  Effective field theory (EFT) methods are applied to density functional theory
(DFT) as part of a program to systematically go beyond mean-field approaches to
medium and heavy nuclei. A system of fermions with short-range, natural
interactions and an external confining potential (e.g., fermionic atoms in an
optical trap) serves as a laboratory for studying DFT/EFT. An effective action
formalism leads to a Kohn-Sham DFT by applying an inversion method
order-by-order in the EFT expansion parameter. Representative results showing
the convergence of Kohn-Sham calculations at zero temperature in the local
density approximation (LDA) are compared to Thomas-Fermi calculations and to
power-counting estimates.
