Abstract
A correction for the self-interaction contribution, which depends only on the total number of electrons, is introduced in the local density approximation. Energies and scattering form factors for rare-gas atoms, positive alkali ions and negative halogen ions are calculated both for the Kohn-Sham form of the exchange potential and for the Slater one, and compared with those calculated from the Hartree-Fock equation. Both the corrected KS and S equations give results very close to the HF ones. For negative ions bound states are obtained without artificial modifications of the potential.