Correlations in a two-dimensional electron system

The correlation energy per particle (expressed in rydbergs) of a two-dimensional electron gas is calculated by summing the ring diagrams. For high densities, this is found to be of the form $C+D{r}_s\ln r_s+O\left(r_s\right)$, where $r_s$ is a dimensionless parameter such that $r_s^{-2\mathrm{}}$ is proportional to the number of electrons per unit area. The value of $D$ is -0.172 and that of $C$ is -0.38 ± 0.04, the latter involves a numerical evaluation. By the same methods, we have also calculated the difference in total energy of the nonmagnetic and ferromagnetic states and we find for $r_s>2.3\mathrm{}$ the system may be ferromagnetic. We have also obtained some exact relationships between the pair correlation function at zero separation and the asymptotic behavior of the structure factor and the momentum distribution function. These are of interest in relation to scattering experiments.