However, due to large cancellations, their difference is finite, well behaved, and much smaller than either term separately. At the compressibility divergence at r s = 5.25, both the direct (screened Coulomb) term and the charge-dependent exchange term in the electron-electron interaction at q = 0 are separately divergent. Exchange and correlation become increasingly important at low densities. Very simple quadratic formulas are presented for the local field factors that quantitatively produce all of the response functions of the electron gas at metallic densities. These are used together with the charge local field factor from previous diffusion quantum Monte Carlo calculations to quantitatively present the full effective spin-dependent electron-electron interaction in three-dimensional electron gas. Variational diagrammatic quantum Monte Carlo calculations of the spin local field factor are reported. The effective electron-electron interaction in electron gas depends on both the density and spin local field factors.
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