Computations of Radial Distribution Functions for a Classical Electron Gas

Abstract

The radial distribution functions $g$ for a classical electron gas computed using the Percus-Yevick (PY) equation, convolution hypernetted chain (CHNC) equation, and the Broyles-Sahlin (BS) method, have been compared with the Debye-Hückel (DH) theory. The quantities $E\equiv \frac{\overline{U}}{\mathrm{Nkt}}$ and $P\equiv \frac{p}{\overline{n}\mathrm{kT}}$ have been computed from these $g\text{'}\mathrm{s}$. Computations have been made for values of $\theta$ of 20, 10, 5, 3, and 1; $\theta =\frac{\mathrm{kTa}}{q^2}$, where $a$ is the ion sphere radius. The PY and BS results show the best agreement, particularly at $\theta <3\mathrm{}$. The BS method has been of particular value in this study of a long-range potential. In the range of $\theta$ studied, $g$ never exceeds one, that is, there is no oscillatory behavior of $g$.