stable but the least accurate method. Our criterion for convergence is when the relative change in the populations is ${\leq}10^{-3}$.

In order to have a more accurate electron density, we first solve the non-LTE problem for hydrogen, where the statistical equilibrium equations are additionally constrained by the charge conservation equation (see Section \[sec:linerized\_eqs\]). The obtained non-LTE electron density is re-used for solving the non-LTE problem for and .

We treat the  K and the  k lines in partial redistribution following the method by .

Model atoms {#sec:model-atom}
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We used three different model atoms to compute the various spectral lines from the model atmosphere.

To model [H$\alpha$]{} we used a three-level plus continuum model atom of , that was constructed by removing the $n=4$ and $n=5$ levels from the atom used by @2012ApJ...749..136L. Following them, we treated [Ly$\alpha$]{} in complete redistribution (CRD) with a Doppler absorption profile, to avoid the large computational cost of treating this line in partial redistribution (PRD).

First, we experimented with the original five-level plus continuum model atom, which produced population inversions in the Ly$\gamma$ and Ly$\delta$ transitions at several places of the model atmosphere. Such inversions cause negative opacities as well as negative source functions. 