Calculation of the spectra parameters for transition-metal ions

In the theory of atomic spectroscopy, calculating Slater integrals, spin-orbit coupling parameters is often the first and important step. Hydrogen-like wave function model, which has been widely used for its easiness to handle and for it can give out approximately correct Slater integrals, is very poor in deciding the spin-orbit coupling parameter. The large discrepancy derives from that the hydrogen-like wave function based on only one effective nuclear charge model is smaller to the real wave function in the vicinity of the nuclear. Based on the above analysis a new one named Corrected Slater Wave Function (CSWF) model is given, which takes the hydrogen-like wave function as its main part and a little correction term as the other small part. The CSWF model is successful in calculating both the Slater integrals and spin-orbit parameter for the transition-metal ions of the first row