The kinetic energy density in Kohn–Sham density functional theory

Abstract

This work continues a program to systematically generalize the Skyrme Hartree–Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn–Sham density functional theory (DFT). When conventional Kohn–Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density τ is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of τ is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. Here we show how to generalize the EFT framework for DFT derived previously to reconcile these approaches. A dilute gas of fermions with short-range interactions confined by an external potential serves as a model system for comparisons and for testing power-counting estimates of new contributions to the energy functional.