Download Auger cascade processes in xenon and krypton studied by electron

AUGER CASCADE PROCESSES IN XENON AND
KRYPTON STUDIED BY ELECTRON AND ION
SPECTROSCOPY
LEENA PARTANEN
REPORT SERIES IN PHYSICAL SCIENCES
Report No. 46 (2007)
AUGER CASCADE PROCESSES IN XENON AND KRYPTON STUDIED BY ELECTRON AND ION SPECTROSCOPY
LEENA PARTANEN
Department of Physical Sciences
University of Oulu
Finland
REPORT SERIES IN PHYSICAL SCIENCES
OULU 2007 • UNIVERSITY OF OULU
Report No. 46
Opponent
Dr. Antti Kivimäki, TASC-INFM National Laboratory, Trieste, Italy
Reviewers
Dr. Antti Kivimäki, TASC-INFM National Laboratory, Trieste, Italy
Dr. Pascal Lablanquie, LCP-MR
CNRS and University Pierre et Marie Curie, Paris, France
Custos
Prof. H. Aksela, Department of Physical Sciences
University of Oulu, Finland
ISBN 978-951-42-8662-9 (Paperback)
ISBN 978-951-42-8663-6 (PDF)
http://herkules.oulu.fi/isbn9789514286636/
ISSN 1239-4327
OULU UNIVERSITY PRESS
Oulu 2007
i
Partanen, Leena: Auger cascade processes in xenon and krypton
studied by electron and ion spectroscopy
Department of Physical Sciences, University of Oulu, Finland
Report No. 46 (2007)
Abstract
In this thesis electronic structure and the dynamics of selected rare gases
were investigated. Auger electron and ion spectroscopies were employed in
the studies for the de-excitation processes of an inner-shell vacancy excited
by synchrotron radiation. The collected spectra were analyzed by combining
information from the Auger spectra created with different excitation methods and from theoretical calculations. The effects of electron correlation on
the Auger spectra were emphasized in the studies.
Keywords: Auger decay, satellite Auger process, electron spectroscopy, ion
spectroscopy, photon excitation, rare gases
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Acknowledgments
This work was carried out at the Department of Physical Sciences, University
of Oulu. I would like to thank the Head of the Department, Professor Jukka
Jokisaari, for placing the facilities at my disposal. I am most grateful to
my supervisor Professor Helena Aksela. She has guided me from the very
first step to the world of atomic physics. It has been inspiring to follow
her aspiration to find new challenges and knowledge. In addition, she has
supported me in many ways during these years. I would also like to thank
Professor Seppo Aksela for his guidance and instruction in the experimental
electron spectroscopy.
I am grateful to the reviewers of the thesis, Dr. Antti Kivimäki and Dr.
Pascal Lablanquie. Their constructive comments made me to understand
more about the research addressed in this study.
This thesis bases on the great power of teamwork. I wish to express my
sincerest gratitude to the experts on atomic physics, Dr. Marko Huttula, Dr.
Rami Sankari, Dr. Valdas Jonauskas, Professor Edwin Kukk, and Dr. Sami
Heinäsmäki, who were the co-authors of the original publications and who
gave me invaluable guidance and comments during the research work. It is my
pleasure to thank also other co-authors and collaborators who participated
the measurements and calculations of the original publications.
I would like to thank former and present members of the Electron Spectroscopy group for pleasant teamwork. In particular, I would like to thank
Anna Sankari and Minna Patanen with whom I have shared the office. They
have had time for discussions, for all the sense and nonsense. Dr. Tommi
Matila is acknowledged for teaching me everything I ever needed to know
about Cowan’s code. I want to thank the staff of the Department of Physical
Sciences as well for enjoyable moments with teaching and coffee breaks.
I want to acknowledged the financial sources. This work was supported
by the Vilho, Yrjö and Kalle Väisälä Foundation, the Tauno Tönning Foundation, and the National Graduate School in Material Physics.
Finally, I would like to express my deepest gratitude to my relatives and
friends. Especially I want thank my loving husband Antti, who stood by me,
and my childen, Taru and Juho, who have kept me busy outside of work. I
am grateful to my parents Eila and Kalevi, brother Esa and Jenny, brother
Antti, my parents-in-law Eila and Esko, and Maija and her family. Thank
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you for being there always when I needed you.
Oulu, December 2007
Leena Partanen
List of original papers
This thesis contains an introductory part and the following five papers which
will be referred in the text by their Roman numbers.
I. L. Partanen, R. Sankari, S. Osmekhin, Z. F. Hu, E. Kukk, and H.
Aksela, Multiple ionization of Xe — comparison of de-excitation pathways following 3d5/2 ionization and 3d5/2 → 6p resonance excitation,
J. Phys. B: At. Mol. Opt. Phys. 38, 1881–1893 (2005).
II. V. Jonauskas, L. Partanen, S. Kučas, R. Karazija, M. Huttula, S. Aksela, and H. Aksela, Auger cascade satellites following 3d ionization in
xenon, J. Phys. B: At. Mol. Opt. Phys. 36, 4403–4416 (2003).
III. L. Partanen, M. Huttula, S.-M. Huttula, H. Aksela, and S. Aksela,
Effects of electron correlation on the M4,5 NN4,5 Auger transitions in
xenon, J. Phys. B: At. Mol. Opt. Phys. 39, 4515–4524 (2006).
IV. L. Partanen, M. Huttula, H. Aksela, and S. Aksela, The M4,5 N-NNN
Auger transitions in Kr, J. Phys. B: At. Mol. Opt. Phys. 40, 3795–
3805 (2007).
V. L. Partanen, M. Huttula, S. Heinäsmäki, H. Aksela, and S. Aksela, Xe
N4,5 O-OOO satellite Auger spectrum, J. Phys. B: At. Mol. Opt. Phys.
40, 4605 - 4615 (2007).
All Papers I–V were prepared as teamwork. The present author is responsible
for the majority of text and data handling in all papers. All the theoretical
calculations using the Cowan’s code package were performed by the author,
excluding the calculations done with the method of global characteristics in
Paper II and the MCDF calculation in Papers III, IV, and V. The present
author participated in the experimental work for Papers II and III.
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Contents
Abstract
i
Acknowledgments
iii
List of original papers
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Contents
vii
1 Introduction
1
2 Overview of theoretical methods
2.1 Hartree-Fock method . . . . . . . . . . . . . . . . . . . . . . .
2.2 Atomic energy states . . . . . . . . . . . . . . . . . . . . . . .
2.3 Configuration interaction . . . . . . . . . . . . . . . . . . . . .
3
3
5
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3 Electronic transitions
3.1 Selection rules for dipole transition .
3.2 Transitions following photoabsorption
3.3 Normal Auger transitions . . . . . . .
3.4 Cascade of Auger transitions . . . . .
3.5 Satellite Auger transitions . . . . . .
3.6 Method of global characteristics . . .
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4 Experiment
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4.1 Synchrotron radiation . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Electron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 Ion spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Summary of included papers
5.1 Papers I–III: Multiple ionization of Xe . . . . . . . . . . .
5.1.1 Partial ion yields following 3d excitation . . . . . .
5.1.2 Paper III: M4,5 -NN4,5 Auger transitions . . . . . . .
5.1.3 Paper II: Interpretation of Auger cascade satellites
5.2 Paper IV–V: Satellite Auger spectra . . . . . . . . . . . .
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CONTENTS
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5.3
Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Bibliography
39
Chapter 1
Introduction
Humankind has been concerned with the structure of matter for thousands
of years, and the term atomos, ”uncuttable”, dates back to around 450 BCE
(coined by Democritus). However, the scientific studies of atoms did not
begin until the 19th century. Atoms were thought of as indivisible units,
until in 1897, J. J. Thomson discovered the electron and its subatomic nature
[1]. In 1909, Ernest Rutherford conducted experiments which proved that
the positive charge and the majority of atomic mass was concentrated in a
nucleus at the center of an atom [2]. Electrons were thought to orbit around
a nucleus like planets around the Sun. The most important starting points
for the development of the quantum mechanical model of the atom were the
Max Planck’s idea of quantized energy in 1900 [3], the photoelectric effect
and the quantized energy of light discovered by Albert Einstein in 1905 [4],
and the atom model with stationary energy states proposed in 1913 by Niels
Bohr [5]. Consequently, the revolution in physics occurred during the 3-year
period from 1925 to 1928, when the foundations of quantum mechanics were
developed by a new generation of young physicists. In those years, Wolfgang
Pauli proposed the exclusion principle [6]; Werner Heisenberg, with Max Born
and Pascual Jordan, discovered matrix mechanics [7], [8]; Erwin Schrödinger
invented wave mechanics [9]; Werner Heisenberg enunciated the Uncertainty
Principle [10]; and Paul A. M. Dirac developed a relativistic wave equation
for the electron [11].
The current model of the atom is based on the quantum mechanics, and
it is usually referred to as an atomic orbital model or sometimes as a wave
mechanics model. According to this model, electrons are described by wave
functions surrounding a nucleus. Electrons are located in atomic orbitals,
which consist of a set of quantum states. The ”tools” for the ab initio calculations of atomic states were available after Hartree formulated a computational method by the year 1935 [12], but applications for multi-electron
systems were too complicated. Not until the end of 1960’s, the calculation of
complex systems was possible when the first effective codes were developed
1
2
CHAPTER 1. INTRODUCTION
for computers. It is evident, that the calculations, which in those days lasted
for months, can be done instantly with the computers of today. Now, computational efficiency is challenged by the inclusion of other interactions, like
relativistic effects and electron correlation, and the simultaneous optimization of several variables. The most striking evidence supporting the atomic
orbital model is that the computational codes which are based on this theory
predict very well measured atomic energy levels and the transitions between
them. Calculation of atomic energy levels is briefly discussed in chapter 2,
and chapter 3 specifies the electronic transitions studied in this thesis.
The studies related to electron spectroscopy started at the University of
Oulu in the late 1960’s, when an electron energy analyzer was constructed
[13], [14]. From the start, the electronic structure of vapors and gases have
been studied mainly by means of Auger electron spectroscopy, but also by
photoelectron spectroscopy and ion spectroscopy. The five articles included
in this thesis, referred to as Papers I–V, are good representations of studies
done by the electron spectroscopy group at the University of Oulu. The papers deal with electronic transitions in free xenon and krypton atoms studied
by means of Auger electron spectroscopy and ion spectroscopy. Synchrotron
radiation was used to induce inner-shell excitations, and an overview of the
experimental methods used in this thesis is given in chapter 4.
In chapter 5, the summary of Papers I–V is given. The original articles
follow chapter 5. The first study, including Papers I, II and III, deals with the
de-excitation processes following the 3d excitation in xenon. In this study, it
was demonstrated how to combine the Auger and ion spectroscopic results
in order to determine the cascade of Auger transitions. Two computational
methods, namely the method of global characteristics and the level-to-level
calculations, were used in predicting the branching ratios of ions and identifying the experimental electron spectra. Another study reported in Papers
IV and V was about the satellite Auger transitions in krypton and xenon,
in which the initial states were populated via two different channels, i.e., an
Auger cascade and a direct photo-double-ionization channel. Krypton and
xenon were compared to each other, and similarities were found between
these two gases. In all the studies, the Auger electron spectra were selected
on the grounds of their sensitiveness to electron correlation, because in this
thesis the spectra were analyzed by taking into account the many-electron
effects within the configuration-interaction treatment.
Chapter 2
Overview of theoretical
methods
In this thesis, the energy states of many-electron atoms, as well as the Auger
transition energies and rates, were computed using Cowan’s code [15, 16].
Within Cowan’s code, the energy levels of a given configuration are calculated
with the Hartree-Fock (HF) method. The Hartree-Fock method is the result
of the work done during the years 1927 to 1935 by many physicists of which
D. R. Hartree, J. C. Slater, J. A. Gaunt, and V. A. Fock were the most
prominent [17]. In the following, the HF method, the calculation of atomic
energy levels, and the configuration-interaction (CI) method are discussed
briefly. The handling is based on the books authored by Cowan [15], but
it is covered by many other books of quantum chemistry or computational
physics/chemistry (e.g. [17, 18, 19]). Electronic transitions are discussed in
chapter 3.
2.1
Hartree-Fock method
Generally, the determination of the total wave function Ψk and the energy E k
of stationary quantum state k for an atom containing N electrons (N ≥ 2)
is based on the solving of the time-independent Schrödinger equation [9]
HΨk = E k Ψk .
(2.1)
The appropriate Hamiltonian operator for the many-electron atom is
H=−
i
∇2i −
2Z
i
ri
+
2
+
ξi (ri )(li · si ),
r
j i>j ij
i
(2.2)
where ri is the distance of the ith electron from the nucleus and rij the distance
between the ith and jth electrons. The terms of equation (2.2) consists of the
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CHAPTER 2. OVERVIEW OF THEORETICAL METHODS
kinetic energy of each electron, the Coulomb interaction energy between each
electron and the nucleus, the electron-electron Coulomb interaction, and the
spin-orbit interaction, respectively. The spin-orbit interaction describes the
magnetic interaction between the electron’s spin magnetic moment and the
magnetic field that the electron sees as a result of its orbital motion through
the electric field of the nucleus. The difficulty in solving the eigenvalue
equation (2.1) arises from the Coulomb interaction between electrons and
a nucleus, as movement of a single particle is coupled with a position and
movement of all other particles. The first approximation made was to neglect
the kinetic energy of the nucleus in the Hamiltonian (2.2).
The HF method can be used in solving the Schrödinger equation (2.1)
with the Hamiltonian (2.2). The method is non-relativistic, but the relativistic corrections can be taken into account by the perturbation calculation,
when the mass-velocity and Darwin terms are included in the Hamiltonian
equation. This method is referred to as an HFR method [15]. To simplify a
solution to the Schrödinger equation, a central-field model of a multi-electron
atom is applied. According to the central-field approximation, any given electron i moves independently from the others in the electrostatic field of the
stationary nucleus and the other N − 1 electrons. Within the central-field
model, electrons are arranged around the nucleus so that every electron has
a different set of the quantum numbers nlms [6] (see table 2.1). A set of
quantum numbers nlms characterizes the stationary energy state of an electron, which is described by the wave function referred to as a one-electron
spin-orbital
1
ϕi (ri) = Pni li (r)Yli mli (θi , φi )σmsi (siz ),
(2.3)
ri
where r i is electron’s position (r, θ, φ) with respect to the nucleus and the
orientation of a spin s, Pnl is the radial wave function, Yml is the spherical
harmonic, and σms is the spin orientation symbol. The HF method assumes
that the wave function of any multi-electron atom can be approximated by
a single Slater determinant constructed by a set of spin-orbitals (2.3)
ϕ1 (r1 ) ϕ1 (r2 ) ϕ1 (r3 ) · · ·
1 ϕ2 (r1 ) ϕ2 (r2 ) ϕ2 (r3 ) · · ·
Ψb = √ ϕ (r ) ϕ (r ) ϕ (r ) · · ·
3 2
3 3
N ! 3 1
..
..
..
...
.
.
.
.
(2.4)
The Slater determinants satisfy the condition that the wave function of an
atom must be antisymmetric upon the interchange of coordinates of two
electrons.
Within the HF method, the
average energy of an arbitrary configuration
(n1 l1 )w1 (n2 l2 )w2 · · · (nq lq )wq , qi=1 wi = N , is calculated with the aid of the
2.2. ATOMIC ENERGY STATES
5
Table 2.1: Quantum numbers valid within central-field approximation
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum number
symbol
n
l
ml
ms
values
1, 2, 3, . . .
0, 1, 2, . . . , n − 1
0, ±1, ±2, . . . , ±l
±1/2
diagonal matrix elements of the Hamiltonian operator (2.2)
b Ψb |H|Ψb .
Eav =
number of basis functions
(2.5)
The matrix elements for the determinantal functions in equation (2.5) can be
written as a summation of the matrix elements for the spin-orbitals. For the
spherically averaged atom, the diagonal matrix elements of the spin-orbit
operator in (2.2) cancel each other out from the summation, because for
any specific value of ni li mli there will be two matrix elements with equal
magnitudes but opposite in signs corresponding to msi = ±1/2. Thus, the
Hamiltonian operates only to parameter r appearing only in the radial wave
function Pnl (r) of the spin-orbital (2.3). So, only the radial factor Pni li for
each q subshell of an electron configuration has to be solved in order to
determine the HF energies.
A set of q HF equations [12, 17] is derived with the aid of the Variational
principle [20]. The HF equations are of a similar form as the single-electron
Schrödinger equation, so they can be solved quite easily by the self-consistent
field method (SCF) [18]: As a starting point, approximate radial functions
Pj (r), which are typically the radial functions for the orbitals of a hydrogenic
atom, are set. With these radial functions, the potential energy and some
coefficients are computed for each i. Then, a new set of radial functions
Pi (r) is yield by solving the HF equations. This new set of radial functions
is then used as a set of trial functions Pj (r) to construct the new set of HF
equations beginning the cycle again. The procedure is stopped when the
solutions Pi (r) are self-consistent, in other words, sufficiently close to the
trial functions Pj (r) between two iterations.
2.2
Atomic energy states
In the Slater-Condon theory [20, 21], the unknown wave function Ψk of an
atom is expanded in terms of a set of known basis functions Ψb , which are
derived with the method described above. In the matrix method, a set of
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CHAPTER 2. OVERVIEW OF THEORETICAL METHODS
expansion coefficients are written in the form of a column vector Yk , and the
Schrödinger equation can be expressed as a single matrix equation
HYk = E k Yk ,
(2.6)
where the energy matrix H consists of the matrix elements of the Hamiltonian
operator between two basis functions
Hbb ≡ Ψb |H|Ψb .
(2.7)
The standard techniques are used in finding the matrix T which diagonalizes
the Hamiltonian matrix H ≡ (Hbb ):
(2.8)
T−1 HT = E k δkb .
The k th diagonal element of the diagonalized Hamiltonian matrix is the eigenvalue E k and the k th column of T represents the corresponding eigenvector
Yk of the matrix H.
The level structure relative to the average energy (2.5) of a configuration
arises from the interaction between the orbital angular momentum and spin
of each electron and from the residual Coulomb interaction between electrons
within an atom. So, the energies of atomic states can be found by calculating
the matrix elements of the spin-orbit and Coulomb interaction. The relative
magnitudes of different interactions define the coupling conditions for product wave functions which gives the form of the level structure. The relative
magnitudes of the different interactions define
the coupling scheme for how
the resultant total angular momentum J = N
i=1 (li + si ) of the atom containing N electrons (N > 1) is calculated. Generally, the stronger interaction
is coupled first followed by the other interactions in an order of decreasing
strength. The determinantal function (2.4) is already an eigenfunction of Jz
with eigenvalue
N
(mli + msi ).
(2.9)
M=
i=1
An eigenfunction of J 2 is formed by taking an appropriate linear combination
of determinantal functions: Each determinant has to involve the same set of
quantum numbers ni li , (1 ≤ i ≤ N ) but different sets of values mli and msi
so that the sum (2.9) of all magnetic quantum numbers have the same value
M for each determinant.
The LS-coupling scheme is valid especially in light atoms, in which the
spin-orbit interaction tends to be small and the electrostatic interactions
between electrons are strong. In a close approximation to pure LS-coupling,
there is no interaction between the coupled total orbital angular momentum
L and total spin angular momentum S, that results in L and S being good
quantum numbers or constants of the motion. Another important coupling
2.3. CONFIGURATION INTERACTION
7
scheme is the jj-coupling scheme, which is valid in heavy atoms. In the jjcoupling scheme, basis functions are formed by first coupling the spin of each
electron to its own orbital angular momentum, and then coupling the various
resultants ji to obtain the total angular momentum J . Since Cowan’s code
uses only LS-coupled wave functions, they are the only one discussed below.
The antisymmetrization and coupling of wave functions involve summations over different parameters so the order in which they are performed is
interchangeable. However, since the Pauli exclusion principle restricts the
possible values of mli and msi of equivalent electrons, it is more convenient
to couple first and antisymmetrize second. Coupled functions can be formed
by taking appropriate linear combinations of the uncoupled products of the
spin-orbitals ϕnlms . The coupled functions for two electrons are
C(LSML MS ; JM )
C(s1 s2 ms1 ms2 ; SMS ) ×
ψnik1 l1 n2 l2 LSJM =
ML M S
×
ms1 ms2
C(l1 l2 ml1 ml2 ; LML ) ϕ1 (ri )ϕ2 (rk ), (2.10)
ml1 ml2
where the coefficients C are known as Clebsch-Gordan (CG), vector-coupling,
or Wigner coefficients. The antisymmetric coupled basis functions are in the
LS-coupling scheme
1 ik
Ψik
ψn1 l1 n2 l2 LSJM − ψnki1 l1 n2 l2 LSJM .
n1 l1 n2 l2 LSJM = √
2
(2.11)
For the equivalent electrons, the orthonormality relations lead to that antisymmetric LS-coupled wave functions (2.11) are null if L + S is odd.
2.3
Configuration interaction
The term electron correlation refers to the interaction between the electrons
of an atom. Within the central-field approximation, the spherically symmetric potential field ignores that the positions of other electrons are correlated
by the position of the ith electron via their mutual Coulomb repulsion. However, this electron correlation plays an important role especially in orbitals
which have a prominent probability distribution spread over a wide space,
e.g., the 4s/5s orbital of Kr/Xe which interacts with the close proximity
4p/5p orbitals [22, 23]. Then, the HF energies deviate from the experimental
values significantly if the antisymmetric wave functions are approximated by
the single-configuration Slater determinants. This was demonstrated in paper III, where the single- and multi-configuration calculations were compared
with each other for the 4p−1 4d−1 and 4d−3 4f electron configurations.
In order to improve the accuracy of the wave functions of atomic energy
states, the CI method is applied. The interaction of configurations means
8
CHAPTER 2. OVERVIEW OF THEORETICAL METHODS
that the states belonging to different configurations are mixed while constructing the total wave function of an atom by taking a linear combination
of basis functions (Slater determinants) for two or more configuration. For
instance within a two-configuration approximation, the Hamiltonian matrix
for any given value of J has the form
c1
c1 − c2
H=
.
(2.12)
c2 − c1
c2
The square diagonal blocks c1 and c2 are calculated in a separate SCF calculation for each configuration, which leads to the breakdown of the orthogonality
conditions between the basis functions of different configurations. The offdiagonal blocks c1 − c2 and c2 − c1 include the configuration-interaction (CI)
matrix elements. The CI matrix elements are calculated in the same way as
the single-configuration matrix elements, except that the bra and ket functions in the expression (2.7) are the basis functions of different configurations.
If there are more than two configurations in an approximation, the energy
matrix (2.12) includes additional diagonal blocks c3 , c4 , . . . and and CI matrix element blocks c1 − c3 , c1 − c4 , . . . corresponding to single-configuration
matrix elements and interaction energies between various configurations, respectively. Within Auger transitions, CI is referred to as IISCI (initial ionic
state configuration interaction) or FISCI (final ionic state configuration interaction) when CI between initial state or final state configurations is accounted
for. In the single-configuration case, an abbreviation SC is used.
There are a few fundamental selection rules, which limit the set of configurations included in multi-configuration calculation. First, since the Hamiltonian operator (2.2) has an even parity, the CI matrix elements are zero
unless the bra and ket functions have a common parity. Thus, only the
configurations having the same parity need to be considered. Second, the
interactions can occur only between the confiurations that differ in, at most,
two orbitals because the Hamiltonian operator involves only one- and twoelectron operators. Finally, the matrix of the Coulomb operator in the LS
representation is diagonal in the quantum numbers LSJM . Therefore, in
order to obtain nonzero Coulomb CI matrix elements, each configuration
must contain a basis state with some common value of LS. In addition to
fundamental selection rules, a few qualitative remarks can be made: The
CI effects tend to be largest between configurations whose center-of-gravity
energies Eav are not greatly different and whose Coulomb matrix elements
are large in magnitude. [15]
Chapter 3
Electronic transitions
When electromagnetic radiation interacts with matter, photons can be either
scattered or absorbed. In this chapter, the photoabsorption processes which
lead to a rearrangement in the electronic core of a multi-electron atom are
considered within the frame of the production of an inner-shell vacancy and
its decay. The photoexcitation processes are approximated as dipole transitions, and the selection rules for the dipole transitions are given in section 3.1.
The most essential electronic transitions within this thesis are introduced by
using a step-by-step model consisting of at least two steps. The first step
defines a primary excitation process, which is discussed in section 3.2. After an inner-shell vacancy is produced, an atom remains in an excited state
which decays by a filling process in the course of a second-step decay. The
possible decay processes are a fluorescent emission of characteristic radiation
or a non-radiative ejection of an electron. Since fluorescence falls outside of
the scope of this study, only an electron emission by the Auger transition
is discussed. Normal Auger decay is discussed in section 3.3, the cascades
of Auger transitions in section 3.4, and satellite Auger transitions in section
3.5. In Paper II, the Auger transitions were calculated with the method of
global characteristics, which is briefly described in section 3.6.
3.1
Selection rules for dipole transition
Electromagnetic radiation consists of alternating, mutually-supporting electric and magnetic fields. The electric field experienced by target atoms is
usually approximated by the electric field of a electric dipole. The electric
dipole approximation can be assumed to be valid if the wavelength of incoming radiation is much larger than the diameter of a target atom. Electronic
transitions following photoabsorption obey then the dipole transition selection rules (3.1). During a dipole transitions, the total energy and momentum
of a photon will be transferred to a target atom, and consequently the total
angular momentum quantum number J, the total magnetic quantum number
9
CHAPTER 3. ELECTRONIC TRANSITIONS
10
MJ and the parity π of an atomic state are allowed to change as
ΔL = 0, ±1 (not from 0 to 0);
ΔJ = 0, ±1 (not from 0 to 0);
ΔS = 0;
ΔMJ = 0, ±1;
πi = −πf . (3.1)
A selection rule for one electron jump, e.g., in a resonant excitation or a
photoionization, is
Δl = ±1,
(3.2)
where l is the orbital quantum number of the transferring electron.
3.2
Transitions following photoabsorption
Resonant excitation
The resonant excitation from an electronic bound state i to another bound
state j can occur if the energy of an absorbed photon equals with the energy
difference of two states as hν = Ei − Ef . In a closed-shell atom, it is possible
for an electron to transit only to an initially non-occupied bound state, which
is usually referred to as a Rydberg state. The orbital quantum number of
an excited electron follows the selection rule (3.2). An atom (A) is left in an
excited state (A∗ ) by a resonant excitation, and a reaction equation can be
written as
A + hν → A∗ .
(3.3)
The de-excitation following the resonant excitation from the 3d5/2 inner-shell
to the 6p3/2 Rydberg orbital of Xe was studied in Paper I. The schematic
picture of the resonant excitation is displayed in figure 3.1 (a) and the possible
resonant Auger de-excitation processes are displayed in figures 3.1 (b)-(d)
(discussed in section 3.5).
Photoionization
In a photoionization, an incoming photon is absorbed by an atom (A) with
the emission of an electron p called as a photoelectron. If the photoelectron
is emitted from an inner-shell, an ion remains at an excited state (A+∗ ). The
reaction function is then
A + hν → A+∗ + p .
(3.4)
The photon energy hν must be (at least) as high as the energy difference
between the initial and final states of an atom. If the photon energy exceeds
this energy difference, the rest is left as the kinetic energy of the photoelectron
as
hν = Ef − Ei + εp .
(3.5)
The 3d photoionization is illustrated in figure 3.2 (a).
3.2. TRANSITIONS FOLLOWING PHOTOABSORPTION
Orbital energy
0
6p
5p
5s
11
7p
4d
4p
4s
3d
(a)
(b)
(c)
(d)
Figure 3.1: Schematic picture of 3d → 6p resonant electronic transitions
for Xe. (a) Inner-shell resonant excitation. Possible resonant Auger deexcitation processes are displayed in (b)–(d). (b) Participator resonant Auger
transition (autoionization), (c) spectator resonant Auger transition, and (d)
spectator resonant Auger transition with 6p → 7p monopole shake-up transition. A closed shell includes 2(2l + 1) electrons of which only two have been
depicted.
Monopole shake-up and shake-off, sudden approximation
When there is a sudden change in an atomic potential, e.g., during the ionization of an inner-shell electron, another atomic electron has a small probability
to be excited from an outer-shell to an unoccupied bound state (shake-up)
or ejected into the continuum (shake-off) via a monopole transition1 . The
shake-up states are located in the binding energies above the resonance states
and the single-ionization threshold.
The monopole shake transition probabilities can be calculated quite easily
with the sudden approximation [24]. If it is assumed that an atom has a set
of one-electron atomic orbitals {ψnl } in its ground state, after the creation of
an inner-shell n0 l0 -vacancy, the atomic orbitals of the core relax whereupon
a new set of one-electron states {ψ̃nl } describes an ion. Within the sudden
1
In the monopole transition, all the other quantum numbers except the principal quantum number are not allowed to change.
12
CHAPTER 3. ELECTRONIC TRANSITIONS
approximation, the square of the overlap integral ψ̃{n ,ε}l |ψnl 2 is the probability of a monopole excitation of the nl-electron into the states of discrete
(n l) or continuous (εl) spectra. Thus, the probability for another (outershell) electron staying in its n1 l1 state after the relaxation of the atomic core
is ψ̃n1 l1 |ψn1 l1 2 . The probability of the n1 l1 electron shaking up or off from
the ion can be expressed as [25]
Pn1 l1 = Nn1 l1 (1 − ψ̃n1 l1 |ψn1 l1 2 ),
(3.6)
where Nn1 l1 is the occupation of the n1 l1 subshell. Dipole approximation
calculations for shake transitions in the rare gases have been reported for
over the last four decades (see e.g. [26, 27] and references therein.)
Photo-double ionization
Different nominations for single-photon double-ionization transitions can be
found in the literature. While the meaning of a shake-off transition is well
defined in the framework of the sudden approximation in the asymptotic
high-energy limit [24], its meaning at finite energies is less clear and has been
the subject of debate recently (see e.g. [28] and references therein). In Papers
IV and V, the one-step double-ionization processes were referred to as direct
photo-double ionization (PDI) transitions according to the recommendation
of Briggs et al [29]. PDI describes the one-photon two-electron nature more
aptly than a double photoionization (DPI) transition which is also used in
the literature. The reaction equation for PDI can be written as
A + hν → A++ + 1p + 2p .
(3.7)
An ion is in an excited state (A++∗ ) if there is a hole in the inner-shell after
PDI. The PDI process competes with the photoionization and the shake-up
transitions with the photon energies above a certain photo-double ionization
threshold.
When a photoabsorption takes place in the outer-shell of an atom, the
change in the potential experienced by other electrons of that shell is small,
and the ejection of two valence electrons simultaneously would be expected
to be very rare. However, much larger double-ionization probabilities have
been observed than what was predicted by calculations based on the singleparticle model (see e.g. [30]-[33] and references therein), which indicates
that the electron correlation effects must be included [34]. Theoretically the
problem of the three-body Coulomb continuum is very challenging, and so
far one, universally applicable, theory does not exist [28]. The review article
written by Briggs and Schmidt [29] about helium atom summarizes rather
completely the theoretical aspects related to the PDI process. Spectroscopic
techniques which allow a simultaneous detection of two particles have been
3.3. NORMAL AUGER TRANSITIONS
13
developed, which makes it possible to study PDI experimentally (see e.g.
the electron-electron coincidence measurements in [35] and the recoil ion
momentum spectroscopic technique in [36]).
3.3
Normal Auger transitions
The one-step model of the photoabsorption and the decay is based on the
unified theory of inelastic x-ray scattering which has been developed by Åberg
et al [37, 38] in terms of the time-independent resonant scattering theory.
This gives a very general and exact description for the Auger effect, among
others. Within the two-step model, the Auger electron emission is usually
considered to be independent of the x-ray absorption process and the decay
process is not affected by the leaving photoelectron. In Papers I–V, the
photoionization is, however, considered to have an effect on the intensities of
detected Auger lines because the population of the initial states depends on
the photon energy used. Also, the other indications of the limitations of the
two-step model were seen. A part of the measured Auger lines were affected
by the post-collicion interaction (PCI) line profile, which was not taken into
account by the theory. Also, the partial Auger rates are known to depend on
the photon energy [41], which complicated the analysis in Papers IV and V.
Within the two-step model of the normal Auger transition2 , the initial
state is generated by an ionization of an inner-shell electron according to the
reaction equation (3.4). During the Auger decay, an electron from an outer
shell fills the initial vacancy while another outer-shell electron is emitted from
the ion due to the Coulombic forces, which results in a doubly ionized final
state. The reaction equation is
A+∗ → A++ + A .
(3.8)
The initial vacancy and the two final vacancies in the core or valence region
are usually labeled by the X-ray spectroscopic labels (K1 , L1,2,3 , M1,2,3 , . . .)
corresponding to the atomic orbitals (1s1/2 , 2s1/2 , 2p1/2,3/2 , 3s1/2 , 3p1/2,3/2 , . . .)
involved in the process. If the initial vacancy is filled by an electron from a
higher subshell of the same shell, i.e. the vacancy and the electron have the
same principal quantum number, the transition is referred to as a CosterKronig (CK) transition. If also the Auger electron is ejected from the same
shell, the Auger transition is referred to as a super-Coster-Kronig (SCK)
transition. In figure 3.2 (b), the initial core hole is created in the 3d subshell
whereas the final vacancies are in the 4p and 4d subshells, in which case the
Auger transition is denoted as M4,5 -N2,3 N4,5 .
2
The radiationless transitions was first discovered by L. Meitner [39] but it was named
after P. Auger who developed the Auger spectroscopy [40].
CHAPTER 3. ELECTRONIC TRANSITIONS
14
0
Orbital energy
5p
5s
4.
3.
4d
2.
4p
4s
1.
3d
(a)
(b)
(c)
(d)
Figure 3.2: Schematic picture of photoionization and subsequent decay processes. (a) 3d inner-shell photoionization. Possible de-excitation processes
are displayed in (b)–(d). (b) M4,5 -N2,3 N4,5 normal Auger transition, (c) 5p
shake-off during Auger decay and (d) cascade of Auger transitions: three consecutive steps following the 3d photoionization (a) and the first step transition
(b), which leads to the 5p−5 final configuration. Every 2(2l + 1) electrons of
closed shells have not been depicted.
By the energy conservation law, the kinetic energy of the Auger electron
EA is given by EA = Ei+ − Ef++ , where Ei+ is the total energy of the single
ionized initial state and Ef++ is the total energy of the double ionized final
state. Since the energy levels of an atom are discrete, the Auger energies are
characteristic of the emitting atom. The Auger transition rate (probability
per unit time) can be determined with the aid of the matrix elements of the
electron-electron Coulombic interaction as [42]
Wi→f
2π
=
2
1
Ψ Ψi ,
rij
(3.9)
where the wave functions for the discrete initial state Ψi and the continuum
final state Ψ is used. The Auger transitions obey the following selection
rules for quantum numbers:
ΔL = ΔS = ΔJ = 0;
πi = πf .
(3.10)
3.4. CASCADE OF AUGER TRANSITIONS
15
To obtain Jf , the quantum numbers of the continuum electron and the remaining vacancies of the ion are coupled together. Detected Auger lines are
broadened by the natural lifetime widths of initial and final states, which
originate from the uncertainty principle [7]. A lifetime of an atomic state
means that if a system was prepared in the state Ψi at a certain instant, it
would decay or become excited during the time interval (in atomic units)
τi =
1
=
,
Γi
Wi
(3.11)
where τi is a natural lifetime of that energy state, Γi is the FWHM (full
width at half maximum) of a Lorentzian line profile describing the probability
distribution as a function of energy, and Wi is the total Auger transition
probability rate of the state i.
PCI
The post-collision interaction (PCI) effect is a special form of electron correlation which involves interaction between the photoelectron and the Auger
electron. The shape of the detected photoelectron line is distorted by PCI in
the near threshold as the ionic field influences the photoelectron so that the
kinetic energy of the photoelectron is decreased. Also the detected Auger
line is distorted by PCI, and it cannot be described by a Lorentzian line
shape. The PCI energy distribution of an Auger line is asymmetric and
broadened, and the maximum is shifted towards high kinetic energies. A
slow photoelectron can even be captured into a discrete state of the residual
ion. [43]
3.4
Cascade of Auger transitions
During the Auger transition, an inner-shell hole is most probably filled by
an electron from the next highest subshells. Thus, the probabilities of the
CK and SCK transitions are usually high (see e.g. [57]). For example in
the case of the 3d excitation, the de-excitation of the primary inner-shell
vacancy leaves two vacancies most probably in the 4s, 4p, and 4d subshells,
which are filled during the subsequent Auger transitions (Papers I and II).
Consequently, the de-excitation of an inner-shell hole leads to a complicated
cascade of Auger transitions increasing the ionization stage at each step and
transferring vacancies to outer shells (illustrated in figure 3.2 (d)). Electrons
are emitted from a vast variety of configurations with spectator vacancies
left by the preceding transitions, and a cascade can continue until all the
vacancies are in the valence-shell. The charge of an ion can be very high
after the Auger cascade, e.g., the de-excitation of the 3d vacancy in Xe
CHAPTER 3. ELECTRONIC TRANSITIONS
16
b
excited state
first step
f
shake-off + Auger
second step
e
h
third step
d
i
g
c
a
ground state
A
A
+
A
2+
A
3+
Figure 3.3: Cascade of Auger transitions following excitation of atom A. A+
ions are produced via b→c,d transitions, A2+ ions via b→e,f→g transitions,
and A3+ ions are produced via b→f→h→i and b→f → i transitions. A
shake-off transition occurs during the step f→i, and two electrons are emitted
simultaneously.
ends up with the final states having the ionization stages of Xe3+ –Xe8+ .
Thus, a cascade of Auger transitions has been traditionally studied by ion
spectroscopic techniques (see e.g. [53]-[56].) The schematic illustration of
the production of multiple ionized atoms via the cascade of Auger transitions
following the excitation of an arbitrary atom is shown in figure 3.3.
Auger transitions between electron configurations with multiple holes may
be weak because the population of initial states is redistributed between numerous final states in the course of the subsequent Auger transitions. A
spectrum of low energy Auger electrons consists of many overlapping lines
from different steps of an Auger cascade (see Paper II). As it is also considered that, besides normal Auger transitions, also shake-up and multiple
shake-off transitions are possible during the de-excitation of an inner-shell
vacancy, it is evidenced that the Auger electron spectrum produced by a
cascade of Auger transitions is very complicated.
3.5. SATELLITE AUGER TRANSITIONS
3.5
17
Satellite Auger transitions
Resonant Auger transitions
The resonance excitation of an inner-shell electron leaves an atom in an
excited state, which may decay by a resonant Auger transition. In the participator resonant Auger transition, the excited electron is ejected from the
atom as an Auger electron. This transition is also called an autoionization
since it leads to the same final states as the direct photoionization process.
For example the participator resonant Auger decay shown in figure 3.1 (b)
and the direct 4p photoionization produce the same final states. Two continuum channels may interfere either destructively or constructively with each
other (see e.g. [44] and references therein).
In the spectator resonant Auger transition, the initially excited electron
does not participate in the subsequent Auger decay (figure 3.1 (c)). In that
case, a resonant Auger spectrum is usually very complicated as compared
to a normal Auger spectrum since the coupling of an electron in a Rydberg
orbital splits both initial and final states leading to numerous overlapping
resonant Auger transitions (see e.g. [45, 46]). Also shake transitions are
more probable during resonant Auger transitions. In a shake transition, the
excited electron is shaken down or up to other orbital during the Auger decay
(illustrated in figure 3.1 (d)).
Simultaneous emission of two Auger electrons
In the literature, the ejection of two electrons during an Auger decay is referred to as a double-Auger transition or a shake-off transition during the
Auger transition (illustrated in figure 3.2 (c)). The latter mentioned designation is usually used in Papers I–V. Only the total kinetic energy of two
outgoing electrons is fixed. The available energy is shared in an arbitrary
ratio by two outgoing electrons, and they show in measured Auger electron
spectrum as continuous background instead of characteristic lines. However,
the shake-off electrons can be discriminated from other sources, particularly
from background electrons, with the coincidence methods, which have been
applied effectively e.g. in [47]-[52].
Besides the measurement, also the theoretical investigation, of two-electron
emission is challenging because the process has to be described by a correlated
two-electron wave function in the continuum. In the independent electron
model (with the frozen orbitals), the emission of two electrons is forbidden.
Therefore, a shake-off during the Auger transition is usually assumed to be
a weak process. Even so, the investigations of the Auger cascades following
the inner-shell excitation have proved the shake-off processes to be essential.
For instance, only the shake-off transitions can produce the measured yield
18
CHAPTER 3. ELECTRONIC TRANSITIONS
of highly charged ions following the 3d excitation in studies [53]-[56].
3.6
Method of global characteristics
The detailed level-to-level calculations of the Auger energies and transition
rates between hundreds of overlapping electron configurations are very timedemanding because they demand a lot of manual work. The method of global
characteristics allows the determination of the configurations populated during a de-excitation process without the need to perform detailed calculations
of lines. The method estimates the average energy and variance of transitions
between two configurations using their explicit expressions [58]. The wave
functions of every configuration are taken, e.g., from the HF calculations.
The array of Auger transitions between two configurations is considered as
an integral transition with energy equal to the average one and with the
total transition rate [58, 59]. Within Auger cascade calculations, every configuration in each step is characterized by its population depending on the
de-excitation history. The intensity of an Auger transition is obtained by
multiplying the population of an initial configuration by the total transition
rate to a final configuration. The probabilities of forbidden transitions by
the energy conservation law are subtracted from the total transition rate
[60]. Also, the multi-electron Auger transitions can be taken into account in
a sudden perturbation approximation. The disadvantages of the method are
briefly discussed in Paper II.
The method was used succesfully in predicting the de-excitation pathways
following the 3d ionization of Xe as well as the configurations participating
in the Auger spectrum located at the low kinetic energy region (reported in
Paper II). The method has also been applied in the theoretical investigation
of the Auger and photoion-yield spectra resulting from the 3d photoionization
and the 3d → 4f excitation of atomic Eu [60].
Chapter 4
Experiment
4.1
Synchrotron radiation
The electronic structure of a target atom can be studied only by exciting an
atom by photon or particle bombardment. Particles can be e.g. high-kinetic
energy electrons or ions, and a primary particle can give any amount of its
kinetic energy to a target atom. This produces a large number of different excitations, which complicates resulting spectra. Instead, a target atom
absorbs the total energy of an incident photon. There are many different
devices applied as photon sources, for example X-ray tubes, which provide
the characteristic Al or Mg Kα radiation, and Helium discharge lamps, which
produce vacuum ultraviolet radiation. However, they can produce only certain wavelengths, which limits their usability. The synchrotron radiation
provides a modern way to produce photons having energies from vacuum ultraviolet to hard X-rays. Synchrotron radiation has very important spectral
characteristics such as a high brilliance and a natural collimation on the orbit
plane of the electrons [61].
Synchrotron radiation is produced when the trajectory of free electrons
moving with a relativistic speed is curved by a special magnetic device such
as a bending magnet (second-generation storage ring) or a wiggler and an
undulator (third-generation storage ring) according to the Lorentz force [61].
Wigglers and undulators consist of a periodic structure of dipole magnets. In
figure 4.1 (a), a static magnetic field is alternating along the length of an undulator with the wavelength λ0 . The electrons traversing through a periodic
magnet structure are forced to undergo oscillations and they start to emit
X-ray radiation. The illustrative figure 4.1 (b) shows a characteristic peak
structure of an undulator spectrum. Generally, undulator sources provide
increased brilliance and tunability of radiation as compared to a continuous
spectrum emitted by second-generation sources, because the most intense radiation peak can be moved to a chosen wavelength by changing a gap between
the magnetic poles of an undulator. Usually a desired, narrow energy band is
19
CHAPTER 4. EXPERIMENT
20
separated from an emitted undulator spectrum with a monochromator. The
undulator sources in two international, third-generation synchrotron radiation facility, MAX-II in Sweden and BESSY II in Germany, were used in the
experiments of Papers I-V. These beamlines are briefly described below.
(b)
Photons
(a)
Photon energy
Figure 4.1: (a) Schematic picture of the undulator’s magnetic structure and
(b) photon spectrum.
MAX-II
The MAX-II storage ring in Lund, Sweden, operates at 1.5 GeV electron
energy providing photon energies from 10 eV to 20 keV. The beamline I411
was used in Papers I, IV, and V. The beamline is equipped with an 87 pole
undulator, which gives radiation between 60 to 1500 eV. A Zeiss SX-700 plane
grating monochromator, consisting of a plane mirror and a plane grating, is
used. A more detailed description of the beamline is presented in [62]. The
I411 beamline is equipped with a hemispherical SES-200 electron energy
analyzer, which is briefly described in chapter 4.2 and more precisely in [63].
A one-meter-long section in front of the experimental station of the beamline
can host other types of setups for atomic and molecular spectroscopy, e.g., a
time-of-flight (TOF) mass spectrometer for ion spectroscopy measurements.
A special differential pumping section is applied between the last re-focusing
mirror and the sample chamber because the high vacuum of the beamline
must be separated from the working pressure of about 10−6 mbar in the
experimental chamber.
Bessy II
The Bessy II storage ring in Berlin, Germany, operates at 1.7 GeV electron
energy, and the photon energy provided is between 6 eV to 10 keV. The
undulator beamline U49-1 (undulator period λ0 = 49.4 mm with 84 periods) was used in the measurements in Papers II and III. The beamline was
equipped with a spherical grating monochromator and a refocusing mirror.
For a more detailed description of the beamline, see [64]. During the gas
4.2. ELECTRON SPECTROSCOPY
21
phase measurements, a differential pumping section was applied between the
beamline and the experimental chamber. A hemispherical SES-100 electron
energy analyzer (see chapter 4.2) was used in data collection.
4.2
Electron spectroscopy
Atomic spectra of different elements and compounds have been measured using photon absorption and emission since the late 19th century. The electron
spectroscopy technique was initiated by Kai M. Siegbahn, who was awarded
the Nobel Prize in physics in 1981, and his coworkers at the University of
Uppsala, Sweden. They published the first electron spectra in 1957 [65, 66].
The ESCA (Electron Spectroscopy for Chemical Analysis) technique proved
to be feasible in studying the properties of gases, liquids as well as solids,
and it provided a new, interesting method to study atomic and molecular
physics, cluster physics, surface physics, liquid interfaces, magnetic materials, molecular materials etc. [67, 68]. Consequently, many other research
groups all over the world also started to use and develop ESCA.
The kinetic energies of electrons emitted by a target are analyzed by
electron spectrometers. The measured electron spectrum depicts the counts
(intensity) as a function of the kinetic energy of detected electrons. Electron energy analyzers separate electrons having different kinetic energies by
magnetic or electric fields with respect to the Lorentz force. The kinetic energies between 0–2 keV are usually measured with analyzers which operate
using electric field. In the following, the effects of the electrostatic electron
spectrometers on measured electron spectra are discussed.
Dispersion, resolution and transmission of an electron
analyzer
Electron analyzers are characterized by dispersion, resolution, and transmission, which all have an influence also on the measured electron spectra. The
dispersion of an analyzer is defined by an ability to separate electrons having
different energies from each other as
∂L
,
(4.1)
∂E
where L is the projection of the flight inside an analyzer and E is the kinetic
energy of electrons. Energy resolution is usually defined by
D=E
R=
ΔE
,
EP
(4.2)
where ΔE is the FWHM of the spectrum line produced by same energetic
electrons and EP is the pass-energy (fixed through measurements to have a
22
CHAPTER 4. EXPERIMENT
constant resolution). Also the inverse of equation (4.2) is sometimes called
resolution. In this thesis, resolution has a meaning of ΔE, which gives the
separating capacity for the smallest energy difference.
During measurements, an analyzer is mounted in a certain direction, usually in 54.7◦ versus the plane of the storage ring1 . The transmission of an
analyzer is defined by a ratio between the number of detected electrons and
all emitted electrons. The transmission of the constant pass energy spectrometers varies along the measured kinetic energies due to the changing
retardation ratio of the electron optics. The transmission function T (Ek )
at a certain pass energy can be measured with the method in which the intensity ratio of a photoelectron and the corresponding normal Auger lines
is determined with the photon energies between Eb + Ekmin and Eb + Ekmax ,
where Eb is the binding energy of the photoelectron and Ekmin – Ekmax is the
desired kinetic energy region [69]. The ratio varies along the kinetic energy
region due to the transmission of a spectrometer, and, consequently, the correction curve for measured data is determined by assuming that the ratio is
independent of the photon energies. In fact, this is not valid because Auger
transition rates have been found to depend on the photon energy [41]. Evidently, the method gives good results if the intensity of the whole Auger
group is taken into account instead of only a few Auger lines.
Electron’s flight inside an analyzer depends on its kinetic energy, the
strength of the electric field as well as the angle between the entrance slit
and the electron’s trajectory. In order to detect data with sufficient statistics,
the variation of the flight and the angle must be allowed, which worsens the
resolution of an analyzer. Analyzer’s contribution to detected line profiles is
approximated with a Gaussian distribution. An ideal analyzer has a large
dispersion and small resolution values, in which case narrow analyzer line
widths are detected. In addition to the natural lifetime width of an ionic
state and the spectrometer function, the Doppler broadening and, for the
photolines only, the distribution function of the bandwidth of a light source
are also disturbing a detected line profile. A final line profile is a convolution
of all the functions, and it is usually described with a Voigt function.
SES-100 and SES-200 analyzers
The commercial hemispherical Scienta SES-100 and SES-200 electron energy
analyzers consist of an entrance lens, hemispherically-shaped metallic electrodes with the mean radius of 100 or 200 mm, and an electron detector. The
electron lens focuses incoming electrons onto the entrance aperture, and at
the same time it retards/accelerates electrons to a fixed pass energy. An ana1
The total intensity of a transition is distributed to different angles as I(θ) = Itotal [1 +
βP2 (cos θ)]. Measuring in ”magic angle” allows the detection of intensities independently
from β because P2 (cos θ) = 12 (3 cos2 θ − 1) is zero with θ = 54.7◦ ).
4.3. ION SPECTROSCOPY
23
lyzer having the spherical symmetry of electrostatic field has a so-called focus
plane, which means that electrons having a small variance of kinetic energies
are converged to different spots after deflection through the angle of 180◦ .
This enables efficient data collection with a multichannel plate (MCP), since
many slightly different energies (channels) can be separated and detected simultaneously. During the measurements reported in this thesis, the detector
systems of the SES-200 and SES-100 analyzers consisted of an MCP combined with a fluorescent screen. The intensity was recorded by monitoring
the fluorescence produced by the hitting electrons using a CCD camera.
4.3
Ion spectroscopy
Even if the electron spectroscopy method has proven to be very effective in
studying electronic properties, in several cases electron spectra are composed
of many overlapping structures which may not be resolved. These processes
can be studied by measuring ion spectra, i.e., the yield of differently charged
residual ions. As demonstrated in Papers I and II, ion spectroscopy offers
complementary methods for determinining the probabilities of different decay
channels.
TOF mass spectrometer
A TOF analyzer measures the time required for a particle to travel a fixed
distance. A TOF mass spectrometer is used to measure the distribution
of particles with respect to their mass m and charge q. A Wiley-McLaren
[71] type of linear TOF mass spectrometer used in Paper I consists of three
sections, which are a source region, an acceleration region, and a field-free
drift tube [70]. When working in a pulse-mode, the pulsed extraction field
pushes ions towards the drift tube and a time measurement starts. When
ions reach the detector, a spectrum is calculated from their time of flight.
In a TOF spectrum of a single-atomic sample, the ions having different
charges are resolved as the flight-time is dependent on a charge within the
relation
m
T ∝
.
(4.3)
q
In a partial ion yield (PIY) spectrum, the yield of ions having a given charge
stage is determined as a function of incoming photon energy. The yield
spectrum of all ions as a function of photon energy is referred to as a total
ion yield (TIY) spectrum. It can be determined either by measuring a mass
spectrum or simply detecting an ion current as a function of photon energy.
24
CHAPTER 4. EXPERIMENT
Chapter 5
Summary of included papers
5.1
Papers I–III: Multiple ionization of Xe
following 3d excitation
The de-excitation pathways and the ion production following the decay of
the 3d hole in xenon were studied in Papers I and II. Ion and electron
spectroscopies were combined successfully with theoretical calculations computed using the method of global characteristics and detailed level-to-level
calculations in order to determine the branching scheme in detail.
The de-excitation pathways of the 3d−1 initial states in Xe were selected
as a topic of our research for many reasons. Firstly, the dominance of the
spin-orbit interaction in the 3d shell of Xe allows the separation of the various excitation and decay channels originated from the 3d3/2,5/2 states, which
are not affected by IISCI. Instead, the 3d5/2 photoionization cross section
shows a second maximum some 30 eV above threshold [72], which was predicted to originate from the spin-orbit activated interchannel coupling [73].
In our studies, the 3d−1 single-configuration approximation was applied in
the calculations and the results were compared with the experiments and
the previous studies. Secondly, Xe has a closed shell electron configuration
as a ground state, so the spectral fine structures are created by the vacancies involved in the de-excitation processes. On the other hand, the complex
de-excitation pathways of the inner-shell 3d excitation consist of several consecutive steps including thousands of possible participating states, which are,
however, quite easily produced by the HF wave functions with Cowan’s code
[15]. Thus, the topic was suitable for testing the capability of the calculation
methods. Thirdly, even if there are other theoretical [74, 75] and experimental [55, 56, 76, 77] studies of the ion yields following the 3d ionization to be
compared with our results, instead, there are no previous studies for the ion
yields or the de-excitation pathways following the 3d−1
5/2 6p resonance excitation in the literature. Only the first-step resonant Auger transitions were
25
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
26
studied previously [45, 78, 79]. Fourthly, the photon energy region of the 3d
ionization threshold and above (from 650 eV to 740 eV) is within the reach
of the beamlines U49-1 at Bessy II and I411 at Max II, where opportunities
were available to carry out measurements with a good resolution and a flux
of the photon beam.
5.1.1
Partial ion yields following 3d excitation
In Paper I, the PIYs of Xen+ (n = 1 − 8) ions were measured using the
TOF mass spectrometer [70] in the photon energy range of 664–707 eV and
the branching ratios of ions were determined. The TIY spectrum depicted
in figure 5.1 was obtained by adding together the measured PIYs, which
corresponded to the absorption spectrum of Xe at the 3d threshold region
[72]. The branching ratios including the ions from all the processes following
the 3d5/2 → 6p (1 P1 ) excitation and the 3d5/2 ionization were determined.
The experimental branching ratios are depicted in figure 5.2 (a) and (b)
labeled as Exp. 1 and Exp. 2. The experimental branching ratios for the
Xen+ (n = 3−8) were found to be almost the same in the resonance excitation
and the ionization. Ions having the charge of up to 8+ were detected but the
yields of Xe4+ and Xe5+ ions were dominant in both cases.
log(Total ion yield)[*104]
10
III 3d3/2
3d5/2
9
8
7
III
3d5/2 –> 6p
6
5
4
3
2
670
680
690
700
Photon energy [eV]
Figure 5.1: TIY spectrum of Xe at the 3d threshold region. The 3d3/2,5/2
ionization thresholds, the 3d−1
5/2 6p resonance energy, and photon energies used
in Paper III are depicted with bars.
The decay of the 3d excitation leads to the cascade of Auger transitions
by transferring the vacancies to the valence shell and increasing the charge of
ions during each step. In order to solve the origin of the measured ion yields,
the kinetic energies and the transition probabilities of possible subsequent
5.1. PAPERS I–III: MULTIPLE IONIZATION OF XE
0.5
(a)
Exp.1
Calc.1
Semiemp.1
Branching ratios
0.4
27
(b)
Exp.2
Calc.2
Semiemp.2
0.3
0.2
0.1
0.0
Xe
2+
Xe
3+
Xe
4+
Xe
5+
Xe
6+
Xe
7+
Xe
8+
Xe
2+
Xe
3+
Xe
4+
Xe
5+
Xe
6+
Xe
7+
Xe
8+
Figure 5.2: Branching ratios of Xen+ (n = 2 − 8) ions following (a) the 3d5/2
ionization and (b) the 3d5/2 → 6p resonance excitation. The experimental
values Exp. 1 and Exp. 2, the results of the single-configuration calculations
Calc. 1 and Calc. 2 as well as the semi-empirical results Semiemp. 1 and
Semiemp. 2 have been given. The details of the calculated and semiempirical
values are given in Papers I and II.
configurations in the cascade of Auger transitions following the 3d ionization
and the 3d5/2 → 6p resonant excitation were calculated.
In Paper II, the branching scheme of the Auger transitions following the
3d ionization involving 130 pairs of configurations was determined by the
method of global characteristics. Such an approximative method was found
to give sufficient results for ionization. For resonance excitation, electron configurations are split into a large number of energy states by a single Rydberg
electron and configurations are overlapping in energies. Thus, the levelto-level transition energies and probabilities were computed for the Auger
cascades following the 3d5/2 → 6p resonant excitation. The monopole shakeup transition probabilities between the 6p → 7p, 8p and 7p → 8p orbitals
were calculated with the sudden approximation and the probabilities were
taken into account in a single-configuration model for the de-excitation of
the resonantly excited state. Many Auger transitions which are energetically
forbidden between the non-resonant states were found to be allowed when
the Rydberg electron generates more energy states, which are shifting towards higher binding energies and spreading out to a wider energy region.
The predicted branching ratios are presented in figure 5.2 with labels Calc.
1 and Calc. 2. The single-configuration calculations were found to underestimate the ion yield of Xe6+ , and the Xe7+ and Xe8+ states were found to be
energetically forbidden.
Obviously, multi-electron processes must be involved in calculations in
order to improve the prediction for the branching ratios of highly charged
28
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
ions. In Paper I, semiempirical branching ratios were produced by taking
into account the two most important electron correlations as follows:
1) The 5s−1 ↔ 5p−2 εl electron correlation was included by describing
10% of the 5s−1 core hole states with the 5p−2 states. Instead, electron
correlation between the 5s−1 and 5p−2 nl, (n = 5d, 6s) configurations
[80], which splits and shifts the energy levels towards higher binding
energies with respect to the single-configuration levels [81]–[83], was
neglected.
−2
2) Electron correlation of the 4p−1
1/2 and 4d εf configurations [84, 85] was
taken into account by estimating that 35% of the 4p−1 4d−1 population
transfers to the 4d−3 states via CI.
Additionally, the shake-off transition probability from the 5p orbital at the
first step of the Auger cascade following the 3d−1 ionization was estimated
to be about 10%. In Paper II, the shake-off probabilities were calculated
by using the sudden approximation, and the total shake-off probability was
found to be 6% for the first-step 3d−1 → (4s, 4p, 5s, 5p)−2 Auger transitions,
while the probabilities for the subsequent steps were even lower. In Paper I,
the 3d−1 6p → (4s, 4p, 4d, 5s, 5p)−2 shake-off transitions with the estimated
probability of 10% were included to compensate for all the possible transitions
in which the Rydberg electron leaves the ion during the cascade of Auger
transitions. Figures 5.2 (a) and (b) depict with labels Semiemp. 1 and
Semiemp. 2 the semi-empirical branching ratios which take into account the
correlations 1 and 2 as well as the shake-off transitions together with other
Auger transitions, which were found to be energetically possible in more
detailed calculations.
The semi-empirical model was found to predict the branching ratios for
the de-excitation pathways of the 3d−1 state better than the single-configuration model. The Xe6+ ion yield was still overestimated, so part of these ions
obviously further decay to produce Xe7+ and Xe8+ states. The prediction for
the ion yields at the 3d−1
5/2 6p resonance was, however, only slightly improved
by the semi-empirical model. The Xe3+ ion production was overestimated
while the yields of Xe4+ to Xe8+ ions were underestimated. In spite of the
deviation between the semi-empirical and experimental results, the electron
correlation effects were concluded to partly explain the discrepancies between
calculations and experiments. The significance of shake processes was previously (e.g. in papers [76], [77]) estimated to be very high. Electron-electron
coincidence measurements published recently by Hikosaka et al [86] revealed
a prominent intensity of the core-core PDI into Xe2+ 4d−2 states. The results confirmed that the two continuum electrons are indeed produced by the
electron correlation with the 4p−1 configuration rather than the 4d shake-off
process.
5.1. PAPERS I–III: MULTIPLE IONIZATION OF XE
29
700
680
3d
-1
-1
Paper II
Paper III
Paper V
-1
4s 4d
300
Energy relative to ground state (eV)
-3
4d
-1
4p 4d-1
250
-2
200
4d 5p-1
-1
4p
4d 5p-3
-1
5p-5
4d-2
150
-1
4d 5p-2
-1
5p-4
4d 5s-1
-1
100
4d 5p-1
4d
-1
5s-2
-1
5s 5p-1
50
-1
5s 5p-2
5p-3
5p-2
+
Xe
2+
Xe
3+
Xe
4+
Xe
5+
Xe
Figure 5.3: Average energies of the Xe configurations calculated with the HF
wavefunctions. The Auger transitions studied in detail in Papers II, III, and
V are marked with the arrows.
30
5.1.2
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
Paper III: M4,5 -NN4,5 Auger transitions
In Paper III, the M4,5 -NN4,5 Auger transitions were studied in detail. The
studied Auger transitions, displayed in figure 5.3 with dotted arrows, are
located at 320 to 550 eV. The spectrum was measured with two different
photon energies in order to separate the Auger transitions originated from
the 3d−1
3/2,5/2 initial states. The pure M5 -NN4,5 Auger spectrum was recorded
at the photon energy of 687.4 eV, and the M4,5 -NN4,5 Auger transitions were
measured at 699.3 eV. The photon energies used in Paper III and the 3d
ionization thresholds are shown in the TIY spectrum in figure 5.1.
Three line groups were resolved in the experimental spectra, and the intensity ratio of the M4,5 -N1 N4,5 , M4,5 -N2,3 N4,5 and M4,5 -N4,5 N4,5 Auger groups
was determined to be 15% : 30% : 55% with the error limit of ±2%. The
partial Auger rates were calculated by taking the wave functions from three
different calculations: the single-configuration HF, the single-configuration
Dirac-Fock and the multi-configurational Dirac-Fock (MCDF)1 . All the methods gave almost similar results, which were in good agreement with the experimental ratios. It could be concluded that, within the error limits, the
Auger transition probabilities predicted in Paper II agree well with the experiments.
Each Auger group was found to display a completely distinct behavior.
The M4,5 -N4,5 N4,5 Auger group, which was already well interpreted in other
studies [87, 88], shows a well-resolved sharp line structure. In the M4,5 N2,3 N4,5 Auger group, the sharp lines h–k and n–s shown in figure 5.4 are
followed by the broad structureless features e–g and l–m, which were found
to gain almost 50% of the total group intensity. These lines are broadened by
the subsequent SCK transitions to the 4d−3 states, which are energetically
possible only from the most uppermost energy states having binding energies
over 254.8 eV (calculated value). The Lorentzian lifetime width of 8 eV was
estimated for the broad lines while the sharp lines have the lifetime width of
about 1 eV. The SCK probability of 35% was found to be underestimated in
Paper I since almost 50% of the 4p−1 4d−1 states were now found to decay to
the 4d−3 states. The M4,5 -N1 N4,5 Auger spectrum also consists of the intense
sharp lines a–d and the following broad structure (no labels in figure 5.4).
In this case, the broad structure was found, however, to originate from the
numerous weak correlation satellites.
The M4,5 -N2,3 N4,5 and M4,5 -N1 N4,5 Auger transitions were simulated with
the aid of the calculated Auger transitions. In the level-to-level calculations
made with Cowan’s code, FISCI was taken into account with the CI treatment by allowing the following configurations to mix with each other:
1
The MCDF [89, 90] calculations for this paper and all the other papers discussed from
here forward were generated using the GRASP92 [91] code.
5.1. PAPERS I–III: MULTIPLE IONIZATION OF XE
31
(a) M5N1,2,3N4,5
k
b
i j
e
Intensity (arb. units)
a
f g
h
(b) M4,5N1,2,3N4,5
p
rs
o
cd
l
320
340
360
m n
380
400
420
Kinetic energy [eV]
440
q
460
Figure 5.4: Experimental (upper panel, markers) and simulated (lower panel,
solid line) (a) M5 N1,2,3 N4,5 and (b) M4,5 N1,2,3 N4,5 Auger spectra. The calculated Auger transitions are illustrated with vertical bars. Assignments for
the Auger transitions a–s are given in Paper III.
1◦ 4s−1 4d−1 , 4p−1 4d−2 4f , and 4d−4 4f 2 with positive parities, and
2◦ 4p−1 4d−1 , 4d−3 4f , and 4s−1 4p−1 with negative parities.
For the configuration set 1◦ , the 4s−1 4d−1 states were found to contribute to
the main lines (labeled as a–d) by about 80% while the correlation satellites
are identified by other states. The 4s−1 4p−1 configuration in configuration
set 2◦ was found to give only a marginal contribution to the predicted M4,5 N2,3 N4,5 spectrum. Instead, a prominent mixing between the 4p−1 4d−1 and
4d−3 4f configurations was observed. It could be concluded that the ratio
of group rates is not sensitive to electron correlation whereas the mixing of
configurations plays an important role in the spectral features.
5.1.3
Paper II: Interpretation of Auger cascade satellites
In Paper II, the Auger electron spectrum in the kinetic energy region of 8–40
eV was measured with the photon energies of 650 and 740 eV , which are
below and above the 3d ionization thresholds of 676.7 and 689.4 eV [92],
32
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
respectively. Measured spectra are depicted in figure 5.5 (a). Many different
Auger transitions, e.g. the N4,5 -OO Auger transitions among others, are located at the same kinetic energy region. In Paper II, only the Auger cascades
produced during the de-excitation of the 3d ionization (referred to in Paper
II as Auger cascade satellites) were studied, and they were separated from
the other structure by subtracting the Auger spectra measured at the lower
photon energy from the high energy data. The data after the subtraction is
depicted in figure 5.5 (b).
The Auger cascade satellites which have kinetic energies between 8–40 eV
were determined with calculations using the method of global characteristics.
Figure 5.5 (c) shows with the bars the calculated average energies and the
relative intensities of the Auger cascade satellites with the envelope spectrum
simulated with the aid of the calculated results. The Auger cascade satellites
located in the studied kinetic energy region were second-, third- and fourthstep transitions. The most intense satellite transitions, labeled as 2, 8, 10,
and 16 in figure 5.5 (c), respectively, are
2 4d−1 5p−3 → 5p−5 ,
8 4d−1 5p−2 → 5p−4 ,
10 4d−2 5p−1 → 4d−1 5p−3 , and
16 4d−2 → 4d−1 5p−2 .
In order to interpret the fine structure of the subtracted spectrum, the levelto-level calculations were carried out for two different paths of Auger transitions, namely
3d−1 → 4p−1 4d−1 → 4d−2 5p−1 → 4d−1 5p−3 → 5p−5 and
3d−1 → 4d−2 → 4d−1 5p−2 → 5p−4 .
The calculated Auger transitions are displayed in figure 5.3 with solid arrows.
The electron spectrum shown in figure 5.5 (d) is a sum of the calculated fine
structures of the Auger transitions 2, 8, 10 and 16 together with the envelope curve shown in figure 5.5 (c) excluding the structures 2, 8, 10 and 16.
Three line groups can be distinguished in both the experimental spectrum in
figure 5.5 (b) and the simulated spectrum in figure 5.5 (c). The calculations
underestimates slightly the intensity ratio between the second and third line
group as the ratios are 1.31 and 1.40 according to the calculations and experiments, respectively. This indicates that the calculations underestimate
the transition probabilities of the last step transitions locating at the lower
kinetic energy region. This was already comprehensively established by the
PIY measurements discussed in section 5.1.1.
5.1. PAPERS I–III: MULTIPLE IONIZATION OF XE
Intensity (arb. units)
3000
33
(a)
2000
1000
0
(b)
2000
1500
1000
500
Intensity relative to creation of one 3d hole
0
0.8
(c)
0.6
0.4
0.2
8
16
10
2
5
4 6 7
9
11
0.0
15
12 13
17
0.16
(d)
0.12
0.08
0.04
0.00
10
15
20
25
30
35
40
Kinetic energy [eV]
Figure 5.5: (a) Electron spectra measured with photon energy of 650 eV
(dashed line) and 740 eV (solid line). (b) Difference spectrum of the detected
spectra in figure (a). (c) Spectrum given by calculations with the method
of global characteristics. The vertical bars show the calculated average energies and intensities of the Auger transitions following the 3d ionization. (d)
Same as in figure (c) except that the spectra given by detailed level-to-level
calculations have been substituted for the structures 2, 8, 10, and 16.
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
34
The correspondence between the subtracted spectrum in figure 5.5 (b) and
the calculated spectrum in figure 5.5 (d) was found to be excellent especially
in the high kinetic energy region. This allowed the identification of the
main lines in the experiment in Paper II. The assignments for the 4d−2 →
4d−1 5p−2 and 4d−1 5p−2 → 5p−4 Auger transitions were later confirmed by
the measurements of Hikosaka et al [86]. They measured two Auger electrons
originated from the 4d−2 (1 D2 /1 G4 ) → 4d−1 5p−2 and 4d−1 5p−2 → 5p−4 Auger
transitions in coincidence, which allowed them to connect the initial states
to the final states.
5.2
Paper IV–V: Satellite Auger spectra
In Paper IV, the M4,5 N-NNN Auger transitions of Kr were studied in detail.
The transitions appear as a satellite structure in the M4,5 -NN Auger spectra.
The 3d−1 4l−1 (l = s, p) doubly ionized states of Kr are produced via CK decay
after the 3p ionization [93], which leads to the M2,3 -M4,5 N-NNN cascade of
Auger transitions. The M4,5 N-NNN satellite spectrum appears also when the
incident photon energy is below the 3p ionization threshold. In that case,
the doubly ionized states are produced via direct PDI from the ground state
[95]. In Paper IV, it was possible to separately investigate the PDI and
Auger cascade channels as the satellite spectra were measured both above
(at 217.6 and 280 eV) and below (at 208 eV) the 3p ionization threshold of
Kr. In figure 5.6, the calculated energy levels of Kr are shown, and arrows
labeled with channel I and II depict the PDI and Auger cascade channels,
respectively. The contribution of the Auger cascade channel in the satellite
production was determined by subtracting the satellite spectrum originated
purely from the PDI channel.
The kinetic energies and intensities of the M2,3 -M4,5 N CK and M4,5 NNNN Auger transitions of Kr were calculated by using the HF wave functions
obtained for the following configurations with the CI treatment: Double
ionized configurations were
1◦ 3d−1 4s−1 and 3d−1 4p−2 4d with positive parities and
2◦ 3d−1 4p−1 with negative parities
and the triply ionized configurations were
3◦ 4s−1 4p−2 and 4p−4 4d with positive parities and
4◦ 4s−2 4p−1 , 4s−1 4p−3 4d and 4p−3 with negative parities.
The 3p−1 configuration of Kr was found to mix with the 3d−2 5p configuration
according to the MCDF calculations, but the mixing was not as prominent as
the CI between the 4p−1 and 4d−2 4f configurations of Xe [57]. The electron
5.2. PAPER IV–V: SATELLITE AUGER SPECTRA
35
correlation related to the 3p orbital was seen to affect the M2 -M4,5 N1,2,3 CK
spectrum.
The M4,5 N-NNN satellite transitions were found to originate mainly from
the 3d−1 4p−1 states. Thus, the population of the 3d−1 4p−1 initial states
produced by PDI was estimated semiempirically. The most intense satellite
transitions were assigned with the aid of the calculations. Many new satellite
lines were identified. Especially, the M4,5 N2,3 -N1 N2,3 N2,3 satellite lines locating at the low kinetic energy region, which were neglected in the previous
studies [95, 96], were now assigned.
The studies for the satellite transitions were continued in Paper V, as the
N4,5 O-OOO satellite transitions of xenon were measured using two photon
energies of 130 eV and 150 eV which are above the 4d−1 5l−1 (l = s, p) and
4p−1 ionization thresholds, respectively. The N2,3 -N4,5 O2,3 -O2,3 O2,3 O2,3 cascade of Auger transitions is illustrated in figure 5.3 with dashed arrows. The
cascade and PDI channels were found to be important in satellite production
at the photon energies just above the 3p/4p ionization threshold both in the
Kr and Xe case.
In the case of xenon, the 4p−1 initial state is highly correlated, which
influences the N2,3 -N4,5 O CK spectrum [57, 94]. However, as according to
[94] most of the total intensity of the N2,3 -N4,5 O Auger transitions originates
from the most populated initial state. So, only the SC 4p−1
3/2 initial state was
included in our calculations. The N2,3 -N4,5 O CK transitions were calculated
by using the SC 4d−1 5p−1 configuration and by including FISCI between the
4d−1 5s−1 and 4d−1 5p−2 5d configurations. These intermediate states were also
used as initial states in the calculations for the subsequent N4,5 O-OOO Auger
transitions. The final states were constructed by the SC 5p−3 configuration
and the mixed 5s−1 5p−2 ↔ 5p−4 5d configurations. The most intense N4,5 O2,3 O2,3 O2,3 O2,3 satellite lines were assigned with the aid of the calculations, while
the N4,5 O2,3 -O1 O2,3 O2,3 transitions show only as a background overlapping
with the intense main lines. Indications that electron correlation effects are
more prominent in the 5s orbital of Xe than in the 4s orbital of Kr were
found. Our results were compared to the previous studies [95] and [98]. The
assignments for the N4,5 O2,3 -O2,3 O2,3 O2,3 satellite lines were revised from the
previous study [95], and our assignments were found to agree well with the
measurements [98].
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
36
230
3p
-1
-2
3d 5p
220
210
Ma,b
2
M3
200
channel II
Binding energy (eV)
150
-1
-1
3d 4s
-1
-2
3d 4p 4d
140
-2
130
3d 4p
-1
-1
-1
-2
-1
4s 4p
-1
-3
4s 4p 4d
120
channel I
110
100
4s 4p
-4
4p 4d
90
4p
80
70
-3
from the ground state
Kr+
Kr2+
Kr3+
Figure 5.6: Energy level diagram of Kr. Kr+ states were calculated with
the MCDF method, and Kr2+ and Kr3+ states were computed using the HF
method. The Auger transitions studied in Paper IV have been marked with
arrows.
5.3. EPILOGUE
5.3
37
Epilogue
This thesis consists of a summary and five articles which deal with the electron spectra of Xe and Kr analyzed by combining experiments with theoretical predictions. Using electron and ion spectroscopical methods and
computational tools, it has been possible to obtain new information from
structures and decay dynamics of Xe and Kr core excited states.
Most of the electronic structures studied in this thesis were well-predicted
by the pseudorelativistic HF wave functions. Still, the limitations of the
approximation were seen especially in predicting highly correlated energy
states, in which cases the use of the relativistic MCDF approximation was
needed in order to properly account for the spin-orbit interaction. However,
as the MCDF calculations are usually time-consuming and may encounter
convergence problems, multi-configurational HF calculations are more suitable when energy states of dozens or hundreds of electron configurations must
be computed.
The efficiency of the multicoincidence technique in separating the different decay processes, in which many electrons are ejected simultaneously,
was demonstrated recently for various atoms and molecules [35, 86, 97]. By
analyzing conventional Auger electron spectra, information about transition
energies and probabilities is obtained. However, a direct observation of multiple ionizations or transitions in which many electrons are emitted during
the Auger decay is impossible. Instead, they can be studied indirectly by
measuring their decay spectra, like it was done in this thesis.
38
CHAPTER 5. SUMMARY OF INCLUDED PAPERS
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