The exact universal exchange-only local field factor of the uniform electron gas and its near-cancellation by parallel-spin correlation near 2kF

I use the microscopically derived, well-known, but underappreciated, exact universal expression for the exchange-only local field factor Gx(q,ω) at ω = 0 to gain physical intuition about the separate exchange and correlation contributions to the static quantum Monte Carlo derived "measured" density and spin local field factors G+(q) and G-(q). I use the decomposition of G+ and G- into their fundamental microscopically defined spin-resolved constituents G↑↑ and G↑↓. This decomposition is possible because both G+ and G- are available from Monte Carlo calculations. Recognizing that G↑↑ includes contributions from both exchange and correlation, G↑↑ = G↑↑x + G↑↑c with G↑↑x = Gx, allows the subtraction that reveals the parallel-spin correlation. The antiparallel-spin G↑↓ depends only on correlation. The exact Gx(q,ω) is universal, independent of density, when plotted against q/kF and ω/εF. This paper focuses on the static value at ω = 0. The density functional theory exchange and correlation kernel is directly proportional to the density local field factor through fxc = -4πe2G+/q2. The local field factors define all of the response functions of the electron gas. The static Gx, known in pieces for fifty years, is assembled here into one expression, evaluated exactly, and released as a short Python module. It has a large peak of 1.99 just below 2kF, passes through π2/6 at 2kF, and tends to 1/3. Used alone in a static linear response, it predicts a spin density wave at rs = 4.96 and a charge density wave at rs = 10.62. Quantum Monte Carlo shows the gas has neither. Near 2kF, the difference is striking. Gx has a large peak near 2kF, and G+ shows no comparable structure. Exchange enters G+ and G- identically, so their difference, which is twice the antiparallel factor G↑↓, contains no exchange at all. That difference is measured directly and is small and smooth through 2kF. Whatever removed the exchange-only peak is in the parallel-spin channel. There, everything beyond first-order exchange, that is, screening and correlation together, is large and negative and mirrors the exchange peak. In the measured G+, the net removal is 40%-48% of the peak at rs = 1-10. The stability of the metallic gas against exchange-driven density waves is, therefore, a parallel-spin effect. The decomposition points to where microscopic calculations of each channel should go.