Solution of the Born-Green-Yvon Equation for a High Density One-Component Plasma

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Abstract
Recent Monte Carlo calculations of the radial distribution function of a one-component, classical, plasma are shown to be well approximated by solutions of the Born-Green-Yvon integral equation, almost up to densities where there is definite short range order. The Born-Green-Yvon solutions appear to be somewhat better than the corresponding solutions of the Percus-Yevick and convolution-hypernetted-chain equations. The Born-Green-Yvon equation is further shown to be related to the original Debye-Hückel equation for an ionic solution. It differs from the latter equation by accounting for more short range correlations, a feature that makes it more accurate at higher densities. The special methods used to obtain numerical solutions of the Born-Green-Yvon equation at high density are briefly discussed.

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