Collisional quenching of a metastable line ($P_{\mathrm{rad}}=A_{ul}/(A_{ul}+n_e{q}_{ul})$)

A schematic statistical equilibrium is $n_l{n}_e{q}_{lu}=n_u(A_{ul}+n_e{q}_{ul})$. The radiative yield per excitation is $A_{ul}/(A_{ul}+n_e{q}_{ul})$. It is near unity below critical density $A_{ul}/q_{ul}$ and decreases above it. Quenching suppresses emission relative to naive low-density excitation scaling; it need not make the absolute emissivity decrease when density rises.