Nomenclature of X-ray transitions-Siegbahn Notation A colleague wanted to understand the notation for X-ray transitions. The main query is about the labeling of alpha, beta and gamma, with K, L, M etc. What is the main distinguishing criterion to label a transition as K, L, M along with the Greek letters alpha, beta and gamma. One of the websites she found said that alpha refers to "one shell" difference i.e., L to K or M to L, beta refers to dropping to two shells, i.e., M to K. However, as in this diagram, taken from Arthur Compton's book on X-rays, N to K transitions are also labeled as beta.
I have checked many resources including the original paper in Nature from Siegbahn, which turned out to a single column paper. Didn't find a clear cut explanation when should we use alpha, beta and gamma. Additionally, what is the rule for associating a number with the Greek letter. Thanks.

 A: It is based on intensity: K$_\alpha$ is the strongest line, K$_\beta$ the second strongest, K$_\gamma$ the third strongest. Yes, in this case it is from the next higher shell (from $2p$, $3p$, $4p$ etcetera).
For L$_\alpha$ and L$_\beta$, again L$_\alpha$ is the stronger one, but the intensities are more similar than between the two strongest K lines. And both of these are transitions from $3d$ orbitals to $2p$. The difference is due to spin-orbit coupling between $2p_{1/2}$ and $2p_{3/2}$. And the much weaker third line L$_\gamma$ is due to transitions to a $2s$ hole. Manne Siegbahn could not know this in 1916.
So there is no physics in the Greek subscripts of these two series (or of the M series). The nomenclature was purely phenomenological.
I notice that you want a source. This should be authoritative:

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.

R. Jenkins, R. Manne, R. Robin and C. Senemaud,  Nomenclature system for X-ray spectroscopy, Pure & Appl. Chem., 63 (5), 735-746, 1991
