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=Z(2) Ry, for ions with charge Z. The rates are usually g
iven for target ions in their ground states, and contributions from all dou
bly excited intermediate states and final singly excited states of the reco
mbined ions are summed over. To facilitate applications of the rates in pla
sma modelling in terms of rate equations, simple rate formulas are often de
vised. However, at finite temperature, a sizable fraction of ions is initia
lly in an excited state, and after recombination, ions are usually left in
singly excited final states. Thus new empirical rate formulas are needed th
at exhibit an explicit dependence on final as well as initial states of the
ions before and after the recombination. We have calculated properly adjus
ted rates where (a) the target ions are allowed to be in their ground and e
xcited states, and (b) contributions to the individual final states are exp
licitly separated. Multiple cascades are important in such calculations. Fo
r Al3+ ions we show that rates for the initial excited states are much larg
er than that for the ground state.