Correlation Energy of an Electron Gas at High Density

Abstract

The correlation energy of an electron gas at high density is evaluated up to terms of orders ${({r}_{s})}^{0}$ and $log{r}_{s}$. It is shown that the correlation energy to this order can be evaluated without using perturbation treatment. The result obtained coincides with the result of formal summation of apparently divergent series arising from small momentum transfer processes which has been discussed fully by Gell-Mann and Brueckner. The method to treat the small momentum transfer effect exactly is given by following the analogy of processes with well-known treatment of systems with Hamiltonians which are bilinear in creation and annihilation operators such as the neutral scalar pair theory. Some simple interpretations of the correlation energy to this order are also given.