Quasiparticle Effective Mass for the Two- and Three-Dimensional Electron Gas

We calculate the quasiparticle effective mass for the electron gas in two and three dimensions in the metallic region. We employ the single particle scattering potential coming from the Sj\"{o}lander-Stott theory and enforce the Friedel sum rule by adjusting the effective electron mass in a scattering calculation. In 3D our effective mass is a monotonically decreasing function of $r_s$ throughout the whole metallic domain, as implied by the most recent numerical results. In 2D we obtain reasonable agreement with the experimental data, as well as with other calculations based on the Fermi liquid theory. We also present results of a variety of different treatments for the effective mass in 2D and 3D.