coefficients and $\vec{y}$ is the vector of abundances with elements $y_{i}$. In order to obtain a unique solution, an additional equation is needed. For this, we require that abundances be normalized so that $$\sum_{i}{y_{i}}=1.
\label{eq:norm}$$ This condition is implemented by replacing one of the rows of Equation (\[eq:ay0\]) with Equation (\[eq:norm\]), see for example @Bryans:ApJS:2006.

Figure \[fig:equilib\] shows the equilibrium ionization balance as a function of temperature, $y_{i}(T)$, for all the iron charge states. The solid lines in the figure show the results of the present calculation, which includes EIMI processes. The figure also includes a set of dashed curves, which show the results when only single ionization is considered, however the differences are smaller than the width of the lines in the figure. Here, our CIE calculations for single ionization are identical to the results given in the CHIANTI database, which are an updating of the CIE calculations of @Bryans:ApJ:2009. This agreement between our results and those of CHIANTI is expected since we used the same single ionization and recombination rate coefficients.

The lower panel of Figure \[fig:equilib\] highlights the differences between CIE calculations including and excluding EIMI. The figure shows the ratio of the abundances calculated with EIMI 