Ions in a plasma recombine with electrons by both direct and resonant modes. The latter, the dielectronic recombination, can be a dominant process at temperature near $T\simeq Z^2$ Ry, for ions with charge Z. The rates are usually given for target ions in their ground states, and contributions from all doubly excited intermediate states and final singly excited states of the recombined ions are summed over. To facilitate applications of the rates in plasma modelling in terms of rate equations, simple rate formulas are often devised. However, at finite temperature, a sizable fraction of ions is initially in an excited state, and after recombination, ions are usually left in singly excited final states. Thus new empirical rate formulas are needed that exhibit an explicit dependence on final as well as initial states of the ions before and after the recombination. We have calculated properly adjusted rates where (a) the target ions are allowed to be in their ground and excited states, and (b) contributions to the individual final states are explicitly separated. Multiple cascades are important in such calculations. For ${\mathrm{Al}}^{3+}$ ions we show that rates for the initial excited states are much larger than that for the ground state.

• Received 7 July 2000

DOI:https://doi.org/10.1103/PhysRevE.63.046407