1. The Quantum Mechanics of Fine Structure Lines: [OI], [OIII]; [CII], [CI]
Hans Zinnecker
Deutsches SOFIA Institut
NASA-Ames and Univ. Stuttgart
FSL Workshop, 8-11 June 2015
MPIA Heidelberg

2. 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.

3. 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).

4. 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)

5. 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 and 3P1 first excited state, 3P0 2nd excited (the other way round for [OIII] and [CI])

6. Oxygen [OI] multi-electron system: outer sub-shell (4 electrons): 2p^4

7. [OI] fact sheet Ionisation potential: 13.62 eV (vs. HI 13.60 eV)
FSL lines: mu (3P1-->3P2 gs), mu
FSL energy levels: E = 228 K (3P1), 327 K (3P0)
Excitation: collisions with electrons, H, H2
High critical density: few x 10(5), few x 10(4) cm-3
for 3P1 and 3P0, respectively
Def n_crit: collisional de-exc equals radiative de-exc
assumption: optically thin case
PS. Gas phase abundance: ~5x10(-4) of hydrogen

8. Fact sheet [CII], [CI], and [OIII]
[CII] mu, E = 91.2K, IP([CI]) = 11.3 eV low n_crit ~=~ 2x10(3) cm-3
[CI] mu, mu; E = 23.6K, 62.4K
n_crit = 620 cm-3, 720 cm-3
[OIII] mu, 51.8 mu; E = 163K , 441K
IP([OIII]) = eV > I(He II, 54.4 eV)

9. Literature (text books)
B.T. Draine: Physics of ISM and IGM (2011)
Peter Bernath: spectra of atoms & molecules
Jonathan Tennyson: atoms in space
R. Genzel: Saas-Fee lectures (1991)

10. Summary The 63 mu / 145 mu FSL lines of [OI]
owe their existence to quantum mech.
(L = 1, S = 1 triplet, spin-orbit coupling)
Similar for [OIII] and [CI] – also FSL triplets.
[CII] S=1/2 FSL singlet (simplest case)
[CIII] S=0, closed shell, no FSL emission
Pauli’s exclusion principle and Hund’s rule 1
demonstrated in action for [OI] (L=0, 1, 2).
What if the [OI] cooling lines did not exist?