Dynamic correlations in an electron gas. II. Kinetic-equation approach

Starting from the exact hierarchy of quantum kinetic equations for the Wigner distribution functions we develop a theory of dynamical correlations in an electron gas. By making a random-phase-approximation- (RPA) like truncation for the second equation in the hierarchy we obtain an expression for the proper polarizability of the form Q=Q⁰+Qᶜ, where Q⁰ is the Lindhard (RPA) function and Qᶜ is an additional term which has the following properties: (i) it includes all the three first-order Feynman diagrams for the proper polarizability, (ii) it incorporates in addition the coupled propagation of two particle-hole pairs, and (iii) it leads to an expression for the density-density response function which satisfies exactly the first- and third-frequency-moment sum rules. Detailed calculations of plasmon dispersion, damping, and compressibility have been made. Calculations have also been made for the complex dynamic local field G(k,ω) for arbitrary values of wave number and frequency. Comparison has been made with the available experimental data for Al (rₛ=2.0). A critique of the theory is presented.