Revised Thomas-Fermi Functional for Singular Potentials*

Approximations to the non-interacting free energy density functional that include the Thomas-Fermi (TF) functional, or a local density approximation, lead to singular densities for singular external potentials (e.g. Coulomb). We address this limitation of the TF approximation by a formal map of the exact functional for a given external potential onto a fictitious TF functional for an effective external potential. The latter functional is found to be a ``regularized'' version of the external singular potential, tempered by convolution with the finite temperature Lindhard response function. The result is a Thomas-Fermi approximation but with the singularity removed. Applications at high and low temperatures are described, including comparison with the Parr-Ghosh cusp-condition procedure for a non-singular TF density at zero temperature.