Dielectronic recombination

A free Electron is resonantly captured while exciting the ionic core, producing a doubly excited state above the parent-ion threshold. Capture becomes permanent recombination only if the state undergoes radiative stabilization rather than autoionization. For resonance $d$, entrance ion $i$, and Maxwellian electrons, ${\alpha }_d=(g_d/(2g_i))(h^2/(2\pi mkT){)}^{3/2}{e}^{-E_d/kT}{A}_{di}^a{A}_{\mathrm{stab}}^r/(A_{\mathrm{tot}}^a+A_{\mathrm{tot}}^r)$. Detailed balance determines the capture rate; a steady population balance determines the survival factor. The rate coefficient has dimensions volume per time.

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.

Radiative stabilization occurs when a photon emission from an autoionizing state leads to a bound state, preventing electron re-ejection. For one radiative channel and one autoionization channel, its probability is $A_r/(A_a+A_r)$. With several channels, use summed losses and the total rate of successful stabilizing decays; a cascade through another autoionizing state requires its eventual survival probability.

Dielectronic capture is the resonant capture stage inverse to a specified autoionization channel. For an entrance ion of weight $g_i$ and resonance of weight $g_d$ and energy $E_d>0$, its Maxwellian coefficient is $C_d=(g_d/(2g_i))(h^2/(2\pi mkT){)}^{3/2}{e}^{-E_d/kT}{A}_{di}^a$. This follows by equating capture and autoionization fluxes at thermodynamic equilibrium. Capture alone need not produce a permanently recombined ion.