Extended Thomas-Fermi approximation to the one-body density matrix

The one-body density matrix is derived within the Extended Thomas-Fermi app roximation. This has been done starting from the Wigner-Kirkwood distributi on function for a non-local single-particle potential. The links between th is new approximation to the density matrix with former approaches available in the literature are widely discussed. The semiclassical counterpart of t he Hartree-Fock energy at the Extended Thomas-Fermi level is also obtained in the case of a non-local one-body Hamiltonian. The semiclassical binding energies and root mean square radii are compared with those obtained using the Strutinsky averaged method. The full Hartree-Fock values are compared w ith those obtained using the Kohn-Sham scheme based on the different approx imations to the density matrix considered in the text. Numerical applicatio ns are performed using the Gogny, Brink-Boeker and BDM3Y1* effective intera ctions. (C) 2000 Elsevier Science B.V. All rights reserved.