Paschen notation for electronic states of Argon atom

[goodphy]

Hello.

I think excited states of Argon atom is described by j,l coupling written as ^(2s+1)[K]_J.

However, when I read some papers describing cross section data for Argon atom, data are quoted with strange notation, Paschen notation. I tried to study the Paschen notation and found that its form is like nl_# (ex: 2p₁₀). n and l here are principal and orbital quantum number for an excited electron. Okay, that's easy. However, I really can't exactly figure out what subscript number # means! I just guess that this number is just a label of each state associated with particular n and l. However...which state is labeled 10? which state is 9? which state is 8??

Could you tell me what labeling order is used in the Paschen notation? I would be very happy if you give me a detailed description of the notation or any good material well describing the notation.

 

[goodphy]

There is a thing that I was wrong in my question. In the Paschen notation nl_#, n is even not same to the principle quantum number of the excited electron! So, I have to ask additional question of what n really is. The Paschen notation really makes me crazy.

 

[goodphy]

Hello.

I think I finally get an answer to the question.

I'm uploading my summary of Racah and Paschen notations here everyone having the same question will benefit from it.