\, \mathrm{cm^{2}}.
\label{eq:lotz}$$ Here $p_0$ is the initial number of electrons in the level where the ionization takes place. The branching ratios for many ions of astrophysical interest have been given by @Kaastra:AAS:1993 and updated calculations for some systems have been given by @Bautista:AA:2003, @Gorczyca:ApJ:2003 [@Gorczyca:ApJ:2006], @Palmeri:AA:2003, @Mendoza:AA:2004, and @Shevelko:JPhysB:2005.

Application of Fitting Formulae to Iron Ions {#subsec:appfe}
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In order to determine the EIMI cross sections for our CSD calculations, we have selected the semiempirical formulae for each system that seem to best reproduce the experimental measurements. Experimental data are not available for every system, so in some cases we have had to estimate the cross section based on the results for nearby charge states. Table \[table:cross\] lists the parameters used for each cross section and also indicates for which data there are experimental results. We denote the initial charge state as $q_{i}$ and the final charge state as $q_{f}$. The total cross section is the sum of the individual cross sections for each ionization channel. That is, $$\sigma_{\mathrm{total}}=\sigma_{\mathrm{D}}+\sum_{N}{\sigma_{\mathrm{IA},i}},
\label{eq:sigtot}$$ where $\sigma_{\mathrm{D}}$ is the direct ionization cross section and the $\sigma_{\mathrm{IA},i}$ represent the IA sections arising from $N$ different IA channels, such as due to holes in different shells. 