兲 The result of subtracting the B1 spectrum from the B⬘1
spectrum in the region where normal Auger structures are expected. The
resulting intensity is well described by two sets of four-peak features, corresponding to the structure of the doubly ionized states
4p4共 1S0 , 1D2 , 3 P0,1 , 3 P2兲. The peaks in each doublet are separated by
⬇0.85± 0.05 eV. Circles: experimental points; thick black line: a sum of
fit-peaks. Dotted and dashed peaks are possible bulk and surface features,
respectively. Light gray line: fit residual. The peak appearing at ⬇59.7 eV
results from singly ionized final states.
FIG. 3. 共Color online兲 The uppermost spectrum is the far-above-threshold
normal Auger spectrum of Kr clusters with the bulk and surface contributions decomposed. The fits for the surface peaks 1S-4S 共due to 5 / 2 ionization兲 are indicated with dotted lines; the corresponding 1B-4B bulk peaks are
shown with dashed lines. The features due to the 3d5/2 ionization are shown
with darker lines, those due to the 3d3/2 state with light gray lines. Lower
spectra from a to d: Dark-colored 3 / 2 final state spectra are the same as in
Fig. 2, but plotted on the kinetic energy scale. Lighter-colored 5 / 2 final state
spectra are aligned with the 3 / 2 spectra according to the identified singly
ionized states. The vertical lines and brackets give the positions of the NAlike features appearing in the 3 / 2 final state spectra. The two clearest extraintensity peaks are indicated separately and also marked with vertical lines.
final states due to the 3d5/2 ionized state should be expected.
In the B1⬘ spectrum it is tempting to ascribe the extra
intensity in the 53.5– 55.5 eV region to two peaks centered at
54.3 and 55.0/ 55.1 eV 共Fig. 3兲. These two peaks are found at
the same kinetic energy positions in the other final state spectra, although they are somewhat less pronounced and obscured by the overlapping atomic lines. From this figure it
becomes obvious that there are features in the final state
spectra that do stay constant on the kinetic energy scale,
which is characteristic of the normal Auger peaks. A more
detailed analysis of the S1⬘, B1⬘, B2⬘, and S2⬘ final state spectra
also speaks for the hypothesis of the normal-Auger-type nature of the extra intensity. The above-mentioned double-peak
structure has its two components separated by ⬇0.8 eV. This
value roughly equals the separation between the surface and
bulk features in each of the ten 3d−1 → 4p4 NA cluster transitions, unambiguously observed in the far-above-threshold
NA spectrum. However, it is difficult to explain why surface
NA features would be strongly populated in the S1⬘ spectrum,
which was measured ⬇0.5 eV below the 3d5/2 IP of surface
atoms. Possibly here, in the vicinity of the thresholds, the
ionization cross sections for the bulk and surface atoms differ, so the intensity ratios are additionally influenced by that.
The discussed double-peak structure within the
53.5– 55.5 eV kinetic energy interval in the S1⬘, B1⬘, B2⬘, and
S2⬘ final state spectra could be due to the final doubly ionized
4p4共 1S0兲 cluster state with the bulk and surface components
resolved. Indeed, in the far-above-threshold NA spectrum the
−1
→ 4p4共 1S0兲 transition leads to the lowest kinetic energy
3d5/2
feature in the 53– 55 eV interval 关Fig. 3共e兲, peaks 1S, 1B兴.
Then in the spectra measured at the S1⬘, B1⬘, B2⬘, and S2⬘ reso−1
state
nances, the other NA-like features 共due to the 3d5/2
decay兲 can be tentatively identified by subtracting the 5 / 2
resonant spectra from the 3 / 2 spectra. Figure 4 shows the
result of such a subtraction for the B1⬘ and B1 spectra. If one
assumes that the double-peak structure in the 53.5– 55.5 eV
region corresponds to the 1S and 1B NA features due to the
−1
→ 4p4共 1S0兲 transitions, then the positions of the other
3d5/2
NA-like features can be sought using the separations of the
Auger peaks in the far-above-threshold spectrum 共or even in
the NA spectrum of Kr atoms兲. To facilitate the assignment
the positions of the NA bulk and surface peaks are shown
shifted ⬇0.7 eV up in energy in Fig. 4. In the difference
spectrum one finds another clear double-peak structure with
the maxima at 56.6 and 57.4 eV at the separation expected
for the 4p4共 1D2兲 final states 关features 2S and 2B in Fig. 3共e兲兴.
Also the splitting in this double-peak structure is close to the
bulk-surface of ⬇0.8 eV separation in the NA spectra. Thus
the origin of the two double-peak features observed cannot
be the spin-orbit splitting in the initial states of the decay, the
value of which in Kr is 1.2 eV. There is also clearly some
intensity at the separations expected for the 4p4共 3 P0,1,2兲
states 关features 3S and 3B, 4S and 4B in Fig. 3共e兲兴. A tentative
fit of the difference spectrum with four NA-like components,
with the bulk-surface relative intensities linked to each other,
strengthens the resemblance to a doubly ionized final state.
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124314-6
J. Chem. Phys. 127, 124314 共2007兲
Tchaplyguine et al.
TABLE II. Energies in eV for the doubly ionized states in free atoms 共Ref. 15兲 and for the cluster surface and
bulk states established in the present work.
Free atom
Surface
Bulk
4p4共 3 P2兲
4p4共 1 P1兲
4p4共 3 P0兲
4p4共 1D2兲
4p4共 1S0兲
38.36
35.16
34.06
38.92
35.72
34.62
39.02
35.82
34.72
40.18
37.00
35.90
42.46
39.26
38.16
Note that the energy separations between the peaks in the
normal and resonant Auger spectra are mainly determined by
the 4p4 electron configuration. A similar peak structure 共as in
a double ion兲 is found when an additional excited electron is
coupled to the 4p4 electron configuration, i.e., in the 4p4nl
final states of the resonant Auger decay. Thus the observed
energy splittings do not prove that they are caused by doubly
charged final states, but only that 4p4 or 4p4nl configurations
are involved. Nevertheless, the constant kinetic energies of
the peaks strongly point to a normal Auger-type origin of the
extra intensity in the S1⬘, B1⬘, B2⬘, and S2⬘ spectra. The remaining question is why close-to-threshold NA features are
shifted up in kinetic energy by about 0.7 eV.
B. The role of postcollision interaction
The higher energy positions of these NA-like features in
the close-to-threshold spectra relative to the “real” NA cluster peaks in the far-above-threshold spectra could, in principle, be due to the so-called postcollision interaction 共PCI兲
phenomenon,26,27 since the kinetic energies of the
M 4,5N2,3N2,3 Auger electrons 共50– 60 eV兲 are much higher
than those of the photoelectrons 共a few hundreds of meV兲.
One can estimate the PCI-induced shift for clusters using the
results of Refs. 4 and 26. For the most pronounced case of
the present study—for the B1⬘ excitation—the initial kinetic
energy of the photoelectron would be ⬇0.1 eV, giving the
PCI shift of 艋0.5 eV. With the excitation energy increase up
to 0.6 eV 共S2⬘ excitation兲, the calculated PCI shift should fall
down to 0.1 eV. This is not the case for the extra cluster
features, which stay constant in kinetic energy over ⬇a 1 eV
photoelectron energy interval. This shift behavior rather
speaks against the PCI effect as the origin of the extra intensity in the S1⬘, B1⬘, B2⬘, and S2⬘ decay spectra. Another argument
against the PCI-related explanation is no obvious presence of
the characteristic strong asymmetry which should be observed in feature profiles when the photon energy is in the
vicinity of the threshold.
C. Photoelectron recapture
In a recent NA studies of large argon clusters where an
additional intensity was observed on the higher kinetic energy side of each NA peak in the spectra,8 it was suggested
that the changes in the spectra were caused by the photoelectron recapture phenomenon earlier observed for different
rare gas atoms.6,28,29 The states occupied due to the recapture
are similar to those populated as the result of resonant Auger
decay 关4p4共 1S0 , 1D2 , and 3 P0,1,2兲nl in Kr兴. In such recapture
processes small exchange energies should be favored by the
system, leading to the population of the singly ionized 4p4nl
states with the highest n—the states which are just below the
double ionization thresholds 共Table II, the 4p4 energies for
clusters have been obtained by subtracting the shifts observed in Ref. 2—4.3 eV for the bulk and 3.2 eV for the
surface—from the energies of the corresponding states in
free Kr atoms兲. In analogy to Kr atoms,6 singly ionized 4p4nl
states with n ⬎ 11 in clusters would be so close to each other
that they could merge in a spectral pattern resembling a
single or double broad peak which gradually transforms into
the PCI-influenced Auger peaks when the photon energy exceeds the threshold. Thus, in principle, in the Kr cluster final
state spectra, the extra features with kinetic energies shifted
0.7 eV up with respect to the real NA peaks could be due to
the recaptured photoelectrons. There are, however, some
considerations that weaken such a hypothesis. For the intensity of the extra features to be comparable with the resonantly populated 4p4nl features with low n 共5,6兲, the probability of the relaxation-through-recapture channel should be
comparable, and this is not the case. The following considerations justify such a statement. First, the probability of
direct, resonant excitations drops dramatically with n. Second, there is no abrupt change between the high-n excitation
and ionization at the threshold 共Ref. 6兲. Third, the 3d photoionization cross section is very low at the threshold.30,31
Quantitatively it all means that, whatever pathway leads to
the population of the higher n final states, resonant excitation
or recapture, its probability is similar across the threshold
and is low in comparison with the case of n = 5 , 6. Thus the
recapture picture has difficulties to explain the rather large
intensities of the observed constant kinetic energy structures
in the spectra. Furthermore, it is not evident that the recapture features would stay at constant kinetic energies when
photon energy is changed above the 3d threshold, since the
4p4nl final states are instead associated with constant binding
energies.
D. Involvement of the cluster conduction band
A localized process, in which the core electron is directly
removed into vacuum, is not the only pathway that can lead
to a core-ionized state of a certain atom in a cluster or solid.
In solid Kr the conduction band has been calculated to
stretch from ⬇92.5 eV to at least ⬇98 eV,9 with a considerable density of states through the whole region. Thus the 3d
localized ionic levels overlap with the conduction bands. The
electron band structure is well formed in large inert gas clusters, which is proven by the spectral patterns in their valence
photoelectron spectra. In a recent study of argon clusters,1
the excitation into the conduction band was used to explain
the presence of normal Auger features in the close-tothreshold resonant Auger spectra. Normal Auger features
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124314-7
Excitations above 3d threshold in Krn
were earlier observed for below-threshold excitations of argon multilayer adsorbates.10 The presence of the NA features
in these cases was explained in terms of internal ionization,
whereby the electron removed from the core orbital is delocalized in the conduction band if the excitation energy
matches the energy of the corresponding transition. In these
terms the direct removal of the electron into vacuum is referred to as an “external” ionization. In contrast to the lower
core-excited states, shifted down out of the conduction band,
the higher excited states can remain coupled to the conduction band. Thus no potential barrier exists for the transfer of
the charge from a locally excited site to the delocalized energy band.
The nature of the normal Auger-type features in the
present case—due to the internal ionization—could be the
reason for the shifted energy positions of the Auger lines in
the Kr cluster final state spectra. Excitation into the conduction band 共=internal ionization兲 can create a core-ionized
−1
. The initial
state energetically different from the real 3d5/2
state for such a decay would be with the excited delocalized
electron at the bottom of the conduction band and not with a
−1
np state. A simple estimate of
localized electron in the 3d3/2
the order of magnitude of the shift compared to the regular
Auger decay can be made using an electrostatic PCI-like
consideration. Assuming that the local surrounding of the
core hole is not affected by the presence of the electron in the
conduction band, the difference in kinetic energy between
this decay compared with the regular Auger case will be
given by the energy exchange between the Auger electron
and the photoelectron. First, the Auger electron travels in the
potential of the doubly charged ion, but after passing the
photoelectron in the conduction band, it will travel in a potential of a singly charged ion. If the charge in the conduction band, as in a metal, is distributed over the surface, the
difference in kinetic energy can be approximately calculated
as 1 / R, where R is the cluster radius. We estimate the cluster
radius to be R ⬇ 3.3– 3.6 nm, which gives a shift of ⬇0.4 eV,
in rough agreement with our observation. This shift should
be size dependent, but in this study, only a single cluster size
has been investigated, and thus this conjecture has not been
tested. The internal and external ionization processes may
compete on the relevant time scale, with the internal one
winning close to the threshold where the direct 3d ionization
cross section is still low.31 The appearance of the doublet
peaks in the final state spectra measured at the 3d threshold
could then be due to the separate conduction bands of bulk
and surface atoms.
E. Further up in energy
Figure 5 illustrates the transformation of the extra intensity with the photon energy and the decay changing from the
resonant to normal Auger channels. For comparison, a farabove-threshold NA spectrum recorded at 110 eV is shown
at the bottom of Fig. 5. The probing photon energy becomes
so high that in the spectra b–e of Fig. 5 even the atomic
normal Auger features, 1A – 6A, finally show up. They are
strongly asymmetric due to the postcollision interaction. The
kinetic energy scale is used for the presentation, so the sat-
J. Chem. Phys. 127, 124314 共2007兲
FIG. 5. 共Color online兲 Final state spectra for five excitation energies and a
normal Auger spectrum at 110 eV. The calculated real NA features at the
PCI-shifted positions are presented in each spectrum. The surface peaks and
bulk peaks are shown with thick lines, and the atomic peaks with thin dotted
lines. The light-gray dotted curve indicates a difference between the experimental spectrum and the calculated NA spectrum in each case. The atomic
peaks 1A-6A in the far-above-threshold NA spectrum, as well as the highest
energy bulk 1B and surface 1S peaks are labeled. Some photoelectron features due to the atomic and cluster states are also marked, like the
4p4共 1D2兲4d one. The change of the energy of the latter feature is shown with
dashed lines for both the atomic and the cluster peaks.
ellite photoelectron features move across the spectra with the
photon energy 关for example, the 4p4共 1D2兲4d atomic and
cluster features兴. A detailed assignment of the spectral features is even more complicated at these excitation energies,
so only the relevant trends can be discussed. The top spectrum 共a兲 is the S2⬘ resonant spectrum from Fig. 3. It is included to facilitate the comparison with the spectra measured
at higher excitation energies. The spectrum b has been measured above the 3d5/2 atomic threshold. This photon energy
of 93.94 eV also exceeds the bulk 3d3/2 threshold, but is still
below the 3d3/2 IPs of the surface and of free atoms. Thus the
atomic normal Auger features are expected only due to the
−1
initial 3d5/2
state. This photon energy is actually the same as
one of those used in Ref. 5 for the study of the atomic PCI
effect. Additionally, this excitation energy is on top of the
−1
−1
estimated surface 3d3/2
9p, 10p, and bulk 3d3/2
11-16p resonances. Corresponding final states must be present in the
deexcitation spectra. In all spectra the normal Auger features
are shown by peaks from a model fit based on the known
far-above-threshold NA spectrum. Using the lower energy
part of each spectrum in Fig. 5, where the features are less
densely overlapping, the amplitudes of the reference NA features have been determined. These were used to estimate the
amplitudes of the other NA features in the higher energy
region where the peaks are not resolved. The expected PCI
shifts and asymmetries for the NA features have been taken
into account in the fitting.
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124314-8
J. Chem. Phys. 127, 124314 共2007兲
Tchaplyguine et al.
The spectrum c in Fig. 5 was recorded at 94.44 eV
which exceeds all cluster IPs. Consequently, all real NA features of cluster atoms should be present 共fitted peaks are
shown with smooth lines兲. This spectrum resembles to a
great extent the previous one with the exclusion of the moving photoelectron features.
In the next two spectra 共d and e兲, one recorded at the
second atomic IP, the other at 1 eV higher, the PCI-distorted
NA features for the atoms are seen. The fits improve with the
increase of the excess energy. Already in the spectrum e
共⬇96 eV photon energy兲, the deviation of the total fitted intensity from the measured spectrum is significant only in the
high-energy region. 共The residual intensity is displayed with
a light-gray line.兲 Though in the spectrum e the photon energy is already 2 eV above the cluster IPs, this residual part
should be, perhaps, attributed to the population of the singly
ionized excited final states due to the recapture process. The
close similarity of all these spectra probably means that the
relaxation processes in this excitation energy region follow
the same pathways, and the difference between the resonantly and nonresonantly populated states is absent in the
vicinity of the thresholds.
V. CONCLUSIONS
The decay of electronic excitations in Kr clusters after
excitation just above the 3d core-level ionization threshold
has been studied in order to find out the dominating pathways in a manifold of possible decay processes in dielectric
solid. The spectra taken at photon energies corresponding to
the 3d3/2 → np excitations in the clusters clearly show intensity due to the resonant Auger decay to the 4p4ml final states,
but also considerable extra intensity which remains at constant kinetic energies. These kinetic energies are, however,
about 0.7 eV higher than the energies of the regular normal
Auger peaks in the far-above-threshold spectrum. Possible
explanations for this extra intensity have been considered,
and all but one—the excitation into the conduction band—
have been ruled out. Indeed, the discussed first external 3d
photoionization should have lead to normal Auger structures
shifted up in kinetic energy due to the PCI phenomenon. This
shift, however, would vary with the excitation energy, and it
has not been the case. For another possible phenomenon—
the photoelectron recapture—the probability was found to be
too small to explain the extra intensity in the spectra. The
conduction band excitation, or internal ionization, can indeed
exist below as well as above the external ionization
threshold.9,10 An estimate of the expected energy shift for the
decay features due to the internal ionization supports the interpretation of the spectra. At slightly larger photon energies,
these extra constant-kinetic-energy peaks are replaced by the
regular normal Auger features that can be seen as a witness
for a smooth transition from the highly excited states coupled
to the conduction band and to the ionized states in clusters.
ACKNOWLEDGMENTS
The authors would like to acknowledge financial support
from the Göran Gustafsson foundation, the Knut and Alice
Wallenberg foundation, the Swedish Foundation for Strategic
Research 共SSF兲, and the Swedish Research Council 共VR兲.
1
A. Kivimäki, S. L. Sorensen, M. Tchaplyguine, M. Gisselbrecht, R. R. T.
Marinho, R. Feifel, G. Öhrwall, S. Svensson, and O. Björneholm, Phys.
Rev. A 71, 033204 共2005兲.
2
S. Peredkov, A. Kivimäki, S. Sorensen et al., Phys. Rev. A 72,
021201共R兲 共2005兲.
3
J. P. Gauyacq, Phys. Rev. B 71, 115433 共2005兲.
4
A. Lindblad, R. F. Fink, H. Bergersen et al., J. Chem. Phys. 123, 211101
共2005兲.
5
K. Helenelund, S. Hedman, L. Asplund, U. Gelius, and K. Siegbahn,
Phys. Scr. 27, 245 共1983兲.
6
H. Aksela, M. Kivilompolo, E. Nõmmiste, and S. Aksela, Phys. Rev.
Lett. 79, 4970 共1997兲.
7
A. De Fanis, G. Pruemper, U. Hergenhahn, M. Oura,M. Kitajima, T.
Tanaka, H. Tanaka, S. Fritzsche, N. M. Kabachnik, and K. Ueda, Phys.
Rev. A 70, 040702共R兲 共2004兲.
8
M. Lundwall, G. Öhrwall, A. Lindblad, S. Svensson, and O. Björneholm
共unpublished兲.
9
R. Haensel, N. Kosuch, U. Nielsen, U. Rössler, and B. Sonntag, Phys.
Rev. B 7, 1577 共1973兲.
10
W. Wurth, G. Rocker, P. Feulner, R. Scheuerer,L. Zhu, and D. Menzel,
Phys. Rev. B 47, 6697 共1993兲.
11
M. Bässler, A. Ausmees, M. Jurvansuu et al., Nucl. Instrum. Methods
Phys. Res. A 469, 382 共2001兲.
12
G. Öhrwall, M. Tchaplyguine, M. Gisselbrecht et al., J. Phys. B 36, 3937
共2003兲.
13
G. C. King, M. Tronc, F. H. Read, and R. Bradford, J. Phys. B 10, 2479
共1977兲.
14
H. Aksela, S. Aksela, and H. Pulkkinen, Phys. Rev. A 30, 2456 共1984兲.
15
J. Jauhiainen, H. Aksela, O.-P. Sairanen, and E. Nommiste, and S. Aksela, J. Phys. B 29, 3385 共1996兲.
16
R. Karnbach, M. Joppien, J. Stapelfeldt, J. Wörmer, and T. Möller, Rev.
Sci. Instrum. 64, 2838 共1993兲.
17
M. Tchaplyguine, R. R. Marinho, M. Gisselbrecht et al., J. Chem. Phys.
120, 345 共2004兲.
18
NIST tables of atomic states, http://physics.nist.gov/PhysRefData/ASD/
19
A. Knop, B. Wassermann, and E. Rühl, Phys. Rev. Lett. 80, 2302 共1998兲.
20
O.-P. Sairanen, A. Kivimäki, E. Nommiste, H. Aksela, and S. Aksela,Phys. Rev. A 54, 2834 共1996兲.
21
H. Bergersen, M. Abu-Samha, J. Harnes, O. Björneholm, S. Svensson, L.
J. Sæthre, and K. J. Børve, Phys. Chem. Chem. Phys. 8, 1891 共2006兲.
22
F. G. Amar, J. Smaby, and T. J. Preston, J. Chem. Phys. 122, 244717
共2005兲.
23
M. Lundwall, H. Bergersen, A. Lindblad, G. Öhrwall, M. Tchaplyguine,
S. Svensson, and O. Björneholm, Phys. Rev. A 74, 043206 共2006兲.
24
R. Feifel, M. Tchaplyguine, G. Öhrwall et al., Eur. Phys. J. D 30, 343
共2004兲.
25
J. Tulkki, H. Aksela, and N. M. Kabachnik, Phys. Rev. A 50, 2366
共1994兲.
26
A. Niehaus, J. Phys. B 10, 1845 共1977兲.
27
P. van der Straten, R. Morgenstern, and A. Niehaus, Z. Phys. D: At., Mol.
Clusters 35, 35 共1988兲.
28
Y. Lu, W. C. Stolte, and J. A. R. Samson, Phys. Rev. A 58, 2828 共1998兲.
29
P. Lablanquie, S. Sheinerman, F. Penent, T. Aoto,Y. Hikosaka, and K.
Yto,J. Phys. B 38, L9 共2005兲.
30
J. J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 共1985兲.
31
D. W. Lindle, P. A. Heimann, T. A. Ferrett, P. H. Kobrin, C. M. Truesdale, U. Becker, H. G. Kerkhoff, and D. A. Shirley, Phys. Rev. A 33, 319
共1986兲.
Downloaded 28 Sep 2007 to 140.105.2.5. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp