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, Failed to parse (unknown function "\sfrac"): {\displaystyle m_s=\pm\sfrac{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
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$

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 notation.

Siegbahn notation is extremely common for describing radiation sources—for example, the vast majority of X-ray characterization systems use a Cu K$\alpha$ 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.

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