and branching ratios.

Double-ionization measurements for $q_i=9, 11, 12$, and $13$ have been measured by @Hahn:ApJ:2011 [@Hahn:ApJ:2011a; @Hahn:ApJ:2012; @Hahn:ApJ:2013]. These data show that there is a small contribution due to direct ionization, starting at the direct-double-ionization threshold. However, the dominant double-ionization process for highly charged Fe ions is initially single ionization of an $L$-shell ($n=2$) electron, followed by autoionization, resulting in a net double ionization. The relative importance of direct ionization compared to IA decreases as the charge state increases. We have found that a reasonable approximation to these experimental data is obtained by using Equation (\[eq:shevtar\]) to represent the direct contribution and including indirect ionization using the Lotz cross section for the $L$-shell ionization scaled by the branching ratios from @Kaastra:AAS:1993. An example of this semiempirical prediction compared to the experiment for the case of Fe$^{11+}$ forming Fe$^{13+}$ is shown in Figure \[fig:fe1113\]. We have extended this scheme beyond the several measured charge states to represent double ionization for Fe$^{7+}$–Fe$^{15+}$. For higher order EIMI, no experimental data exist so we use the Lotz formula scaled by the branching ratios.

For Fe$^{16+}$ and higher charge states, we are not aware of any experimental data for EIMI. For these ions, we 