X-ray Notation

In X-ray spectroscopy and other X-ray characterization techniques, a special form of notation is used to indicate atomic orbitals and the movement of electrons between discrete energy levels when interacting with X-ray radiation. This nomenclature is known as X-ray notation, as opposed to the spectroscopic notation (1s, 2s, 2p, 3s, 3p, 4s, 3d, …) used in most areas of chemistry. Additionally, Siegbahn notation is used to indicate characteristic emission lines, most commonly during in XRF/XES and EDS.

About X-ray & Spectroscopic Notation

Spectroscopic notation is based off an electron's quantum numbers—in chemistry, 4 quantum numbers can uniquely identify any electron.

• $n$ : principle quantum number, corresponds to s/p/d/f orbitals
• $\ell$ : orbital angular momentum (azimuthal) quantum number
• $m_{\ell }$ : magnetic quantum number
• $m_{s}$ : internal angular momentum (spin) quantum number, $m_{s}=\pm {\frac {1}{2}}$

However, another quantum number is commonly used in quantum mechanics to properly account for spin-orbit coupling effects:

• $j$ : total angular momentum quantum number, $j=\ell +m_{s}$

X-ray notation translates the principle quantum number $n$ into a capital letter, and each combination of $\ell$ and $j$ into a number.

Notation Translation

Quantum numbers			Spectroscopic notation	X-ray notation
$n$	$\ell$	$j$
1	0	1/2	1s	K (K1)
2	0	1/2	2s	L1
	1	1/2	2p1/2	L2
		3/2	2p3/2	L3
3	0	1/2	3s	M1
	1	1/2	3p1/2	M2
		3/2	3p3/2	M3
	2	3/2	3d3/2	M4
		5/2	3d5/2	M5
4	0	1/2	4s	N1
	1	1/2	4p1/2	N2
		3/2	4p3/2	N3
	2	3/2	4d3/2	N4
		5/2	4d5/2	N5
	3	5/2	4f5/2	N6
		7/2	4f7/2	N7
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$

Use in XPS and XAS

Databases use X-ray notation when describing each electron’s specific binding energy. In X-ray photoelectron spectroscopy (XPS), peaks can be labeled with the corresponding ejected electron’s energy level (e.g. Sample B showed a shift in platinum’s N₆ and N₇ peaks). For X-ray absorption spectroscopy (XAS), jumps in absorption correspond to a new electron level being able to “absorb” a specific source energy. These jumps are considered edges of electron levels, and can also be labeled using X-ray notation (e.g. L₂ edge).

Siegbahn & IUPAC Notation

In many X-ray spectroscopy techniques, source radiation is used to generate an electron vacancy, which must then be quenched by an electron of higher energy. This quenching releases a discrete amount of energy for each element—the notation used to describe which energy levels produced this corresponding energy release is represented using either Siegbahn or IUPAC (International Union of Pure and Applied Chemistry) notation.

Siegbahn notation is extremely common for describing radiation sources—for example, the vast majority of X-ray characterization systems use a Cu Kα source ($\lambda =1.5406\mathrm {\AA}$). However, note that Siegbahn notation is irregularly labeled because emission lines were named in order of discovery—for this reason, IUPAC notation may be preferred. IUPAC notation simply lists the vacancy being quenched, followed by which electron quenced it (with a dash inbetween). Siegbahn always lists the vacancy level first, but the latter Greek letter and number have an insignificant correlation between the emission line described.

Notation of Common Emission Lines

Electron movement	Siegbahn notation	IUPAC notation
L3 $\rightarrow$ K	Kα1	K-L3
L2 $\rightarrow$ K	Kα2	K-L2
M3 $\rightarrow$ K	Kβ1	K-M3
M5 $\rightarrow$ L3	Lα1	L3-M5
M4 $\rightarrow$ L2	Lβ1	L2-M4
N7 $\rightarrow$ M5	Mα1	M5-N7

Auger Notation for AES

Since the Auger electron in AES comes from a third energy level, a separate convention is used. Auger notation lists the vacancy first, then the quenching and Auger electron, in no particular order (KL₂L₃ and KL₃L₂ are the same). This is because the detector cannot differentiate which electron quenches the vacancy versus the Auger (third) electron that it detects. Families of AES emissions simply list the X-ray notation letter for each electron, which corresponds to the principal quantum number (e.g. KLL or LMM).