Probability Density of Electron Separation in a Uniform Electron Gas

We briefly report here a new method of approach to the correlation problem in a uniform electron gas, within the framework of density matrix theory. The earlier important paper of Mayer (1955) using this method has been shown independently by Tredgold (1957) and Koppe (1957) to lead to a variational scheme which is not complete, due to difficulties associated with subsidiary conditions. We propose here a uniform method of describing the electron correlations throughout the entire density range, and show that our method does indeed lead to accurate results in the high and low density limits. We hope to report detailed calculations for intermediate densities later, but at least we show in this note how a reasonably accurate picture of the correlation effects may be obtained over a wide density range…