Frequency‐Dependent Exchange Correction to the Dielectric Function of the Electron Gas

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Abstract
The equation of motion of the Wigner distribution function in the homogeneous electron gas is decoupled using the Hartree‐Fock prescription. After linearization, the variational procedure, used by Rajagopal and Jain and by Langreth is applied. The transverse and the longitudinal dielectric functions in the Hartree‐Fock approximation are derived, and the consistency of the equations for the charge density and the current density is examined. Several limits are calculated. The slope of the plasmon mode is substantially lowered by the exchange interactions, and the damped acoustic mode disappears for the densities that give a negative bulk modulus in the Hartree‐Fock approximation. The exchange interaction only slightly influences the dispersion of the transverse collective modes.