Explicit approximate relation between reduced two- and one-particle density matrices

Abstract A class of approximation of the two-particle density matrix d2 resembling the Hartree-Fock dependence on the one-particle density matrix d1 is suggested. The integral relation between d2 and d1 is exactly maintained. An optimal choice is performed by means of the Pauli principle. The smallness of the error when applied to Coulomb systems, is qualitatively discussed. Extended Thomas-Fermi theory, as recently introduced by the authors is shortly outlined for the case of Coulomb interaction.