Scaling properties of the dielectronic recombination amplitudes

The dielectronic recombination amplitude is given in the resonance approximation by a product of the radiationless capture amplitude $S$ to one of the resonant intermediate states and the radiative decay amplitude $R$ of that resonant state. For highly charged ionic targets, both $S$ and $R$ are expected to scale approximately in the nuclear core charge $Z_C$ for each isoelectronic sequence, and we study the scaling property and its breaking as the number of electrons in the ion increases. The effects of Coulombic and exchange correlations as well as the relativistic correction are considered. Based on the explicit evaluation of the $S$ and $R$ amplitudes using Hartree-Fock wave functions, we have determined an effective scaling function, which has been used to predict the radiation and Auger-emission probabilities $A_r$ and $A_a$ for Ar, Mo, and W from the available values for Fe.