Part VIII. Nomenclature system for X-ray spectroscopy ...

Part VIII. Nomenclature system for X-ray spectroscopy
(Recommendations 1991 )
(Originally prepared for publication by R. Jenkins, R. Manne, R. Robin and C. Senemaud)
1.
INTRODUCTION
This document is the eighth in a series on the nomenclature for spectrochemical analysis issued
by IUPAC. Part IV is concerned with spectroscopy in the X-ray region and deals with the
nomenclature, symbols and units related to X-ray emission spectroscopy and its application to
quantitative analysis. No particular attention to the nomenclature of X-ray spectra was given in
that document. This is instead the topic of the present document.
The nomenclature used for X-ray emission spectra was introduced by M. Siegbahn in the 1920's
and is based upon the relative intensity of lines from different series. It gives no information about
the origin of these lines. Since it was introduced, a number of lines have been observed which
have not been classified within the Siegbahn nomenclature, particularly for the M and N series.
Another problem is that its unsystematic nature makes the nomenclature difficult to learn. Many
spectroscopists agree upon the need for a new and more systematic nomenclature for X-ray
emission spectra. The aim of this document is therefore to present a new notation for X-ray
emission lines and absorption edges to be called the IUPAC Notation. Surveys among X-ray
spectroscopists have indicated a desire to have the existing Siegbahn nomenclature replaced by a
system based upon the energy-level designation. This IUPAC X-ray nomenclature has the
advantage of being simple and easy to extend to any kind of transitions. It is consistent with the
notation used in electron spectroscopy and is closely related to that of Auger electron
spectroscopy.
The present document, in addition, gives units and conversion factors for X-ray wavelengths and
energies.
2.
TERMS CURRENTLY USED TO DESCRIBE X-RAY SPECTRA
2.1 X-ray radiation
X-ray radiation may result from the interaction of high energy particles or photons with matter.
Bremsstrahlung is the name given to the radiation emitted as a result of the retardation of high-
energy particles by matter. Synchrotron radiation results from the acceleration of charged
particles in circular orbits by strong electric and magnetic fields. Bremsstrahlung and synchrotron
radiation are used in X-ray spectroscopy as sources of continuous X-ray radiation.
Characteristic X-ray emission originates from the radiative decay of electronically highly excited
states of matter. Excitation may be by electrons often called primary excitations by photons,
called secondary or fluorescence excitation or by heavier particles such as protons, deuterons, or
heavy atoms in varying-degrees of ionization. The emission in the latter case is called article-
induced X-ray emission (PIXE).
Emission of photons in the X-ray wavelength region also occurs from ionized gases or plasmas at
high temperatures, from nuclear processes (low-energy end of the gamma-ray spectrum), and
from radiative transitions between muonic states. In the following we will be concerned primarily
with characteristic X-ray emission following electron or photon excitation.

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Alternatively, electronically highly excited states may decay by radiation-less transitions leading
to the ejection of additional electrons. Specific types of radiation-less transitions are known as
Auger and Coster-Kronig transitions. The fluorescence yield is the probability that the decay of
the excited state takes place with the emission of a photon.
2.2 X-ray levels
The electronic states occurring as initial and final states of a process involving the absorption or
emission of X-ray radiation are called X-ray levels. This term is used here with the same meaning
as in the description of many-electronic states in atomic spectroscopy, i.e. as part of the
conceptual hierarchy, configuration, term and level. It represents a many-electron state which, in
the purely atomic case, has total angular momentum (J = L+S) as a well-defined quantum
number. The word term in atomic spectroscopy denotes a set of levels which have the same
electron configuration and the same value of the quantum numbers for total spin S and total
orbital angular momentum L.
Normal X-ray levels or diagram levels are described by the removal of one electron from the
configuration of the neutral ground state. These levels form a spectrum similar to that of a one-
electron or hydrogen-like atom but, being single-vacancy levels, have the energy-scale reversed
relative to that of single-electron levels. Diagram levels may be divided into valence levels and
core levels according to the nature of the electron vacancy.
Diagram levels with orbital angular momentum different from zero occur in pairs and form spin
doublets. In the nomenclature of atomic spectroscopy they belong both to the same configuration
and the same term.
X-ray levels have various degrees of ionization – single, double or higher – and may in some
cases also be electrically neutral. An excitation level also called exciton is an electrically neutral
X-ray level with an expelled electron bound in the field of a core electron vacancy. Such levels
may give rise to the Rydberg series.
Multiply ionized and excited levels may be produced by many-electron processes often called
electron relaxation processes and which leads to electron shake-off or secondary ionization.
Electron relaxation also produces electron shake-up, i.e. states with a core hole and excited
valence-electron configuration. Other mechanisms leading to multiply ionized states include
Auger and Coster-Kronig transitions. In collisions with heavy particles as in PIXE, multiply
ionized states often dominate over the singly ionized diagram states.
The energy of X-ray levels of atoms and molecules in the gas phase is usually given relative to
that of the neutral ground state; for solids it is usually given relative to the Fermi level. In the
latter case, level energies are often referred to as electron binding energies. The problem of
defining the reference level in insulating solids is non-trivial.
2.3 Selection rules
X-ray emission and absorption follow the selection rules for emission and absorption of
electromagnetic radiation. These are the electric dipole selection rules leading to most intense
lines, the magnetic dipole and the electric quadrupole selection rules attributed to certain weak
features in X-ray emission spectra. Lines forbidden according to the electric dipole selection rules
are sometimes called multipole lines or forbidden lines. The use of the latter term is discouraged.
2.4 X-ray absorption
An X-ray absorption spectrum observed at low resolution consists of one or several absorption
continua terminated at their low energy by absorption edges or limits below which the
photoabsorption coefficient is significantly lower. The absorption limit represents the minimum

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energy required to excite an electron from a given one-electron state. The nature of the absorption
limits varies with the nature of the system investigated. In some gases and in insulators it
represents a transition to an excitation level, while in metals it represents the transition to the
bottom of the conduction energy band.
The position of absorption limits and continua relative to the X-ray emission spectrum is of
importance for analytical applications of X-ray spectroscopy due to the process of self-absorption.
Maxima in the absorption spectrum may be due to the presence of excitation levels as mentioned
above. They may also be caused by shape resonances or by many-electron interaction resulting
from electron-relaxation or "shake" effects. Structure in X-ray absorption spectra remote from the
edge and extending to higher energies is called extended X-ray absorption fine structure
(EXAFS). It is due mainly to the scattering of the expelled electron by neighbouring atoms and is
not covered by the present nomenclature. Structure closer to the absorption edge is sometimes
called near-edge X-ray absorption fine structure (NEXAFS).
2.5 X-ray emission
The characteristic X-ray emission consists of series of X-ray spectral lines with discrete
frequencies, characteristic of the emitting atom. Other features are emission bands from
transitions to valence levels. In a spectrum obtained with electron or photon excitation the most
intense lines are called diagram lines or normal X-ray lines. They are dipole-allowed transitions
between normal X-ray diagram levels.
The radiative decay of an excitation level may proceed to the neutral ground state and would thus
occur at the same energy as the corresponding line in the absorption spectrum. Such a line is
called a resonance line and the process is called resonance emission.
An X-ray satellite line is a weak line in the same energy region as a normal X-ray line. Another
name used for weak features is non-diagram line. Recommendations as to the use of these two
terms have conflicted. With the term diagram line defined as above the term non-diagram line
may well be used for all lines with a different origin. The majority of these lines originate from
the dipole-allowed de-excitation of multiply ionized or excited states, and are called multiple-
ionization satellites. A line where the initial state has two vacancies in the same shell, notably the
K-shell, is called a hypersatellite. Other mechanisms leading to weak spectral features in X-ray
emission are, e.g., resonance emission, the radiative Auger effect, magnetic dipole and electric
quadrupole transitions and, in metals, plasmon excitation. Atoms with open electron shells, i.e.
transition metals, lanthanides, and actinides, show a splitting of certain X-ray lines due to the
electron interaction involving this open shell. Structures originating in all these ways as well as
structures in the valence band of molecules and solid chemical compounds have in the past been
given satellite designations.
In PIXE multiple-ionization lines often have greater intensity than diagram lines. In such a case
the designation of the former as satellites is obviously out of place.
The multitude of mechanisms collected under the term satellite and the intensity ambiguities
observed in PIXE make the unqualified use of the satellites concept meaningless except as a
temporary measure. If the origin of a weak line or structure is known, it should be named after
that origin and not as a satellite.
3.
PRINCIPLES OF THE IUPAC NOTATION
3.1 X-ray levels

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X-ray levels are defined as those states which occur as initial and/or final states in X-ray
transitions. Diagram levels are those which can be described by the removal of one electron from
a closed-shell electron configuration. Table 1 shows the relation between X-ray diagram levels
and electron configurations. Note that the level notation is used for many electron systems with
vacancies, not for the electrons removed from these systems. This usage conforms with common
principles of spectroscopy but differs from that of, e.g. solid-state physics which uses a one-
electron description with the energy level ordering reversed relative to that of spectroscopic
conventions. Fig. la shows schematically the ordering of X-ray levels. Fig. 1b shows the ordering
of one-electron levels. It is recommended that one electron levels are denoted by the orbital
notation (1s, 2s, 2p1/2 etc.). The importance of separating the two kinds of notation will be further
exemplified in Sect. 3.2 (Compare also L. G. Parratt, Rev. Mod. Phys. 31, 616 (1959)).
The X-ray level notation follows earlier conventions except for a minor point. The IUPAC
notation prescribes Arabic numerals for subscripts. This agrees with common usage, e.g., in
Auger electron spectroscopy, but differs from the original notation which used Roman numerals
(LII and LIII, instead of L2 and L3)
The subscripts may be dropped when they are unknown or irrelevant. When the spin-orbit
interaction is unresolved one may write, e.g. L2,3 for a state with a 2p vacancy.
The atomic description is not valid for the outermost valence electrons in molecules and solids
where chemical interactions and/or solid-state effects are important. States with a valence-electron
vacancy are denoted by V.
States with double or multiple vacancies should be denoted by:
K2
1s-2
KL1
1s-1 2s-1
Ln2,3 2p-n
Due to electron interaction this notation does not in general give a complete description of the
level structure. When desired one may therefore add the electronic term symbol of atomic or
molecular spectroscopy in parenthesis after the level symbol, e.g. KLl (1S) or KLl (3S).
So far, the X-ray level nomenclature has not had a symbol for the neutral ground state nor for
states with electrons in orbitals which are empty in the neutral ground state. The IUPAC Notation
recommends the notation X for the neutral electronic ground state. This convention is close to that
used for molecular electronic spectra.
There is no precedent for the notation for X-ray levels with electrons in normally empty orbitals
or bands. IUPAC recommends the use of the letter C (or C*) to denote a state with an electron
added in an orbital or band which is empty in the neutral ground state. In X-ray emission this
letter will only occur in combinations with letters denoting vacancies, e.g. for a diatomic molecule
: KC(1π) meaning the state with a K-shell electron promoted to an empty orbital resulting in a
quasi-bound state of π symmetry. Alternatively, one may write KC*(1π). The superscript * is
optional and is intended to separate the neutral KC* state from, e.g., a double ionized state KL1.
3.2 X-ray transitions
As the main rule, transitions between X-ray levels are denoted by the level symbols for initial and
final state separated by a hyphen. The initial state is placed first, irrespective of the energetic
ordering. As explained in Sec. 3.1. The X-ray level notation conforms with a many-electron
description of electronic structure. The notation for transitions will therefore frequently differ
from that obtained from an "active electron" or one-electron approach. See further below.

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Table VIII.1. Correspondence between X-ray diagram levels and electron configuration
electron
electron
electron
level
Configuration
level
Configuration
level
Configuration
K
1s-1
N1
4s-1
O1
5s-1
L
-1
-1
1
2s-1
N2
4p1/2
O2
5p1/2
L
-1
-1
-1
2
2p1/2
N3
4p3/2
O3
5p3/2
L
-1
-1
-1
3
2p3/2
N4
4d3/2
O4
5d3/2
M
-1
-1
1
3s-1
N5
4d5/2
O5
5d5/2
M
-1
-1
-1
2
3p1/2
N6
4f5/2
O6
5f5/2
M
-1
-1
-1
3
3p3/2
N7
4f7/2
O7
5f7/2
M
-1
4
3d3/2
M
-1
5
3d5/2
KL2,3
K
KC*
Valence
band
2p3/2
L1
2p1/2
L22,3
K-V
L2
L3
2s
K-L2,3
V
X
1s
Figure VIII.1a. A schematic X-ray level diagram. Non-diagram levels and transitions are
indicated by dashed lines. (Not drawn to scale).
Figure VIII.1b. The corresponding one-electron energy level diagram with diagram transitions
indicated.

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3.2.1 X-ray absorption
X-ray absorption takes place from the neutral ground state to excited states with an inner vacancy.
The ejected electron may go into either a bound-state or a continuum orbital. When the ejected
electron is not considered the corresponding symbol is omitted.
Examples:
X-K
ejected electron not considered
X-KC or
X-KC*
ejected electron bound
In the "active electron" picture the X-KC (X-KC*) transition might be denoted 1s ––> np. The
difference between this picture and the IUPAC Notation has to be kept in mind.
X-ray absorption edges can also be denoted by the word "abs" in front of the final-state level. X-
K and abs K are thus synonymous.
3.2.2 X-ray emission
When possible the main rules are followed. X-ray emission diagram lines are written with the
initial and final X-ray levels separated by a hyphen. The hyphen is essential in order to avoid
confusion with double-hole levels. As examples we quote
K-L3 (Kα1 in the Siegbahn notation) denotes the filling of a 1s hole by a 2P3/2 electron, i.e. in
the "active electron" picture 2P3/2 ––> 1s.
K-V (for elements and compounds of Na to Cl previously denoted by Kβ1, Kβ', Kβ" etc.)
denotes the filling of a 1s hole by an electron from the valence shell.
The correspondence between Siegbahn and IUPAC Notation is given in Sect.4.
3.2.3 Special notation for X-ray emission satellites
The principles laid down for X-ray levels, Sect. 3.1 and X-ray emission lines, Sect. 3.2.2. should
also be followed when the states involved are not X-ray diagram levels. Since the Siegbahn
nomenclature applies also to lines which do not have level designations. It was originally desired
that the IUPAC nomenclature should contain special rules for this purpose. Such a set of rules
creates several problems which are best exemplified by considering K~ high-energy satellites for
which the level assignments are known. The Siegbahn system contains satellite lines named from
Kα3 to Kα11 in addition to lines named Kα', Kα", Kα'3, Kα"3 etc.
Theory predicts many more lines than are seen experimentally. Some lines are unresolved only in
certain elements, and some lines are ordered differently in different elements. Although the level
notation is cumbersome for satellites, particularly if it is written out in full, any simple descriptive
system would soon acquire the same deficiencies as the present Siegbahn notation. Such a system
would serve a purpose only if (i) the information required for the level notation is not available
and (ii) there is no previous name in the Siegbahn nomenclature. For this limited case the
following naming procedure has been proposed :
Satellites of obscure origin are labeled according to the closest structure which has already been
given a level designation. In the following this structure is referred to as the main line. It may very
well be a non-diagram line. The level designation of the main line is preceded by Satn where n is
an integer or decimal number. The number n is assigned after the following rules :
1. Integer numbers are assigned in order according to the energetic separation from the main
line.

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2. Positive numbers are given to high-energy structures, negative numbers to low-energy
structures.
3. Previous assignments for the same type of spectra take precedence.
4. In the case where additional assignments have to be made to this system, decimal numbers
may be used.
This system has disadvantages and at present, it is unlikely to be widely applied. Empirical
investigations of satellite structure without simultaneous level assignments are seldom performed
today. A need for this kind of system would appear, however, when structures without level
assignments interfere in analytical applications of X-ray emission spectro-scopy .
3.3 Auger electron emission
The ordinary Auger electron emission process may be viewed as a radiation-less decay of a singly
ionized X-ray level into a level described by two vacancies and one electron in the continuum.
Disregarding the continuum, Auger electron emission is thus a transition from a singly to a
doubly ionized X-ray level. The conventional notation for Auger emission lines and bands is
based upon this concept and the level notation of Sect. 3.1. In order to conform with the present
IUPAC Notation of X-ray spectra the hyphen separating initial and final-state levels should be
introduced also into the Auger electron notation. IUPAC thus recommends writing, e.g., K–
L1L2,3 instead of KL1L2,3
3.4 Photoelectron spectroscopy
The IUPAC X-ray notation can be extended easily to photoelectron spectroscopy. Since the
physical process is the same, and the difference from X-ray absorption lies in the recording
process, one would thus obtain the same nomenclature as for X-ray absorption with the expelled
electron disregarded, e.g. X-K. The current practice is to denote photoelectron lines by either the
final-state level or by the orbital notation, i.e. K or 1s. There is no risk of confusion with this
practice and there is not need for changes in this area.

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4.
CORRESPONDENCE BETWEEN THE SIEGBAHN AND IUPAC NOTATIONS
The IUPAC Notation is compared with the Siegbahn notation in the following table.
Table VIII.2. Correspondence between Siegbahn and IUPAC notation diagram lines
Siegbahn
IUPAC
Siegbahn
IUPAC
Siegbahn
IUPAC
Siegbahn
IUPAC
Kα1
K-L3
Lα1
L3-M5
Lγ1
L2-N4
Mα1
M5-N7
Kα2
K-L2
Lα2
L3-M4
Lγ2
L1-N2
Mα2
M5-N6
Kβ1
K-M3
Lβ1
L2-M4
Lγ3
L1-N3
Mβ
M4-N6
KIβ2
K-N3
Lβ2
L3-N5
Lγ4
L1-O3
Mγ
M3-N5
KIIβ
'
2
K-N2
Lβ3
L1-M3
Lγ4
L1-O2
Mζ
M4,5-N2,3
Kβ3
K-M2
Lβ4
L1-M2
Lγ5
L2-N1
KIβ4
K-N5
Lβ5
L3-O4,5
Lγ6
L2-O4
KIIβ4
K-N4
Lβ6
L3-N1
Lγ8
L2-O1
Kβ
'
4x
K-N4
Lβ7
L3-O1
Lγ8
L2-N6(7)
KIβ
'
5
K-M5
Lβ7
L3-N6,7
Lη
L2-M1
KIIβ5
K-M4
Lβ9
L1-M5
Ll
L3-M1
Lβ10
L1-M4
Ls
L3-M3
Lβ15
L3-N4
Lt
L3-M2
Lβ17
L2-M3
Lu
L3-N6,7
Lv
L2-N6(7)
In the case of unresolved lines, such as K-L2 and K-L3, the recommended IUPAC notation is K-
L2,3
5.
UNITS AND CONVERSION FACTORS
5.1 Units
The SI units for X-ray wavelengths are the nanometre (nm) and the picometre (pm) with 1 nm =
10-9 m and 1 pm = 10-12 m. However, the commonly used metric unit for X-ray wavelengths is
the angstrom with 1 Å =10-10 m. Siegbahn introduced the X-unit in 1919, and it soon became the
practical unit for X-ray wavelengths. It was chosen as 10 Å but was implicitly defined from the
value 3029.04 Xu for the lattice constant of crystalline calcite at 18°C. This definition however
turned out to be insufficient since relative measurements of X-ray wavelengths could be made
with higher precision than absolute determinations and since lattice constants may differ between
different samples of the same crystal. For this reason X-ray spectra were calibrated against X-ray
emission lines which had been determined with high precision. Two such lines were used, Cu K-
L3 (Kα1) with the wavelength λ = 1537.400 Xu (Ref. 1) and Mo K-L3 (Kα1) with λ = 707.831
Xu ( Ref. 2). After investigating several lines as possible wavelength standards, Bearden in 1965
defined a new practical angstrom unit for X-ray wavelengths written Å* from A = 0.2090100 Å*
for W K-L3 emission (Ref.3). Recent high-precision determinations of the X-ray wavelength scale
have made both the X-unit and the Å* obsolete (Ref. 4). The use of Å* is discouraged.

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5.2 Conversion factors
Conversion factors between X-units and Å* on the one hand and metric units on the other have
been obtained from accurate measurements of X-ray wavelengths in terms of optical standards.
The most accurate results currently available are from the U.S. National Bureau of Standards
(Ref. 4), namely
Lines
λ/Å
Standard deviation
Cu K-L3
1.5405974
0.0000015
Mo K-L3
0.7093184
0.0000004
W
K-L3
0.20901349
0.00000019
The combination of these values with those used to define the Xu and Å* scales gives the
following conversion factors:
In the X-ray scale for which λ (Cu K-L3) = 1.5374000 kXu
Λ = 1.0020797(10) Å/kXu = 100.20797(10) pm/kXu
In the X-ray scale for which λ (Mo K-L3) = 0.707831 kXu
Λ = 1.0021013(6) Å/kXu = 100.21013(6) pm/kXu
The conversion factor from the Å* emerges as
Λ* = 1.0000167(9) Å/Å* = 100.00167(9) pm/Å*
The numbers in parenthesis are the standard deviations in the last digits of the quoted values.
According to the 1973 least-squares adjustment of fundamental constants (Ref. 5) the energy
wavelength conversion factor is
hc = 1.2398520(32) x 10-6 eV m = 1.986447461 x l0-25 J m.
The error given here is the standard-deviation uncertainty computed on the basis of internal
consistency.
REFERENCES
1.
J.A. Bearden and C.H. Shaw, Phys. Rev. 48, 18 (1935)
2.
A. Larsson, Philos. Mag. 3, 1136 (1927)
3.
J.A. Bearden, Phys. Rev. 137, B455 (1965)
4.
E.G. Kessler, R.D. Deslattes, and A. Henins, Phys. Rev. A 19, 215 (1979)
5.
B.N. Taylor and E.R. Cohen, J. Phys. Chem. Ref. Data 2, 663 (1973)

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