Boltzmann excitation ($n_j/n_i=(g_j/g_i)e^{-(E_j-E_i)/(k_{B}T)}$)

In local thermodynamic equilibrium, the ratio of two internal-level populations includes their energy-level degeneracies $g_i,g_j$ and their excitation-energy difference. Temperature-sensitive spectral line ratios can constrain the excitation temperature when line formation and radiative transfer are modelled consistently. Ionization fractions additionally require the Saha equation.