Collisional-radiative recombination in cold plasmas

We have investigated the electron-ion three-body collisional-radiative recombination for electron temperatures below 4000 °K using the Mansbach-Keck rates of electron-impact-induced transitions between hydrogenic energy levels of high principal quantum number. At such temperatures and for a wide range of electron densities, the statistical recombination process is simultaneously governed by collisional and radiative transitions between excited levels near the ionization limit, where many atomic and molecular systems possess a hydrogenic energy-level structure. In order to also take into account radiative transitions, we have numerically solved a system of coupled equations, describing the quasi-steady-state populations of 100 bound levels. These equations are expressed in, and solved for, the first differences between the reduced population densities $\rho \mathrm{}\left(p\right)\mathrm{}$, which improves the computing precision and establishes the location of the "bottleneck" in the recombination sequence. Our results are consistent with the following approximation for the collisional-radiative recombination rate coefficient (in ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$): ${\alpha }_{\mathrm{cr}}=1.55\mathrm{}\times {10}^{-10\mathrm{}}{T}^{-0.63\mathrm{}}+6.0\mathrm{}\times {10}^{-9\mathrm{}}{T}^{-2.18\mathrm{}}{\mathrm{}\left[e\right]\mathrm{}}^{0.37}+3.8\mathrm{}\times {10}^{-9\mathrm{}}{T}^{-4.5\mathrm{}}\mathrm{}\left[e\right]\mathrm{}$, where the electron temperature $T$ is in °K and the electron density [$e$] is in ${\mathrm{cm}}^{-3\mathrm{}}$; the first and last terms describe purely radiative and collisional recombination, respectively, and the second term results from the complex interplay of collisional and radiative processes. Agreement with experimental data is reasonable.