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

Abstract

The one-body density matrix is derived within the Extended Thomas–Fermi approximation. This has been done starting from the Wigner–Kirkwood distribution function for a non-local single-particle potential. The links between this new approximation to the density matrix with former approaches available in the literature are widely discussed. The semiclassical counterpart of the 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 with those obtained using the Kohn–Sham scheme based on the different approximations to the density matrix considered in the text. Numerical applications are performed using the Gogny, Brink–Boeker and BDM3Y1 ∗ effective interactions.