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 and Siegbahn notation, as opposed to the spectroscopic notation (1s, 2s, 2p, 3s, 3p, 4s, 3d, ... ) used in most areas of chemistry.

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 combinatation 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
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$