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I was trying to analyze some atomic emission spectroscopy data and I encountered unfamiliar notation of the terms for me.

Commonly, the electronic states of the atoms can be described by quantum numbers using the term notation ("L-S coupling"). The terms are given as: $^{2S+1}L_{J}$, where $S$ is the total spin quantum number, $J$ is the total angular momentum quantum number and $L$ is the total orbital quantum number in spectroscopic notation.

However, in this table there are also terms having notations without letters ($S$,$P$,...), like $^{2}[\,1/2]^\mathrm{o}$ (black box). What does that mean and why are there separate cases for $J = 0$ and $J = 1$?

[Edit] The data has been taken from NIST Atomic Spectral Database for Ne I (neutral neon in spectroscopic notation). NIST database The notation, asked in this posted has already been explained here Notation key by NIST

enter image description here

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    $\begingroup$ The notation of coupling schemes are explained here nist.gov/pml/… $\endgroup$
    – M. Farooq
    Sep 2 '21 at 3:23
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    $\begingroup$ I am not familiar with this type of coupling but it is called LK couping. The number in square brackets is K. It is always good to a give a reference when you paste an image. $\endgroup$
    – M. Farooq
    Sep 2 '21 at 3:26
  • $\begingroup$ I dont understand that notation. But my lecturer told me to study up L-S coupling so this kind of notation confused me. $\endgroup$
    – user76255
    Sep 2 '21 at 14:31
  • $\begingroup$ But the transition looks like this? For example: I have a wavelength 352 nm so the transition is $^2[1/2]$ to $^2[1/2]^0$? $\endgroup$
    – user76255
    Sep 2 '21 at 14:33
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    $\begingroup$ This notation is certainly not LS coupling. Ask your professor if he expects you to learn LK coupling. $\endgroup$
    – M. Farooq
    Sep 2 '21 at 15:19

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