Effect of the Electron Correlation on the Multiplet Structure of the(3d)2Configuration of Ti III and Cr V

The effect of the electron correlation of the two valence electrons has been investigated for atoms with ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2s\right)\mathrm{}}^2{\mathrm{}\left(2p\right)\mathrm{}}^6{\mathrm{}\left(3s\right)\mathrm{}}^2{\mathrm{}\left(3p\right)\mathrm{}}^6{\mathrm{}\left(3d\right)\mathrm{}}^2$ ground configuration. The atom is taken as a two-electron system with each electron moving in a Hartree-Fock type effective potential. A correlation factor ($1+c{r}_{12}$) is inserted in the wave function of each of the multiplet members obtained from the Hartree-Fock type one-electron orbitals, and the values of $c$ are determined by the variation method. The use of the correlated wave function has improved, though overcorrected, the multiplet spacings of both Ti iii and Cr v.