QUASI-PARTICLE EFFECTIVE-MASS FOR THE 2-DIMENSIONAL AND 3-DIMENSIONALELECTRON-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 Sjolander-Stott theory a nd enforce the Friedel sum rule by adjusting the effective electron ma ss in a scattering calculation. In three dimensions (3D) our effective mass is a monotonically decreasing function of r(s) throughout the wh ole metallic domain, as implied by the most recent numerical results. In two dimensions (2D) we obtain reasonable agreement with the experim ental data, as well as with other calculations based on the Fermi-liqu id theory. We also present results of a variety of different treatment s for the effective mass in 2D and 3D.