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 (q), varying between the plasma frequency for small q and {q^2}2m for large q. The coupling strength between the electron and the plasma modes is found by imposing the f sum rule. (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 k₅ which causes the effective mass m^* to be less than unity, even though the mean mass (between k=0 and k₅) is greater than unity. A specific local approximation to the exchange and correlation potential Aₗ₂=-2. 07 (n{a₀^3) }^0. 3Ry, analogous to Slater's n^1{3} exchange potential, is accurate over 3 orders of magnitude in density. The (bare) momentum distribution n (k), and the fraction of electrons excited above k₅, are calculated as a function of density. For Li and Na, excluding band-structure effects, =0. 11 and 0. 14, respectively.