Simplified Theory of Electron Correlations in Metals

A model is developed which allows one to easily calculate correlation effects of interacting electrons. Upon considering a particular electron one replaces the excitation spectrum of all other electrons by a single mode ω(q), varying between the plasma frequency for small q and q²2m for large q. The coupling strength between the electron and the plasma modes is found by imposing the f sum rule. ω(q) is determined by requiring the model to have a correct dielectric response. The exchange and correlation contributions to $E(k)$ have nearly opposite k dependence. However, there is a residual oscillation near kF which causes the effective mass m* to be less than unity, even though the mean mass (between $k=0$ and kF) is greater than unity. A specific local approximation to the exchange and correlation potential Axc=-2.07(na₀³)0.3Ry, analogous to Slater's n1/3 exchange potential, is accurate over 3 orders of magnitude in density. The (bare) momentum distribution $n(k)$, and the fraction ζ of electrons excited above kF, are calculated as a function of density. For Li and Na, excluding band-structure effects, ζ=0.11 and 0.14, respectively.