On the relaxation effect in the Slater transition state

The meaning of the X alpha eigenvalues, Slater transition state eigenvalues and their relation to ionisation potentials is discussed. It is shown that the main effect of the transition state is to correct for the self energy of the electron in the Hartree-Fock-Slater potential. The extent of electron relaxation in the Slater transition state is quantitatively analysed. A linear relationship is found between the relaxation effect and the self energy of the ionising electron. This relationship enables a straightforward calculation of relaxed ionisation potentials using the wavefunction of the neutral atom alone. The existence of the relation is explained on the basis of the simple screening model of the atom. Many features of the relaxation effect in the Hartree-Fock theory are also explained by this model.