resulting hole [e.g., @Muller:PRL:1980; @Cherkani:PhysScr:2001; @Hahn:ApJ:2011].

Fitting Formulae {#subsec:form}
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Because quantum-mechanical calculations for multiple-ionization cross sections are challenging, EIMI cross sections are generally estimated using semiempirical formulae. Here, we review several semiempirical formulae that have been proposed to model EIMI cross sections. Later we apply these formulae to EIMI cross sections for iron ions.

@Shevelko:PhysScr:1995 [@Shevelko:JPhysB:1995] presented a semiempirical formula that describes cross sections for direct multiple ionization of at least three electrons, i.e., triple ionization, from neutral and ionic targets. @Belenger:JPhysB:1997 extended their formulae to double ionization. The cross sections are approximated by: $$\sigma_{\mathrm{D}}=\frac{p_{0} p_{1}^{p_{2}}}{\left(E_{\mathrm{th}}/E_{\mathrm{Ryd}}\right)^2}\left(\frac{u+1}{u}\right)^{p_{3}}\frac{\ln{(u)}}{u} 
\times 10^{-18} \,\mathrm{cm^{2}},
\label{eq:shevtar}$$ where $u=E/E_{\mathrm{th}}$ is the incident electron energy $E$ normalized by the multiple-ionization threshold $E_{\mathrm{th}}$ for the process being considered and $E_{\mathrm{Ryd}}=13.606$ eV. Here $p_{0}$ and $p_{2}$ are parameters that depend on the number of electrons being removed and have been tabulated by @Shevelko:JPhysB:1995 and @Belenger:JPhysB:1997. The parameter $p_{1}$ is the number of electrons in the target ion and $p_{3}=1.0$ for neutral targets or $0.75$ for ionic targets. The fits were performed to experimental measurements of ionization from neutral and relatively low charged ions, for which the dominant EIMI process is direct ionization. Thus, this formula is reasonable for describing 