= Electron-density diagnostic from metastable populations
In a two-level ground system, balancing collisional upward excitation against radiative and collisional downward loss gives $n_2/n_1=n_eq_{12}/(A_{21}+n_eq_{21})$. Excited lines fed in different proportions by these levels have a density-sensitive ratio. At low density the population ratio is proportional to density; at high density it saturates at $q_{12}/q_{21}$. A reliable calibration uses a full multilevel model when upper-state branching and cascades matter.
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