Thermodynamic Properties of an Electron Plasma

The thermodynamic properties of an electron plasma are investigated on the basis of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy equation. The correlation energy has been calculated up to the ${\epsilon }^2$ term ($\epsilon$ is the standard plasma parameter) in terms of an exact solution of the binary correlation function taking into account the short-range collision effect. The contribution of ternary correlations to the correlation energy has been determined in lowest order, which turns out to be of the second order in $\epsilon$. The total sum of the corrections due to the short-range collision effect and the ternary correlation effect is found to be in agreement with the result obtained by Abe, Bowers, and Salpeter within the regime of Gibbs' statistical thermodynamics. Although the appearance of the binary correlation function obtained in the present studies differs from those derived by Bowers-Salpeter and by O'Neil-Rostoker, it is shown that all of these expressions are essentially equivalent. According to the present analysis, however, it is proven that these expressions do not describe correctly the way in which correlation effects diminish at large distances and therefore the statement made by DeWitt saying that $g\left(x\right)\mathrm{}\sim \frac{1}{8}\left(\ln 3\right){\epsilon }^2\exp (-k_{D}r)$ as $r\to \infty$ is not correct.