Effective recombination coefficient (${\alpha }_{\ell }^{\mathrm{eff}}$)

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.