 Electron-density diagnostic from metastable populations

In a two-level ground system, balancing collisional upward excitation against radiative and collisional downward loss gives $n_2/n_1=n_e{q}_{12}/(A_{21}+n_e{q}_{21})$. 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.