Recombination cooling of ionized hydrogen

Radiative recombination removes the kinetic energy of captured electrons from a plasma. The thermal cooling per event is not the entire emitted photon energy: binding energy had been stored as ionization energy. If recombination is the only cooling and ionization is balanced, the mean removed kinetic energy equals the mean photoelectron heating energy.

The mean kinetic energy removed per recombination is $⟨E{⟩}_{\mathrm{rec}}=\int E{f}_T(E){\sigma }_{\mathrm{rec}}(E)v(E)dE/\int f_T(E){\sigma }_{\mathrm{rec}}(E)v(E)dE$. The capture-rate weighting generally differs from averaging an unselected Maxwell distribution, so $⟨E{⟩}_{\mathrm{rec}}=3k_{B}T/2$ is only an additional approximation.