Dynamic correlations in an electron gas. I. First-order perturbation theory

Properties of a uniform electron gas in the jellium model are investigated by means of perturbation theory in the electron-electron interaction. First-order diagrams for the proper polarizability are evaluated for arbitrary wave vector and frequency, their singularities and analytical properties are examined, and a reliable numerical procedure for calculating them is established. Quantities such as the dielectric function $\epsilon (k,\omega )$, the dynamic-complex-local-field factor $G(k,\omega )$, dynamic structure factor $S(k,\omega )$, static structure factor $S\left(k\right)\mathrm{}$, and pair correlation function $g\left(r\right)\mathrm{}$ are calculated and compared with the corresponding quantities in the random-phase approximation (RPA). The plasmon dispersion in a wide range of momentum transfers and the shape of $S(k,\omega )$ versus $\omega$ agree well with experimental data for Al, indicating that the first-order theory is reasonable even at $r_s$ as large as 2. Significant improvement over RPA is observed.