 Recombination-weighted electron 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.