Abstract
We discuss the free energy of an electron gas with the long-range Coulomb interaction by using the dielectric-response function which includes the higher-order exchange processes. Our result reproduces earlier results of Gell-Mann and Brueckner; Nozières and Pines; Hubbard; Englert and Brout; and others as special cases. The longitudinal spin-fluctuation effect is included in the present result, but its role seems to be significantly different from what is expected in the Hubbard-type model due to the large cross effect of the spin fluctuation and charge fluctuation even in the paramagnetic state.