Validity of analytical formulas for autoionization and dielectronic capture rates used in collisional-radiative models

Large-scale level-by-level calculations were carried out to obtain as accurate autoionization and dielectronic capture (DC) rates of Ni-like Au51+ and Cu-like Au50+ as possible by including adequate electron correlations. The accuracy is estimated to be better than 20% for strong autoionized levels. Our results of the dielectronic recombination (DR) process through 3d94lnl' (n=4,5) agree excellently (within 10%) with other theoretical results also obtained by detailed level-by-level calculations reported in the literature. The level-by-level results were transformed to configuration-by-configuration autoionization and DC rates (which are estimated to be better than 30% in accuracy) and used to check the validity of the rate coefficients in collisonal-radiative (CR) models by using an analytical formula. Large discrepancies were found between the detailed calculated rates and those predicted by the analytical formula. The autoionization and DC rates predicted by the analytical formula can be more than two orders of magnitude larger than the detailed calculated rates, in particular for the autoionized configurations whose energy is near the ionization potential (IP). However, for those autoionized configurations whose energy is far above the IP, the autoionization and DC rates predicted by the analytical formula can be nearly one order of magnitude smaller. Differences between different theoretical methods found in this work, when approximate methods are used to calculate the autoionization and DC rates, would result in differences when non-local-thermodynamic-equilibrium (NLTE) models used the less accurate methods to obtain these atomic data.