IOP PUBLISHING
JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 3435–3451
doi:10.1088/0953-4075/40/17/011
Many-electron effects in 2p photoionization and Auger
decay of atomic aluminium
K Jänkälä1, S Fritzsche2,3, M Huttula1, J Schulz1, S Urpelainen1,
S Heinäsmäki1, S Aksela1 and H Aksela1
1
2
3
Department of Physical Sciences, 90014 University of Oulu, PO Box 3000, Finland
Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany
Gesellschaft für Schwerionenforschung (GSI), D-64291 Darmstadt, Germany
E-mail: [email protected]
Received 27 June 2007, in final form 20 July 2007
Published 21 August 2007
Online at stacks.iop.org/JPhysB/40/3435
Abstract
High-resolution 2p photoionization and subsequent Auger decay of atomic
Al have been investigated both experimentally and theoretically. Finestructure-resolved experimental main and satellite photoelectron spectra
were reproduced using extensive relativistic multiconfiguration Dirac–Fock
calculations. Emphasis was placed on the electron correlations and how they
affect the coupling of the valence and semi-valence electrons. The Auger
electron spectrum was used to probe the electron correlation between the
three electrons above the ionized 2p orbital and a breakdown of the twoelectron picture describing the Auger emission was observed. Continuum
wave selection was used to expound the intensity behaviour seen in the Auger
electron spectra. Direct double photoionization thresholds and behaviour of the
relative partial cross section as a function of photon energy during 2p ionization
were experimentally obtained from the Auger spectra.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Solid aluminium and its compounds are among the most frequently used materials. Therefore,
it is surprising that the semi-valence 2p ionization and subsequent Auger decay of atomic
aluminium is nearly unstudied. The 2p ionization and Auger decay of atomic Al provide
several interesting features. Due to the long lifetime (calculated 0.4 ps) of the ionized 2p shell,
the photoelectron spectra (PES) and Auger electron spectra (AES) can be resolved to the fine
structure level using 3rd generation synchrotron radiation sources and modern electron energy
analysers. Usually, the low kinetic energy range of AES is governed by overlapping lines from
various decay channels. This makes the comparison of experimental relative intensities of the
0953-4075/07/173435+17$30.00 © 2007 IOP Publishing Ltd Printed in the UK
3435
3436
K Jänkälä et al
different Auger decay branches to the theoretical predictions difficult. Because the main 2p
photoelectron spectrum of atomic Al is very compact and the subsequent decay results in very
simple states, the Auger lines and branches can be resolved from the 2p AES. Therefore, the
electron correlation can be mainly attributed to the initial states of the Auger emission. Auger
emission thus can be used to study electron correlation in the 2p hole state, and vice versa, to
study the effect of electron correlation to the Auger decay. The open outermost 3p shell of
Al makes the decay of 2p holes interesting and surprisingly laborious to calculate, therefore
multiconfiguration Dirac–Fock (MCDF) wavefunctions were applied.
Experimental and theoretical studies on the valence ionization of atomic Al have been
presented (see, e.g., [1, 2]), but to the best of our knowledge, no experimental and theoretical
results of the 2p ionization and Auger electron spectra have been published since the work
of Malutzki et al [3] in 1980s. The 2p photoionization, Auger decay and production of UV
lines were investigated more recently theoretically by Kochur et al [4]. In the 1970s Manson
[5] theoretically studied the 2p ionization of Al by charged particles. The latest study of
2p ionization and Auger decay on aluminium compounds was published by Timmermans
et al [6].
Due to the modest resolution of the previously published experimental 2p PES and AES
of atomic Al [3], no fine structure lines were resolved and the precise analysis of the Auger
spectrum was missing. Recent experimental resolution and computational improvements
allowed us to find several new aspects on the behaviour of the ionization of the semi-valence
2p shell in the open-shell Al atom. In this paper, we present the high-resolution 2p photo and
Auger electron spectra including the involved satellite structures. The experimental findings
are interpreted with extensive MCDF calculations carried out in the jj -coupled basis. In
addition, the double ionization during 2p ionization was studied via subsequent Auger decay
of the doubly ionized 2p−1 3s2 3p−1 state.
2. Experiment
The experimental work was carried out at the 1.5 GeV 3rd generation synchrotron storage ring
MAX-II at the high-resolution gas phase beamline I411 [7] in Lund, Sweden. The electron
spectrometer is a modified rotatable Scienta SES-100 hemispherical analyser mounted at the
experimental setup build in Oulu [8, 9]. The atomic beam was produced from solid Al using
a home-made induction heated oven at the temperature of 900 ◦ C. The high voltage RF power
supply used to drive the oven was a Hüttinger AXIO 5/450 model. The aluminium sample was
placed in a tungsten crucible. The total opening angle of the main Al beam was approximately
30◦ and the Doppler broadening about 14 meV.
In order to avoid effects from possibly deviating angular distributions of different lines,
all the electron spectra were measured at the so-called magic angle of 54.7◦ , with respect to
the polarization vector of the linearly polarized synchrotron radiation. The photon energy
used to measure the 2p photoelectron spectrum was 110 eV with the beamline slit of 15 µm
corresponding approximately 12 meV photon bandwidth. The modified Zeiss SX-700 plane
grating monochromator at beamline I411 can also be used only as a double mirror. Due to the
fact that Auger electron lines are not sensitive to the photon energy bandpass, we were able
to measure the Auger spectrum without monochromatization using the first-order undulator
peak, as in our previous study of atomic Rb [10]. The maximum of the first harmonic undulator
peak was set to 110 eV well above the photoionization thresholds, in order to minimize the
photon-energy-dependent effects to the photoionization cross sections. Contribution from
the ionization of the 2s shell at the binding energy of 127 eV [11] by the higher undulator
harmonics was found to be negligible. The high photon flux allowed us to use constant pass
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
3437
12
5
Expt.
Intensity (arb. units)
10
1
2p 3p main lines
(a)
8
6
4
satellites
1
2
0
96
Intensity (arb. units)
1.2
94
92
90
88
86
Binding energy (eV)
s5
Expt.
s2
84
10
(c)
3
7
s6
5
8
0.9
s8 s11
s9
s7 s10 s12
0.6
80
8
Expt.
(b)
82
6
2
4
6
9
4
s4
s3
0.3
s13
s17
s16
s14
s15
s1
0.0
5
2
0
1
Calc. 2p 4p
Calc.
(e)
(d)
5
1
2p 4s
5
1
2p 3d
92
91
Binding energy (eV)
90
82.5
82.0
81.5
Binding energy (eV)
81.0
Figure 1. (a) Experimental 2p PES of atomic Al. (b) Magnified experimental 3s2 3p → 2p5 3s2 nl
satellite structure and (c) the main 2p lines. The dots are original data points and the solid lines are
least-squares fits to the data. (d) Theoretical satellite structure and (e) the main spectrum. Dashed
lines denote the PES from 3p 2 P1/2 initial states, dotted lines from 3p 2 P3/2 initial states and the
solid lines are sums of the two spectra arising from the two initial states. The simulated spectra
are generated using experimental average linewidths.
energy of 5 eV in the detailed measurements. The overview spectrum in figure 1(a) and all
the double ionization studies in section 5.3 were measured using 10 eV pass energy. The
spectrometer entrance slit was set to 0.4 mm (curved) for PES and to 0.2 mm (curved) for
AES measurements. The total broadening from the Doppler effect and from the experimental
setup using 5 eV pass energy was approximately 23 meV.
3438
K Jänkälä et al
The transmission correction for all spectra was done by using the constant relation of the
N4,5 photoelectron lines and N4,5 O1 O2,3 and N4,5 O2,3 O2,3 Auger spectra of Xe, as described
in [12]. The binding energy calibration for 2p photoelectron lines was obtained using Kr M4,5
lines [13] and the kinetic energy calibration for Auger spectrum using Kr M4,5 N2,3 N2,3 Auger
spectrum [14].
3. Theory
Due to the small separation (0.0139 eV [15]) of the ground state [Ne]3s2 3p 2 P1/2 and the
first excited state [Ne]3s2 3p 2 P3/2 , both states are populated at the temperatures needed to
evaporate Al. Because PES from the two initial states deviate, proper knowledge of the
distribution of the states at the interaction region is essential. Moreover, the separation is
smaller than the natural linewidth of the 2p ionized states. Therefore, only the sum of the
calculated spectra from the two initial states can be directly compared to the experiment. The
density of the initial states at the temperature of 900 ◦ C was calculated using the Boltzmann
distribution
ρi = gi e−Ei /kT
,
−Ej /kT )
j (gj e
(1)
where Ei is the energy difference of the state i from the ground state and gi = 2Ji + 1 is
the degeneracy of the state. At the temperature used, the population of the [Ne]3s2 3p 2 P1/2
state is 37% and [Ne]3s2 3p 2 P3/2 state 63%. Thermal excitation of the [Ne]3s2 4s, [Ne]3s2 3d
or even higher states is negligible.
The electronic state calculations were carried out using the MCDF method, where
the relativistic atomic state functions (ASFs) are formed as linear combinations from the
jj -coupled configuration state functions (CSFs) with the same parity π and total angular
momentum J :
cαi |ψi (πα Jα Mα ).
(2)
|α (πα Jα Mα ) =
i
The coefficients cαi describe the mixingof the corresponding CSF at the ASF and they represent
the electron correlation. The relation i |cαi |2 = 1 holds for the mixing coefficients.
To obtain the photoionization (and shake-up) spectra, the dipole amplitudes γβ πβ Jβ , κc :
πt Jt |D(ω)|γi πi Ji from the initial 3s2 3p 2 P1/2,3/2 states to one of the 2p−1 hole states are the
main building blocks for calculating the relative intensities and shake-up probabilities (3).
In the framework of the MCDF method, these many-electron photoionization amplitudes are
traced back always to the computation of the corresponding interaction matrix within the given
CSF basis, using a decomposition into one-particle matrix elements as described in [16]. From
these amplitudes, the cross sections for the photoelectron lines are obtained by taking the sum
over all the possible scattering states of the total (N-electron) system: ‘photoion + electron’,
i.e. by including the summation over the partial waves of the photoelectron as well as the total
parities πt and angular momenta Jt :
4π 2 αω Qiβ (Ji , Jβ ) =
|γβ πβ Jβ , κc : πt Jt |D(ω)|γi πi Ji |2 .
(3)
3(2Ji + 1) κ J
c t
While for the (direct) photoionization lines, the intensities can be calculated rather easily
by using the expansion (2), more care has to be taken if the ionization is accompanied by the
excitation of the 3p valence electron to either an np orbital (n = 4, 5, . . .) or ns, nd orbitals
(conjugated shake-up). Such an ionization with excitation requires the correlated motion of
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
3439
the electrons, and hence the occurrence of an additional electron–electron interaction. In
the present formalism this corresponds to the nonorthogonality of the single particle orbitals
between the initial and final states. Using MCDF wavefunctions, these shake-up amplitudes
can be estimated quite well, when the initial and final ionic states of Al are optimized
independently. This leads to two sets of electron orbitals which are not quite orthogonal
to each other and allows that a non-zero amplitude arises for the shake-up processes already in
the first order, if the overlap of all the one-electron orbitals is treated properly in the evaluation
of the photoionization amplitudes, cf [17].
The relative Auger emission intensity to the magic angle at the two-step model is given as
Tfβ (Jf , Jβ )
,
(4)
ρi Qiβ (Ji , Jβ )
n(Jf , Jβ ) =
Pβ (Jβ )
i
where Qiβ (Ji , Jβ ) is the photoionization cross section (3) and Pβ (Jβ ) is the total decay rate
of the initial state. The Auger decay rate Tfβ (Jf , Jβ ) is calculated as
N−1 2
Tfβ (Jf , Jβ ) = 2π
cf µ cβν ψµ (Jf )A lA jA ; Jβ Vij ψν (Jβ ) ,
(5)
µν
lA jA
ij
where the final ionic state has been coupled with the energy normalized continuum
wavefunctions in order to obtain the antisymmetric final state functions. The two-electron
operator Vij is simply the Coulomb operator which causes the coupling of the bound state
density to the continuum. Note that ψµ (Jf ) and ψν (Jβ ) represent antisymmetric CSFs as they
occur on the right-hand side of expansion (2). For more detailed description about the theory
see [18] and the calculations [19, 20].
4. Calculations
The relativistic wavefunctions were obtained by applying the GRASP92 package [21] together
with the RELCI extension [22]. GRASP92 applies the Dirac–Coulomb Hamiltonian in order to
determine the self-consistent field and the relativistic radial wavefunctions. In order to avoid
shift of the average energy and the electric potential field by the highly excited correlation
configurations, the calculations were performed at the extended average level (EAL) scheme.
The photoionization and Auger decay amplitudes have been calculated using the RATIP program
[19, 23], utilizing the PHOTO and AUGER components. The velocity gauge was chosen for the
photoionization calculations.
Table 1 lists the electron configurations which were used in the wavefunction expansions
calculating the initial, intermediate and final states. Since in the 2p ionization and subsequent
Auger decay of Al, the electron correlation was found to take place in the 2p ionized state,
special care was placed on the construction of the intermediate state. The calculations were
done by increasing stepwise the number of configurations and observing the changes in
the Auger intensities. Direct coupling of the CSF set A (see table 1) gives 6194 intermediate
states. The total amount of effective CSFs reduces to 4676 (J = 0, 1, 2, 3 states), because
only the ASFs with the leading configuration of 2p5 3s2 3p was noted to be populated in
the direct 2p photoionization. Further attempts to enlarge the CSF basis failed because of the
rapid increase in the size of the CSF basis and due to convergence problems. For comparison,
the photoionization calculations were also carried out by representing the 2p ionized state
with a small CSF basis B, including even and odd parity configurations. The CSF basis B
was used especially in the photoionization and shake-up calculations in order to allow the
full relaxation of the atomic orbitals. The final state CSF basis (see table 1) shows that the
3440
K Jänkälä et al
Table 1. Configurations used in MCDF calculations.
Ground state
Intermediate state
CSF set A
CSF set B
Final state
2p6 3s2 (3p1 + 3d1 + 4s1 + 4p1 + 4d1 + 5s1 + 5p1 + 5d1 )
2p5 3s2 (3p1 + 4p1 + 5p1 ), 2p5 4s1 (4p1 5s1 + 5s1 5p1 + 4p1 5d1 ),
2p5 3d2 (3p1 + 4p1 + 5p1 ), 2p5 3s1 3p1 (4s1 + 4d1 + 5s1 + 5d1 ),
2p5 3s1 3d1 (3p1 + 4p1 + 5p1 ), 2p5 5p1 (4p2 + 4d2 + 5s2 + 5d2 ),
2p5 3s1 4s1 (4p1 + 5p1 ), 2p5 3s1 4p1 (4d1 + 5s1 ), 2p5 3s1 5p1 5s1 ,
2p5 3p1 (4p1 5p1 + 4s2 + 4p2 + 4d2 + 5s2 + 4s1 5s1 + 3d1 4d1 +
3d1 5d1 + 4d1 5d1 + 5d2 ), 2p5 3p2 (4p1 + 5p1 ), 2p5 5s1 5p1 5d1 ,
2p5 4p1 (4s2 + 4d2 + 5s2 + 5d2 ), 2p5 (3p3 + 4p3 + 5p3 )
2p5 3s2 (3p1 + 3d1 + 4s1 + 4p1 + 4d1 + 5s1 + 5p1 )
2p6 (3s1 + 3p1 + 3d1 + 4s1 + 4p1 + 4d1 + 5s1 + 5p1 + 5d1 )
Table 2. Experimental and calculated binding energies and relative intensities of the main
2p−1 3s2 3p photoelectron lines of Al. Intensities are given as percentages from the total intensity.
Purities refer to the jj coupling.
Experiment
1
2
3
4
5
6
7
8
9
a
b
Assignment
Eb (eV)
Intensities
2p5 3s2 3p 1 S0
2p5 3s2 3p 3 P1
2p5 3s2 3p 1 D2
2p5 3s2 3p 3 P0
2p5 3s2 3p 1 P1
2p5 3s2 3p 3 P2
2p5 3s2 3p 3 D1
2p5 3s2 3p 3 D2
2p5 3s2 3p 3 D3
2p5 3s2 3p 3 S1
84.23
82.20
2.25
8.81
82.15
16.02
82.05
81.86
81.71
81.57
81.46
80.81
9.15
13.29
8.85
14.49
18.71
8.42
Calculations
Eb (eV)a
Intensitiesa
Intensitiesb
Puritya
82.90
80.48
80.43
80.41
80.33
80.13
79.97
79.82
79.73
79.14
2.18
7.04
13.67
2.48
9.21
11.49
9.94
18.37
18.67
6.95
3.27
6.99
13.32
2.48
9.26
11.77
9.55
18.31
18.57
6.49
0.47
0.67
0.80
0.51
0.56
0.91
0.35
0.81
0.92
0.41
Extensive MCDF calculation in jj -coupled basis without relaxation (CSF set A).
MCDF calculation in jj -coupled basis including relaxation (CSF set B).
final state electron correlation is small, because only the configurations with the same l of the
outermost electron can mix. This is due to the different parity of the [Ne]ns1/2 -[Ne]n p1/2,3/2
and [Ne]np1/2,3/2 -[Ne]n d3/2,5/2 states and different J values of the [Ne]ns1/2 -[Ne]n d3/2,5/2
states. Then, the large energy separation of the same l states reduces the allowed correlation
to nearly zero.
5. 2p photoionization of atomic Al
Figure 1(a) shows the 2p PES measured at the photon energy of 110 eV. Figure 1(b) shows the
magnified 3s2 3p → 2p5 3s2 nl satellite structure and figure 1(c) the main 2p PES, measured
with a better experimental resolution than the long scan in figure 1(a). For comparison,
figures 1(d) and (e) show the calculated satellite and main spectra using CSF set B. The
energies of the calculated spectra are shifted by −1.5 eV to coincide with the experiment. The
assignments to the labelled peaks, as well as the experimental and theoretical binding energies
and relative intensities, are given in tables 2 and 3. The assignments which give the leading
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
3441
Table 3. Experimental and calculated binding energies and relative intensities of the satellite
2p−1 3s2 nl photoelectron lines of Al.
Experiment
s1
s2
s3
s4
s5
s6
s7
s8
s9
s10
s11
s12
s13
s14
s15
s16
s17
a
b
c
Calculations
Assignment
Eb (eV)
Intensitiesa
Intensitiesb
Eb (eV)c
Intensitiesb,c
2p5 3s2 4p 1 S0
2p5 3s2 4p 1 D2 + 3 P1 + 3 D1
–
2p5 3s2 4p 3 P0
2p5 3s2 4p 3 P2 + 1 P1 + 3 D2
2p5 3s2 4p 3 D3
2p5 3s2 4p 3 S1
2p5 3s2 3d
2p5 3s2 3d
2p5 3s2 3d
2p5 3s2 3d
2p5 3s2 3d
2p5 3s2 3d
2p5 3s2 4s 1 P1
2p5 3s2 4s 3 P0
2p5 3s2 4s 3 P1
2p5 3s2 4s 3 P2
92.92
91.89
91.72
91.65
91.51
91.43
91.35
91.27
91.17
91.04
90.93
90.86
90.73
90.08
90.04
89.69
89.62
0.9
14.3
1.8
2.7
20.9
14.1
4.5
6.3
8.4
5.0
5.7
5.0
4.4
0.8
0.4
1.0
1.7
1.7
27.1
–
5.1
39.5
24.6
7.8
18.1
24.2
14.4
16.5
14.3
12.5
21.5
9.8
25.3
43.5
89.88
89.36
–
89.20
88.93
88.89
88.82
88.39
88.30
87.98
87.91
87.81
87.74
87.63
87.59
87.22
87.16
0.7
31.1
–
2.2
37.9
19.9
8.8
8.0
25.4
16.7
18.6
31.9
9.6
23.9
8.5
25.3
42.4
Percentages from the total intensity of the satellite structure in figure 1(b).
Percentages from the total intensity of the corresponding configuration.
MCDF calculation in jj -coupled basis including relaxation (CSF set B).
CSF LSJ term are used for labelling the lines, but it must be emphasized that the only valid
quantum number according to the calculations is the total angular momentum J . The LSJ
terms were obtained by taking the standard unitary transform from jj to LS-coupled basis.
The purities obtained in LS coupling are about the same as in [3].
5.1. Main 2p photoelectron spectrum of Al
It can be seen from figure 1(c) and table 2 that the 2p PES lines are clearly separated to singlets
and triplets, which is typical for strongly LS-coupled systems. On the other hand, the energy
ordering of the lines deviates from Hund’s rules. Deviation can be explained by the nonnegligible spin–orbit interaction of the electrons. Energy calculations in the jj -coupled basis
shows that the peaks 2–4 rise from transitions whose final states leading CSFs have a hole in the
2p1/2 orbital, whereas peaks 5–9 correspond to final states having hole in the 2p3/2 orbital. The
2p5 3s2 3p 1 S0 state, labelled as 1 in figure 1(a), comes from ionization to a state with a hole in
the 2p3/2 orbital, forms an exception to the relativistic orbital interpretation in the jj coupling.
The spin–orbit effects cause energy shift and regrouping of the 2p5j =1/2 3s2 3pj =1/2 (3 P0 ) line
with the 2p5j =1/2 3s2 3pj =1/2 (1 P1 ) line, because the lines rise from 2p1/2 coupling, whereas
2p5j =3/2 3s2 3pj =1/2 (3 P1 ) and 2p5j =3/2 3s2 3pj =1/2 (1 D2 ) lines rise from 2p3/2 coupling.
Weak spin–orbit coupling of the state 2p5j =3/2 3s2 3pj =3/2 (1 S0 ) is seen also from purity
0.47 and large mixing with the state 2p5j =1/2 3s2 3pj =1/2 (3 P0 ). Peak 1 in figure 1(a) is also
clearly wider than the other structures. This peculiar behaviour is explained by a very rapid
Auger decay to the 2p6 3s 2 S1/2 state. Auger calculations showed that the transition rate of
the 2p5 3s2 3p 1 S0 state is about 100 times larger than of the other states. This corresponds
3442
K Jänkälä et al
well with the experimentally observed Lorentzian linewidth, which for the peak 1 is indeed
about two orders of magnitude larger than for the other peaks. The purity column shows that
specially J = 1 states are not well described by jj coupling which partially rises from the
small energy separation of all mixing J = 1 states. On the other hand, from [3] is seen that
actually the purities of the states are not much larger in LS coupling.
The overall agreement between calculations and experiment in table 2 is remarkably
good. Comparison of the chi-squared statistics gives χ 2 ≈ 0.22 for CSF A and χ 2 ≈ 0.27 for
CSF B. By observing only the PES this leads to the conclusion that the electron correlation effects are negligible in 2p ionized Al, which is clearly not the case as it will be shown in section 6.
Comparing the two intensities obtained using CSF bases A and B one can see that the extended
electron correlation influences the calculated intensities slightly. The clearest effect is seen
in peak 1, where the CSF basis A gives the best correspondence. The relaxation of the
atomic orbitals does not seem to cause considerable effects to the calculation of the direct 2p
photoionization. The ionization cross section obtained from calculations (CSF set A) for the
2p shell from the ground state 3s2 3p 2 P1/2 is 4.5 Mb and from the 3s2 3p 2 P3/2 state 3.5 Mb.
The ground state value agrees with the value 4.6 Mb from R-matrix calculations [4].
Using conventional PES studies, direct comparison of calculations to the experiment is
possible only for the sum spectrum from the two initial states. On the other hand, some hint of
the internal structure can be obtained from [24] where Cubaynes et al measured and calculated
the 2p PES of 3s 2 S1/2 → 3p 2 P1/2 and 3s 2 S1/2 → 3p 2 P3/2 excited Na atoms, which leads
to the 2p5 3p final states (i.e. the same final states as Al but without the 3s electrons). The
similarity between Al PES in figure 1(c) and 2p PES from Na∗ atoms in [24] is striking.
The shapes of the two experimental spectra from 3p 2 P1/2 and 3p 2 P3/2 initial states of Na∗
in [24] were explained by calculated results using generalized geometrical model and the socalled dynamically forbidden transitions (i.e. destructive interference between mixing CSFs
which cannot be predicted by the usual selection rules and non-correlated models). Our
current calculations for Al shown in figure 1(e) are nearly identical to the calculated results
obtained for Na∗ . This also suggests the occurrence of dynamically forbidden transitions
arising from mixing of configurations in atomic Al, and that the calculated individual 2p PES
from 2 P1/2 and 2 P3/2 initial states in figure 1(e) are correct. To verify this explicitly one needs
to experimentally separate the two spectra from the two initial states.
5.2. Satellite 2p photoelectron spectrum of Al
Numerical values and peak identifications of the experimentally and theoretically obtained
3s2 3p → 2p5 3s2 nl satellite structure shown in figures 1(b) and (d) are given in table 3.
Comparing the experimental and theoretical satellite spectra in figures 1(b) and (d) it can
be seen that the agreement is much worse than for the main lines. This is due to the
fact that the energy separation of the lines is more difficult to calculate correctly, but more
importantly the satellites are caused by many-electron processes, which obviously makes the
intensity calculations more difficult and sensitive to the correctness of the wavefunctions. The
intensity calculations were carried out including full relaxation of the atomic orbitals, which
was found to predict intensity also to the shake-up transitions where the l quantum number
of the shaking electron can change, i.e. conjugated transitions. The satellite structure has
been previously suggested to rise partially from the 3s2 3p → 2p5 3s2 4p shake-up transitions
[3]. According to our calculations the structure is also due to the 3s2 3p → 2p5 3s2 3d and
3s2 3p → 2p5 3s2 4s conjugated shake-up transitions. Identification of the lines s8–s13 is
also based to the experimental knowledge that the 2p5 3s2 3d → 2p6 3d Auger lines are found
at the energy difference corresponding the 3s2 3p → 2p5 3s2 3d shake-up energy from the
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
3443
Table 4. Relative shake-up probabilities (%) during 2p ionization of Al.
Shake-up transition
Experiment
Calculations
3p →
3p → 2p5 3s2 3d
3p → 2p5 3s2 4p
3p → 2p5 3s2 4d
3p → 2p5 3s2 5s
3p → 2p5 3s2 5p
0.80
5.91
11.93
0.34
0.00
1.88
4.43
5.23
21.18
0.25
0.01
1.39
2p5 3s2 4s
2p5 3s2 3p → 2p6 3d Auger lines. The same approach was also used in identifying the peaks
s2–s7. No attempt was made to assign the individual spectral terms for peaks s8–s13. Also
the peak s3 and small structures between peaks s13 and s14 remained unidentified.
The interpretation of the spectral terms is primarily based on the calculations, which
makes the identification of the structures s5–s7 rather uncertain. The assignment of the peak
s1 to 2p5 3s2 4p 1 S0 is supported by the shape of the peak which is clearly wider than the other
peaks similarly as for the main 2p5 3s2 3p 1 S0 line. This shows that the 3s2 3p → 2p5 3s2 4p
shake-up does not prefer the 1 S0 state, on contrary to what was suggested in [3]. The peak s4
corresponding to the 2p5 3s2 4p 3 P0 state is confirmed by the line found at the correct splitting
form the experimental AES.
As expected, the 3s2 3p → 2p5 3s2 4p satellite spectrum shows that spacing of the energy
levels decreases, when compared to the 3s2 3p → 2p5 3s2 3p spectrum. The total width of the
3s2 3p → 2p5 3s2 4p spectrum is about 1 eV while the main 3s2 3p → 2p5 3s2 3p spectrum is
about 4 eV wide. The peak corresponding to the 2p5 3s2 4p 1 S0 final state is still at the highest
binding energy, but the other lines are separated more clearly to two groups (s2 and s5–s7)
characterized by a leading CSF with a hole in the 2p1/2 or 2p3/2 orbitals. This shows that the
effects arising from the spin–orbit interaction are more important. The relative strength of
the spin–orbit interaction increases even more on the 2p5 3s2 4s final states. Peaks s14–s17 in
figure 1(b) and table 3 show that the lines are very clearly separated to two peaks corresponding
to 2p1/2 and 2p3/2 ionizations and the singlet–triplet structure is broken completely. Effects
from the Coulomb interaction can be seen from the energy order of the 2p5 3s2 4s 1 P1 and
2p5 3s2 4s 3 P0 lines which is expected to be opposite for 2p5j =1/2 3s2 4sj =1/2 (J = 0) and
2p5j =1/2 3s2 4sj =1/2 (J = 1) states in the pure jj -coupled case. Considering the 2p5 3s2 3d
final states one can see that the clear 2p1/2 –2p3/2 splitting is missing and the states are thus
more clearly LS coupled. This change can be understood from the radial wavefunctions of
the outermost electron in different states. The 3d radial wavefunction is broad and localized
close to the nucleus whereas 4s and 4p wavefunctions are concentrated much further. This
makes the two-electron interaction integrals larger for the 2p5 3s2 3d state and thus increases the
Coulomb interaction. This illustrates the very sensitive competition between the spin–orbit
and Coulomb interactions in atomic Al.
Experimental and theoretical total shake-up probabilities are compared in table 4. The
intensities are given with respect to the main spectrum. To correctly predict the intensities of
conjugated shake-up transitions is known to be very difficult task (see, e.g., [25] and references
therein). Our current calculations including full relaxation of the atomic orbitals seems to
give fairly reasonable results. The intensity of the 3s2 3p → 2p5 3s2 3d shake-up is in good
agreement, but 3s2 3p → 2p5 3s2 4s shake-up is overestimated and the 3s2 3p → 2p5 3s2 4p
monopole shake-up probability is quite drastically overestimated. The overestimation follows
3444
K Jänkälä et al
0.55
0.50
2
Relative probability (x10 )
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
98
100
102
104
106
108
Photon energy (eV)
110
112
114
Figure 2. Experimental relative double ionization probability during 2p ionization of atomic
Al. The upper markers correspond the 2p5 3s2 2 P3/2 double ionization and the lower markers the
2p5 3s2 2 P1/2 double ionization. The dashed lines are drawn to guide the eye.
partially from the photoionization calculation (3) allowing the full relaxation of the atomic
orbitals, which was seen from the 3p → 4p shake-up probability of 17.5% calculated without
relaxation from the CSF set B. Then, the other part follows from the 4p wavefunction of the
CSF B, because the small CSF space B was not able to produce the 4p radial wavefunction
correctly. The same shake-up probability calculated from CSF set A without relaxation is
12.4% and corresponds well with the experiment. Still, the shape of the 3s2 3p → 2p5 3s2 4p
satellite spectrum remained the same as calculated using CSF set B. The calculated
3s2 3p → 2p5 3s2 4p shake-up probability 11.9% from [4] also agrees well with the experiment,
whereas 0.86% for 3s2 3p → 2p5 3s2 5p shake-up is slightly underestimated.
A peak assigned to the 3s2 3p → 2p5 3s2 4d shake-up was found at the binding energy
of 93 eV and two peaks assigned to the 3s2 3p → 2p5 3s2 5p shake-up at the binding energy
94 eV (see figure 1(a)). A peak indicating the 3s2 3p → 2p5 3s2 5s shake-up did not appear in
the experimental spectrum.
5.3. Double ionization on 2p photoionization of Al
A double photoionization process produces two electrons to the continuum. The two electrons
can take any energy value between 0 and hν − Eb2+ . Therefore, studying the double ionization
process directly requires the use of a coincidence setup. If the doubly ionized state can decay
further via Auger emission, the lines can be identified from the AES. This allows obtaining
the double ionization thresholds indirectly and thereby studying the behaviour of the double
ionization probability as a function of photon energy.
Figure 2 depicts the relative 2p6 3s2 3p → 2p5 3s2 2 P1/2,3/2 + 2e− direct double
photoionization probabilities as a function of photon energy. The values in the figure were
obtained by measuring the whole Auger spectrum at each photon energy and dividing the
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
9
100
10
5
Experiment
8
s-o
60
2
Intensity (arb. units)
(a)
6
80
40
3445
1
3
7
4
20
s1
s2
s5
s3
s4
s6
0
35
40
45
50
Kinetic energy (eV)
55
60
65
100
(b)
80
Theory
60
40
20
0
35
40
45
50
Kinetic energy (eV)
55
60
65
Figure 3. (a) Experimental and (b) theoretical 2p Auger spectrum of atomic aluminium. For better
visibility the low kinetic energy range is magnified.
Auger line intensity corresponding to the double ionized initial states by the intensity from
the Auger lines following the main 2p ionization. Because the radiative decay probability of
the 2p5 3p states is small, the obtained values are comparable with the shake-up values given
in table 4. Figure 2 shows that the behaviour of the double ionization probability during 2p
ionization is quite monotonous. The probabilities reach their maxima at the photon energy of
103.5 eV, about 5.5 eV over the double ionization threshold, and after that start to decrease
slowly. Extrapolating the functions to cross the photon energy axis we were able to obtain
the double photoionization threshold 97.72 ± 0.08 eV for the 2p5 3s2 2 P3/2 state and 98.09 ±
0.14 eV for the 2p5 3s2 2 P1/2 state. The results agree with the optically obtained values 97.69
and 98.14 [15]. The calculated MCDF values of 95.76 and 96.42 are averages from the
two initial states. The calculated energies are again shifted by about 1.5 eV but the energy
difference 0.44 eV is in line with the current experimental value 0.37 eV and with the optically
obtained value of 0.45 eV [15].
The double ionization probability at the photon energy of 103 eV is quite large. The
experimental result is about five times larger than the calculated value 0.86 from [4]. Due to
the large double ionization probability, this could be a suitable case to study the process using
a coincidence setup to obtain angle-resolved double photoionization data from an open-shell
atom.
6. 2p Auger decay of Al
Experimental photoinduced 2p AES of atomic Al is shown in figure 3(a) and simulated
spectrum using equations (4) and (5) in figure 3(b). The main structures of the spectrum in
3446
K Jänkälä et al
Table 5. Experimental and calculated relative intensities of the 2p
Auger
decay3 branches. Principal
2
configurations for the Auger rate and their weights wi (wi =
i ci × 10 ) on the initial state
ASF expansions.
Experiment
Intensities
Assignment
1
2
3
4
5
6
7
8
9
10
→
2p5 3s2 3p → 2p6 5d 2 D3/2,5/2
2p5 3s2 3p → 2p6 5p 2 P1/2,3/2
2p5 3s2 3p → 2p6 5s 2 S1/2
2p5 3s2 3p → 2p6 4d 2 D3/2,5/2
2p5 3s2 3p → 2p6 4p 2 P1/2,3/2
2p5 3s2 3p → 2p6 4s 2 S1/2
2p5 3s2 3p → 2p6 3d 2 D3/2,5/2
2p5 3s2 3p → 2p6 3p 2 P1/2,3/2
2p5 3s2 3p → 2p6 3s 2 S1/2
2p5 3s2 3p
2p6 (6s + 6p + 6d)
2.97
2.31
2.50
0.69
6.67
7.71
2.47
44.84
97.95
100.00
Calculations
Intensities
Main configurations
wi
–
–
2p5 3s3p5d
2p5 3p2 5p
2p5 3s3p5s
2p5 3s3p4d
2p5 3p2 4p
2p5 3s3p4s
2p5 3s3p3d
2p5 3p3
2p5 3s2 3p
–
0.65
2.16
0.03
6.84
2.79
0.09
33.37
121.28
100.00
0.46
1.18
0.13
5.04
1.30
0.80
28.71
32.78
916.53
figure 3(a) have been previously identified in [3]. Identifications based on [3], our calculations
and optical data [15] are given in table 5 with the experimental and theoretical intensity values.
Table 5 also gives the nonrelativistic configurations of the initial state which cause the highest
Auger decay contributions to the corresponding final state and their average total weight to
the ASF expansions (see equations (4) and (5)).
It is obvious that single-configuration calculations fail in describing the very rich 2p
Auger decay structure in figure 3(a). This is because the 2p5 3s2 3p configuration can decay
only to the 2p6 3s and 2p6 3p final states. In practice, it was found transitions to the 2p6 3p
final states cannot be calculated without including the 2p5 3p3 configuration to the intermediate
state ASF expansion. The existence of 2p5 3s2 3p − 2p5 3p3 correlation was also recognized
in [3], but its importance in the Auger emission was not appreciated. Lines arising from
configuration interaction (CI) in the initial or final states of the Auger decay are often called CI
satellites. In the Al case, CI satellite notation loses its meaning completely, since even the high
intensity 2p6 3p final states cannot be explained without CI. The strong interaction between the
three electrons above the ionized 2p shell leads to a breakdown of the two-electron picture in
the Auger decay. This CI is not seen in the 2p PES because photoionization is essentially
sensitive to the ground state CSF contribution at the 2p ionized state, whereas AES is sensitive
to the amount of each individual CSF in the intermediate state, as also pointed out in [26].
According to calculations, there is an initial state configuration with the largest Auger
rate for each final state. The configurations and their total weights are given in table 5. For
example, the 2p5 3p3 configuration which is responsible for the very intense Auger amplitudes
to 2p6 3p states appears in the ASF expansion with the total weight of only 0.03. The
2p5 3s3p5d configuration leading to 2p6 5d final states has a total weight of only 0.000 46, but
the Auger lines are still clearly seen in the experimental spectrum. The results demonstrate the
remarkable sensitivity of the Auger decay to probe electron correlation in the intermediate ionic
states. Total calculated intensities of the branches leading to 2p6 ns configurations compared
to the 2p6 3s ones are clearly underestimated. This suggests that despite the large size of the
wavefunction expansion of the CSF basis A the basis is not sufficient to correctly account for
the electron correlation.
The structures s2 and s4–s6 in figure 3(a) were previously [3] identified to be caused by the
decay of the 2p5 3s2 4p states to 2p6 4p, 2p6 3d, 2p6 3p and 2p6 3s states, respectively. The peaks
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
3447
Table 6. Experimental and calculated intensities of the individual Auger transitions to 2p6 3s 2 S1/2 ,
2p6 3p 2 P1/2,3/2 , 2p6 3d 2 D3/2,5/2 , 2p6 4s 2 S1/2 , 2p6 4p 2 P1/2,3/2 and 2p6 4d 2 D3/2,5/2 final states.
The different peaks are labelled according to their initial state LSJ term. The intensities are
given as percentages from the total intensity of the corresponding final state.
Calculationsa
Experiment
Label
1
2
3
4
5
6
7
8
9
a
1S
0
3P
1
1D
2
3P
0
1P
1
3P
2
3D
1
3D
2
3D
3
3S
1
3s
3p
3d
4s
4p
4d
4.6
3.4
0.3
17.9
0.0
1.5
0.0
3.7
0.0
16.3
0.0
1.3
13.5
22.3
11.0
14.8
21.7
10.2
5.6
6.3
9.0
16.1
21.2
20.6
11.6
24.3
6.0
8.7
8.0
0.9
10.6
5.9
14.1
23.5
32.7
0.7
9.7
4.0
13.3
21.6
29.5
3.4
12.5
22.3
6.5
9.7
10.2
0.7
11.1
5.0
13.8
24.8
33.7
0.0
3s
3p
3d
4s
4p
4d
10.1
0.4
3.4
3.2
4.9
1.4
11.7
21.3
27.8
15.8
0.1
14.5
12.7
14.6
12.2
23.5
5.7
12.6
3.4
0.6
0.1
1.5
5.3
0.3
7.9
2.7
15.5
26.7
38.8
1.0
18.9
0.0
7.6
4.7
4.5
4.3
10.4
22.3
24.1
3.2
0.4
4.1
1.5
0.5
19.8
0.8
17.7
21.2
27.8
6.9
0.1
1.2
5.2
0.2
7.5
2.4
15.5
26.8
40.5
0.5
Initial state populations and Auger amplitudes were calculated using CSF set A.
labelled s–o are caused by double ionization as discussed in the previous section. In addition,
we found that structure labelled as s1 is caused by Auger decays to the 2p6 4d final states and
s3 to 2p6 4s final states. Structure s3 also rises partially from the 2p6 3s2 3d → 2p6 3d Auger
decay. High intensities of the structures s5 and s6 can be explained by the overlapping lines
from the 2p6 3s2 3d → 2p6 3p and 2p6 3s2 3d → 2p6 3s Auger decays, respectively. According
to our calculations, the observed structures from initially 3s2 3p → 2p5 3s2 nl excited states
have the same origin as the so-called CI structures. For example, the 2p5 3s2 4p → 2p6 3s
decay can be reached without considering any three-electron process, but 2p5 3s2 4p → 2p6 3p
cannot. The main contribution to the Auger decay leading to the 2p6 3p final state from ASF
described by 2p5 3s2 4p state was found to rise from mixing with the 2p5 3p2 4p configuration.
Comparing structures 5 and 8 caused by Auger decays to the 2p6 4d and 2p6 3d final states
and structures 6 and 9 caused by decays to the 2p6 4p and 2p6 3p final states in figure 3(a)
shows that the shapes of the structures with the same l quantum number of the outermost
electron are nearly the same. This is due to the fact that the angular integrals of the active
electrons of CSFs which cause the highest Auger amplitudes are identical in 2p6 np and 2p6 nd
branches. The smaller total intensity of the structures 5 and 6 is due to the multiplying mixing
coefficients (see (5)). On the other hand, comparing of structures 7 and 10 caused by Auger
decays to 2p6 4s and 2p6 3s final states shows striking differences. The line caused by the decay
from 2p5 3s2 3p 3 S1 state, seen on the left side of the structure 10, is strongly suppressed in
structure 7. The 2p5 3s2 3p 3 S1 → 2p6 4s Auger peak is seen in the middle between structures
6 and 7 at the energy on 40.2 eV. The behaviour of the line is predicted by calculations, as
seen from table 6, even though the calculated total intensity of the structure 7 is drastically
underestimated.
The 2p5 3s2 3p 3 S1 initial state decays only to the 2p6 3s final state is due to CI of the other
decay branches. The Auger amplitudes from 2p5 3s2 3p 3 S1 CSF to the 2p6 3s final state are
of about the same magnitude as from 2p5 3p3 (J = 1) or 2p5 3s3p3d(J = 1) configurations
which mix with the 2p5 3s2 3p 3 S1 state, but more than two orders smaller mixing coefficients
reduce the intensity significantly. The decays from 3,1 PJ - and 3,1 DJ -type initial states are
obviously also reduced by the same reason, but the Auger matrix elements are large enough to
compensate the reduction. This is also why the 2p5 3s2 3p 3 S1 state does not decay to the 2p6 4s
3448
K Jänkälä et al
final state. The 2p6 4s final state is not reached from 2p5 3s2 4s initial states (configuration
has even an opposite parity than the 2p5 3s2 3p configuration), but from states 2p5 3s3p4s, as
seen from table 5. The fact that 2p5 3s3p4s → 2p6 4s Auger transitions have the same active
electrons (3s3p) as 2p5 3s3pnd → 2p6 nd transitions indicates that the observed AES should
resemble each other. Indeed, comparison of structure 7 to structures 8 and 10 in figure 3(a)
shows that the decay pattern to the 2p6 4s final state clearly resembles more the structure
coming from transitions to the 2p6 3d states than 2p6 3s state. No clear explanation was found
for the overestimated calculated decay rate to the 2p6 4s 1 S0 final state.
The high decay rate of the 2p5 3s2 3p 1 S0 state to the 2p6 3s final state is explained by a
very large angular matrix element of the s1/2 continuum wave, as also noted in [3]. The
calculated 2p5 3s2 3p 1 S0 → 2p6 3s Auger intensity in [3] was drastically overestimated (about
two orders of magnitude), whereas table 6 shows that our calculated intensity is still too large
but agrees fairly well with the experiment. The drastic overestimation in [3] was suggested
to rise from difficulties on calculating the proper wavefunction for the initial state. This
is not correct; the overestimation was actually due to the method on calculating the Auger
rates. The Auger intensities were calculated in [3] by applying the so-called Fermi’s golden
rule, which has (in coincidence) the same form as Tfβ (Jf , Jβ ) factor in equations (4) and
(5). The Auger amplitude Tfβ (Jf , Jβ ) in our calculations was also considerably large for
2p5 3s2 3p 1 S0 → 2p6 3s decay, but in order to obtain intensities comparable to experiment, the
decay rate has to be divided by the total decay width of the initial state. If the total Auger
decay widths are about the same for all states, comparison to the experimentally obtained
relative intensities does not show differences between our model based on scattering theory
and the first-order perturbation theory. As shown, if the total decay widths differ considerably,
the first-order perturbation expansion without proper normalization may fail drastically.
Figures 4(a)–(f) depict the magnified experimental and calculated AES to
2p6 3d 2 D3/2,5/2 , 2p6 3p 2 P1/2,3/2 and 2p6 3s 2 S1/2 final states (i.e. structures 8–10 in figure 3).
Comparing figures 4(a)–(c) indicates that the parity of the final state has some influence to
the decay patterns. The spectra from decays to the same parity 2p6 3s and 2p6 3d final states
resemble clearly each other, whereas decay to the 2p6 3p states deviate. The parity of the
final state determines the symmetry of the continuum waves, which has a significant role on
different decay channels as will be shown below. The transitions to 2p6 3s and 2p6 3d final states
are reached by even parity continuum waves, specially s1/2 and d3/2,5/2 waves, whereas the
2p6 3p states are reached only by odd parity waves, especially p1/2,3/2 continuum waves.
Numerical values of the individual fine structure states are given in table 6. Intensities
to 2p6 np and 2p6 nd final configurations in table 6 are sums of two fine structure final states,
which were not resolved from the experiment. The 29.0 meV splitting [15] between the final
states 2p6 3p 2 P1/2 and 2p6 3p 2 P3/2 is seen as asymmetric line shapes, specially on peaks 1 P1
and 3 D1 in figure 4(b). The symmetric shape of the line 3 P2 in figure 4(b) is predicted by the
calculation shown in figure 4(e). The peak is caused by transitions to 2p6 3p 2 D3/2 states only.
Otherwise the calculations give quite equal transition probabilities to both 2p6 3p 2 P1/2,3/2 final
states. The transition probability from the 3 D3 state to the 2p6 3p 2 P1/2,3/2 states is smaller than
from 3 D2 initial state because the 2p6 3p 2 P3/2 state cannot be reached by the p1/2 continuum
wave from 2p5 3p3 (J = 3) states. On the other hand, the p1/2 continuum wave has a very
large Auger matrix element in 2p5 3p3 (J = 2) → 2p6 3p 2 P3/2 decays. The 2p6 3p 2 P1/2 final
state cannot be populated from 2p5 3p3 (J = 3) states via p waves at all, which is possible by
p3/2 continuum wave from 2p5 3p3 (J = 2) configurations. The decay rate of the 3 P1 initial
state to the 2p6 3d and 2p6 3s states is smaller than to 2p6 3p states. This can be explained by
looking at the continuum waves and symmetry. The 2p6 3p final states can be reached from
3
P1 states by two considerably large non-interfering same l-valued continuum waves p1/2
Many-electron effects in 2p photoionization and Auger decay of atomic aluminium
8 (a)
60
(b)
100
5
100
3
7
3449
9
(c) 8
7
80
80
3
40
6
20
Intensity (arb. units)
2
60
60
6
4 3
40
5
8 7
4
6
2
0
40
20
20
0
0
42.0 42.2 42.4 42.6 42.8 43.0
49.8 50.0 50.2 50.4 50.6
100
(d)
20
0
56.0
42.2 42.4
56.4
56.8
57.2
57.6
56.0
56.4
56.8
(f)
80
80
60
60
40
40
20
20
0
41.8 42.0
4
2
(e)
40
41.6
5
0
49.2 49.4 49.6 49.8 50.0
55.2
55.6
Kinetic energy (eV)
Figure 4. Magnified experimental (upper) and calculated (lower) Auger electron spectra to
2p6 3d 2 D3/2,5/2 (left), 2p6 3p 2 P1/2,3/2 (centre) and 2p6 3s 2 S1/2 (right) final states. Solid lines in
the experimental spectra are least-squares fits and dots the original data points. The line markings
are given in table 6. Bars in the theoretical spectra are calculated intensities and solid lines
convolutions using experimentally obtained widths.
and p3/2 , whereas 3 P1 state decays to 2p6 3d and 2p6 3s states only by a single s1/2 wave.
Transitions via d3/2,5/2 waves are also possible, but according to calculations they do not
receive considerable intensity.
The 3 P0 state decays to the 2p6 3s state by s1/2 wave, and the active electrons are the
same as for the decay of the 1 S0 state. Therefore, one would expect similar behaviour for
both the channels. The transition rate from 3 P0 initial state to the 2p6 3s 2 S1/2 final state is not
particularly large due to destructive interference between very large Auger amplitudes from
2p5j =3/2 3s2 3pj =3/2 (J = 0) and 2p5j =1/2 3s2 3pj =1/2 (J = 0) CSFs. For the 1 S0 initial state the
amplitudes are about of the same magnitude, but the interference is constructive. This is a
clear example of CI-induced interference in Auger decay.
The splitting of the 2p6 3d 2 D3/2 and 2p6 3d 2 D5/2 final states is only 0.3 meV [15]. The
splitting is not seen in vertical bars in figure 4(d) and therefore only the higher of the two
bars is seen. The effect from the other final state is seen in how much the convolved solid
line deviates from the vertical bar. The small deviations from the line in figure 4(d) show
that in nearly all decays to the 2p6 3d final states transition to 2p6 3d 2 D3/2 or to 2p6 3d 2 D5/2
final state dominates over the other. The reason for this behaviour is again in the continuum
waves. Auger transitions from the 2p5 3s3p3d initial states (see table 5), the continuum wave
channel which allows transitions to the 2p6 3d 2 D3/2 final state, are in the most cases forbidden
for the 2p6 3d 2 D5/2 state and vice versa. This behaviour is the opposite to what is seen on
3450
K Jänkälä et al
transitions to the 2p6 3p 2 P1/2 and 2p6 3p 2 P3/2 final states. The Auger decays from 2p5 3p3
states, the continuum channel which has the largest Auger amplitude, are allowed for the
final states 2p6 3p 2 P1/2 and 2p6 3p 2 P3/2 . It must be noted that continuum wave selection does
not cause the distinct exception of the transition from the 3 P2 initial state allowing only the
other final state (as seen from figure 4(e)). The high Auger rate from the 3 P2 initial state to
the 2p6 3p 2 P3/2 final state rises from a coincidently very large Auger matrix element form
2p5j =3/2 3p3j =3/2 (J = 2) CSF.
7. Conclusion
High-resolution 2p photo and subsequent Auger electron spectra of atomic Al have been
measured and interpreted. A wide variety of different quantum mechanical phenomena is
needed for detailed understanding of intuitively simple but experimentally rather complex
photoinduced 2p electron spectra. It is shown that the electron correlation of the 2p hole does
not affect the PES, but gives rise to considerable structures in AES. CI in the 2p ionized state
was seen to affect the total intensities of the different Auger branches as well as individual
line intensities, whereas parity of the final state defining the continuum wave symmetry of the
Auger emission and angular integrals between active electrons prescribes mainly the intensity
distribution between the fine structure lines.
Acknowledgments
The work has been financially supported by the Research Council for Natural Sciences
of the Academy of Finland and the European Community-Research Infrastructure Action
under the FP6 ‘Structuring the European Research Area’ Programme (through the Integrated
Infrastructure Initiative ‘Integrating Activity on Synchrotron and Free Electron Laser
Science’). KJ would like to thank the Tauno Tönning foundation for support. SF acknowledges
support by the DFG under the Project No FR 1251/13. Ari Mäkinen is acknowledged for
assistance during the experiments. We also thank the staff of MAX-Lab for their kind help
during the measurements.
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