Siegbahn-IUPAC conversion

[Brian Joy]

During the recent discussion of Ti K X-ray lines, I found myself getting confused as to which electronic transitions produced the Kβ₁, Kβ₂, Kβ₃, Kβ₄, and Kβ₅ X-ray lines.  (Note that the ground state electronic configuration of Ti is [Ar]3d²4s².)  So I’ve put together a table that shows the various transitions along with the Siegbahn notation for the X-ray line that represents the energy lost in the transition (e.g., Kβ_1,3 [Siegbahn] = K-M_2,3 [IUPAC]).  The table below is attached as a Word file as well.

Could I get some feedback on this table?  In particular, I’m a little confused on the transitions that produce the Mζ₁ and Mζ₂ X-rays.  For instance, according to IUPAC, Mζ = M_4,5-N_2,3 with no distinction between Mζ₁ and Mζ₂ (though these lines are in fact EPMA resolvable).

[Brian Joy]

The table as shown is consistent with the tabulation of Bearden (1967), which I've attached.

EDIT:  I found a few discrepancies.  According to Bearden (1967), Siegbahn and IUPAC notation correlate as such:
Kβ₄ = K-N_4,5
Lγ₄ = L₁-O₃
Lγ₄' = L₁-O₂
Lγ₁₁ = L₁-N₅
Lv = L₂-N₆

[xllovet]

Hi Brian,

According to the Handbook of X-ray Data (Zschornack, Springer Verlag, 2007), the Mζ2 line would correspond to the M4-N2 transition (not the M5-N2 transition). I've attached the M-lines of Uranium listed in this book - it's clear that in this case the IUPAC notation is much better!

Hope this helps,
Xavier

[Brian Joy]

Hi Xavier,

Thanks for pointing that out -- I've modified the table so that it's consistent with Zschornack (2007).  I've extended it to include Lγ₁₃ = L₁-P_2,3.

Brian

[JonF]

A good table - I kept getting lost during the Ti X-ray discussion too!

It might be a good idea to blank out the forbidden transitions for clarity (e.g. K-L1), although that does lead on to the even more confusing discussion of how we get Li and Be Ka X-rays.

I've always been under the impression that the Siegbahn notation was derived from the relative intensity(/probability) of a particular transition (e.g. the Ka1 is the brightest), rather than a fixed transition from one shell to another. This is probably insignificant for core-core transitions, but as we look more at those valence-to-core transitions (e.g. light elements, L/M lines etc), does the Siegbahn notation switch between different lines of varying probability? Or do we just use more and more complicated notation to identify lines of specific compounds (the Ti Kb'' in particular coming to mind!)?

[sem-geologist]

It might be a good idea to blank out the forbidden transitions for clarity (e.g. K-L1), although that does lead on to the even more confusing discussion of how we get Li and Be Ka X-rays.

not only Li and Be Ka, but also M lines of LREE, which are also forbidden... but it exists. There Is something fundamentally wrong in these theories.

[JonF]

It might be a good idea to blank out the forbidden transitions for clarity (e.g. K-L1), although that does lead on to the even more confusing discussion of how we get Li and Be Ka X-rays.

not only Li and Be Ka, but also M lines of LREE, which are also forbidden... but it exists. There Is something fundamentally wrong in these theories.

The theories are ok, but I think we generally over-simplify them in order to make them comprehendible! It's one of those "spherical cow" moments...

https://en.wikipedia.org/wiki/Spherical_cow

[Probeman]

I've always been under the impression that the Siegbahn notation was derived from the relative intensity(/probability) of a particular transition (e.g. the Ka1 is the brightest), rather than a fixed transition from one shell to another. This is probably insignificant for core-core transitions, but as we look more at those valence-to-core transitions (e.g. light elements, L/M lines etc), does the Siegbahn notation switch between different lines of varying probability? Or do we just use more and more complicated notation to identify lines of specific compounds (the Ti Kb'' in particular coming to mind!)?

Yes, the origin of the Siegbahn notation was based on the order of observation (essentially the strongest emissions first), so the K emission was the "alpha" notation for that group, "beta" was the second, and then it was a "greek/roman salad". 

The reason the "K" designation was chosen for the first observed emissions was because it was not realized that this was already the inner most ionization, so they started at "K" (in the middle of the alphabet) in case there were more energetic shells further in.

The "Flash of the Cathode Rays" is a great history of this time:

https://www.amazon.com/Flash-Cathode-Rays-Thomsons-Electron-ebook/dp/B07CST5H3N

[Brian Joy]

It might be a good idea to blank out the forbidden transitions for clarity (e.g. K-L1), although that does lead on to the even more confusing discussion of how we get Li and Be Ka X-rays.

Also, strictly speaking, the transitions that produce the Kβ₄ = K-N_4,5 and Lγ₁₁ = L₁-N₅ X-rays are forbidden because the difference in the angular momentum quantum number is greater than one.  These X-ray lines should be characterized by very low intensity.  I’ve never seen evidence of these X-rays, but maybe I’ve never looked hard enough?

EDIT:  I forgot about Kβ₅ = K-M_4,5.  That one should be forbidden as well based on the same criterion, and its intensity is in fact very low.  Also, Lβ₉, Lβ₁₀, Lu, and Lv, none of which I've ever seen in a wavelength scan(?).

More "forbidden" lines:  Ls, Lt, Lβ₁₇.

Happy Canadian Thanksgiving!

[Nicholas Ritchie]

I've always been under the impression that the Siegbahn notation was derived from the relative intensity(/probability) of a particular transition (e.g. the Ka1 is the brightest), rather than a fixed transition from one shell to another. This is probably insignificant for core-core transitions, but as we look more at those valence-to-core transitions (e.g. light elements, L/M lines etc), does the Siegbahn notation switch between different lines of varying probability? Or do we just use more and more complicated notation to identify lines of specific compounds (the Ti Kb'' in particular coming to mind!)?

I believe that you are correct about the definition of Siegbahn notation being originally defined in terms of the brightness of lines.  This leads to oddities like the C Ka line being the C K-L2.  This is why I prefer IUPAC for computational work.  It is totally unambiguous.

WRT forbidden lines:  It is worth remembering that the levels (K, L1, L2 etc) we discuss are an approximation - eigenstates of hydrogenic atoms (single electron around a point nucleus).  They are not eigenstates of multi-electron atoms.  The levels in more complicated atoms are admixtures of the hydrogen eignestates. The small admixture of a permitted level allows transitions between supposedly forbidden levels - albeit at very low rates such that auger transitions usually dominate.  The admixture can become larger (in valence shells) when bonds and other interactions between adjacent atoms are present.  Thus Li can produce X-rays in some bonding environments and not others.

[Brian Joy]

Noting the warning from Nicholas, below is a new version of the table with "forbidden" transitions highlighted in orange.  Let me know if I've made any mistakes!

I've applied the following selection rules using the principal quantum number (n) and the angular momentum or azimuthal quantum number (ℓ), with Δ representing the final state minus initial:
1.  Δn > 0
2.  Δℓ = ±1

EDIT 2021-10-16 2:49 AM:  I just realized that I had "final" and "initial" states mixed up in the table.  The new image below as well as the attached Word file are correctly labeled.