Density response in an electron liquid

Based on the Mori memory-function approach, the theory of Vashishta and singwi for the density response function of the electron liquid is analyzed and modified. The effects of the following modifications are studied numerically: (i) introduction of a frequency-dependent local field factor, such that both the compressibility sum rule and the third-frequency-moment relation are satisfied; (ii) introduction of the proper electron-momentum distribution in the Lindhard function, yielding the correct Compton profiles at large momentum transfer, and removing certain difficulties associated with the kinetic contributions to the response function; (iii) introduction of the single-particle lifetime. The dynamic structure factor $S(\overrightarrow{\mathrm{q}},\omega )$ is calculated and compared with earlier calculations and with the experimental data of Platzman and Eisenberger.