The statistical thermodynamics of a gas with long and short-range forces

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Abstract
If a gas has long-range Coulomb interactions and short-range interaction, e.g. bard core repulsions, three lengths enter the problem: the radius of the repulsive core, d, the mean interparticle distance, r o, and δD the Debye-Huckel radius, (8πNc 2/VkT)−1/2. This paper presents a method of obtaining the equation of state when, in the first instance δD≫r o d, which enables one to obtain higher-order terms in a simple way, and these are calculated. In order to relax the condition δD≫r 0, a variational method is employed which shows that the usual Debye-Huckel theory makes the grand thermodynamic potential an extremum, the exact result lying between the perfect gas and the Debye-Huckel gas. The results enable one to estimate the contributions to the virial expansion of collective oscillations and of shielded particle encounters, whilst avoiding difficulties such as are associated with redundant coordinates. The extension of the results to the quantum mechanical case are briefly commented upon.