Pair Correlations and Exchange Phenomena in the Free Electron Gas

Abstract:

We present a rigorous derivation of the formulae of Dirac-Bloch and Wigner-Seitz for the quantum mechanical exchange energy and the ‘exchange hole’ of the free electron gas. More precisely we establish that for arbitrary determinantal ground states of the underlying finite system of N free electrons in a box, subject to periodic or zero boundary conditions, the formulae are accurate to order $N^{-1/3}$ (per electron) and $N^{-1/2}$ respectively.