Resonance-temperature dependence of dielectronic recombination (${\alpha }_d(T)\propto T^{-3/2}{e}^{-E_d/kT}$)

For temperature-independent atomic rates and an isolated positive-energy resonance, dielectronic recombination has the displayed dependence. Differentiating its logarithm gives a maximum at $kT=2E_d/3$. A sum of resonances can have several peaks, and near-threshold resonances change the low-temperature behavior. Collisional destruction of captured high levels can introduce density dependence.