Local approximation for the Hartree-Fock exchange potential: A deformationapproach

We present a method for deriving local approximations of the exchange-term in the Hartree-Fock equation for a system of fermions interacting with a Co ulomb-force. Within our model, we give a justification of the Slater-approx imation where the exchange-term is replaced by the third root of the local density. Our approach is based on deformations, i.e. local scaling transfor mations of a constant density, combined with the "high density limit" of in finite number of particles.