(updated for 2013)

How do we deal with the distribution over **different **states of ionization r? In thermodynamic equilibrium, the Saha equation gives:

,

where and are the partition functions as discussed in the previous section. The partition function for electrons is given by

For a derivation of this, see pages 103-104 of this handout from Bowers and Deeming.

If and are approximated by the first terms in their sums (i.e. if the ground state dominates their level populations), then

,

where is the energy required to ionize from the ground (*j* = 1)* * level. Ultimately, this is just a function of and . This assumes that the only relevant ionization process is via **thermal **collision (i.e. shocks, strong ionizing sources, etc. are ignored).

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