Direct radiative recombination of electrons with atomic ions: Cross sections and rate coefficients

Abstract

Simple expressions are obtained which permit systematic estimates of the rate coefficients for direct radiative recombination (DRR) of fast electrons with atomic ions of various ionic species. The analysis utilizes a set of cross sections obtained through numerical calculations combined with the use of an interpolation scheme to smoothly connect reduced cross sections (apart from normalizations) of the bremsstrahlung tip region and the low-lying DRR region. It is shown that these numerical cross sections can be reproduced by the predictions of a modified semiclassical Kramers formula with an appropriate effective charge ${Z}_{\mathrm{eff}}$, which is larger than the effective charge which reproduces the energy levels of the states into which capture occurs. In accord with this modified Kramers formula, the numerically obtained total cross sections are shown to scale with $\frac{{Z}_{\mathrm{eff}}^{2}}{K}$ for each isoelectronic sequence, and with a parameter ${({n}_{0})}_{\mathrm{eff}}$ which characterizes each isoelectronic sequence. Using these scaling properties, simple analytic expressions are obtained for recombination rate coefficients, for the rate of electron kinetic-energy loss, and for the rate of radiated power loss, assuming a classical Maxwell-Boltzmann thermal distribution of continuum electrons.