Radiative recombination ($A^{+}+e^{-}\to A+\gamma$)

A free electron can be captured by an ion while a photon carries away binding and kinetic energy. This radiative recombination process contributes free-bound radiation to plasma cooling and balances collisional ionization in a collisional-equilibrium plasma.

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.

A recombination line is a spectral line produced after a free electron is captured, often through a subsequent radiative cascade among bound levels. Its emissivity is computed with an effective recombination coefficient, distinct from the free-bound recombination continuum.

The effective recombination coefficient for a spectral line counts recombinations and subsequent radiative cascades producing that line. At sufficiently low density, its photon production rate per volume is $n_e{n}_{\mathrm{parent}}{\alpha }_{\ell }^{\mathrm{eff}}$. It depends on gas temperature, optical-depth assumptions such as Case B recombination, and sometimes density. It differs from the total rate coefficient removing the parent ion.