Outline
                                                  Motivation: [OI] 1s^2 2s^2 2p^4  S=1 
                                               Discovery stories of FSL (Martin Harwit)
                                               spectro. notation (term symbols) : S, L, J   
                                               Spin-orbit-coupling (Russell-Saunders 1925) 
                                                         -   Pauli’s exclusion principle 
                                                                -        Hund’s rules (ground states) 
                                               CASE by CASE: 
                                                 -   particularly why for [OI] spin S = 1 (triplet)
                                                 -    [OIII] and [CI] similar e-config, [CII] S=1/2
                                                 -    energy levels, critical densities, ionis. pot. 
     Pauli’s exclusion principle
   –Pauli (1925), based on empirical spectral data:
   “No two electrons in an atom can exist in the same 
   quantum state; each electron must have a different 
   set of quantum numbers n, l, m_l, m_s. “
   Pauli noticed that certain missing transitions would 
   correspond to two or more electrons in identical 
   quantum states (e.g. no He triplet lines observed). 
         Hund’s rules
 • Hund 1927, based on empirical atomic spectra
 Rule 1:   unpaired, parallel spins preferred 
 Rule 2:   maximizing orbital A.M. L is preferred 
 Rule 3:   ground state: higher J, when shell > half full
                 E_J = A/2 [J(J+1) – L(L+1) – S(S+1)],     A < 0   
 Reason: electrons with same spin need to have a wider 
 spatial distribution (which according to Pauli’s principle 
 correspond to different values m_l). The larger electron 
 separations (less overlap, less repulsion) indeed lead to 
 energetically more stable electronic configurations! (BE)   
       Oxygen [OI] spin-orbit states
        3P states (S=1, L=1)   fine structure lines
           1D states (S=0, L=2)   no spin, no FSL
           1S states (S=0, L=0)    no spin, no FSL 
            oxygen p sub-shell is more than half full
            Hund’s rule then says 3P2 is ground state
                               nd
            and 3P1 first excited state, 3P0 2  excited
            (the other way round for [OIII] and [CI]) 
     Oxygen [OI] multi-electron system: 
     outer sub-shell (4 electrons): 2p^4