Small-distance expansion of the interacting linear response function of the homogeneous phase of the jellium model, and the local field factor

Abstract

The linear response function F ₀(r) of a free Fermi gas sums even moments of the momentum distribution n ₀(p) to infinite order. This motivates us to define an interacting response function F _I(r) as a functional of the true momentum distribution n(p) of the Fermi liquid. It is demonstrated that only the second and fourth moments of n(p) exist. The relation between the Fourier transform of F _I(r) and the charge susceptibility involves a redefinition of the local field factor, which now tends to a constant at large k, fixed by zero-range electron-electron correlations.