Statistical equilibrium of atomic level populations (${\sum }_{j\ne i}(n_j{R}_{ji}-n_i{R}_{ij})=0$)

An atomic population is in statistical equilibrium when the total rate into each level equals the total rate out, subject to conservation of the total number of atoms or ions. The rates can include electron-impact transitions and spontaneous emission. This is weaker than thermodynamic equilibrium: a collisionally excited, radiatively decaying dilute gas generally does not have Boltzmann level populations.