direct multiple ionization, but other contributions must be added in for systems in which IA becomes important.

@Shevelko:JPhysB:2005 presented a semiempirical double ionization formula that accounts for both direct ionization and IA for initially He-like to Ne-like ions. The total cross section is a sum of a direct and an IA cross section. The direct cross section is given by $$\sigma_{\mathrm{D}}=1-\mathrm{e}^{-3\left(u-1\right)}\left\{ \frac{p_0}{E_{\mathrm{th}}^3}\left[\frac{u-1}{\left(u+0.5\right)^2}\right] \right\}
\times10^{-13} \, \mathrm{cm^{2}}.
\label{eq:shev5a}$$ Here $p_0$ is a tabulated fitting parameter that varies depending on the initial isoelectronic sequence of the ion. $E_{\mathrm{th}}$ is again the threshold for the ionization process being considered, i.e., here direct EIMI. The indirect cross section, due to IA, is given by $$\sigma_{\mathrm{IA}}=f \frac{p_{0}}{E_{\mathrm{th}}^2}\frac{u-1}{u \left(u+p_{1}\right)} 
\times10^{-13} \, \mathrm{cm^{2}},
\label{eq:shev5b}$$ where $E_{\mathrm{th}}$ is the relevant threshold for the process, i.e., the threshold for single ionization of a core electron. The parameters $p_{0}$ and $p_{1}$ depend on the isoelectronic sequence of the initial ion configuration. The quantity $f$ is the branching ratio for autoionization of the intermediate state that is missing an inner-shell electron. @Shevelko:JPhysB:2005 have calculated these branching ratios for K-shell vacancies having configurations $1s 2s^2$ through $1s 2s^2 2p^6 3s$ for nuclear charges $Z=3$–$26$.

For certain ions where experimental data exist, @Shevelko:JPhysB:2006 