Spin-Up-Spin-Down Pair Distribution Function at Metallic Densities

Abstract
Correlations in an electron gas are particularly important at metallic densities because the potential energy cannot be ignored in comparison with the kinetic energy; in particular, interactions are not weak as r → 0, so that a simple Born approximation does not hold in this limit. Short-range correlations between oppositely-spinned electrons can be accounted for by an infinite series of particle–particle ladder diagrams. It leads to a Bethe–Goldstone type of equation which can be solved by an angle-averaged approximation. The resultant spin-up-down p.d.f. is positive over a wide range of metallic densities. A further correction by including particle–hole scattering effects changes the previous results only slightly.