Meaning of $^2[\,1/2]$ terms in atomic spectroscopy

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 $$J = 1$$?

 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 • The notation of coupling schemes are explained here nist.gov/pml/… Sep 2 '21 at 3:23
• 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. Sep 2 '21 at 3:26
• I dont understand that notation. But my lecturer told me to study up L-S coupling so this kind of notation confused me.
– user76255
Sep 2 '21 at 14:31
• But the transition looks like this? For example: I have a wavelength 352 nm so the transition is $^2[1/2]$ to $^2[1/2]^0$?
– user76255
Sep 2 '21 at 14:33
• This notation is certainly not LS coupling. Ask your professor if he expects you to learn LK coupling. Sep 2 '21 at 15:19