Effects of collisions on level populations and dielectronic recombination rates of multiply charged ions

A generalization of previously reported statistical theories is developed for determining the excited-level populations and the ionization-recombination balance of multiply charged atomic ions in an optically thin high-temperature plasma. Account is taken of the most important collisional and radiative processes involving bound and autoionizing levels in three consecutive ionization stages. We obtain a set of rate equations for the population densities of the low-lying levels which contains effective excítation, ionization, and recombination rates describing indirect transitions through the more highly excited bound and autoionizing levels. The familiar corona-model equations for the ground-state populations are recovered by making the assumption that all excited states decay by only spontaneous radiative or autoionization processes. When collisional processes become efficient in depopulating the highly excited levels important in dielectronic recombination, the effective rate of recombination must be described by a collisional-dielectronic recombination coefficient. Results of calculations are presented for the collisional-dielectronic recombination rate coefficients for recombination of ${\mathrm{Fe}}^{+8\mathrm{}}$-${\mathrm{Fe}}^{+13\mathrm{}}$ ions. At an electron density of ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, dielectronic recombination is still the dominant recombination process. However, the collisional-dielectronic recombination rate coefficients are found to be reduced by about an order of magnitude from their corona-model values due to the effects of multiple-collisional excitations on the populations of the highly excited bound levels of the recombined ion. The dielectronic recombination rates into these highly excited levels are found to be enhanced by the effects of collisionally induced angular momentum redistribution on the populations of the autoionizing levels.