**5.2.1. Ionization equilibrium**

In equilibrium, the ionization state is determined by the balance between processes that produce or destroy each ion:

(5.15) |

Here *n*(*X*^{i}) is the number density of the ion
*X*^{i} (*x* is the element), *T*_{g} is the
electron temperature, and *c*(*X*^{i},
*T*_{g}) and
(*X*^{i},
*T*_{g}) are the rate coefficients
for collisional ionization out of ion *X*^{i} and
recombination into ion *X*^{i}, respectively.

The collisional ionization rate is the sum of two processes: direct
collisional ionization and collisional excitation of inner shell
electrons to autoionizing levels
which decay to the continuum. This last process is often referred to as
autoionization. Recombination is also the sum of two processes, radiative
and dielectronic recombination. Recent compilations of ionization and
recombination rates and discussions of their accuracy include
Mewe and Gronenschild
(1981),
Shull and Van Steenberg
(1982),
and Hamilton *et
al.* (1983).

The electron density dependence drops out of equation (5.15), and the equilibrium ionization state of a diffuse plasma depends only on the electron temperature. Tables of ionization fractions of various elements are given by Shull and Van Steenberg (1982). Generally, each ionization fraction reaches a maximum at a temperature that is some fraction of its ionization potential. At the temperatures which predominate in clusters, iron is mainly in the fully stripped, hydrogenic, or heliumlike stages.