Equation of State of Gases and Liquids at Low Temperatures

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Abstract
Application of a quantum-mechanical many-particle perturbation method is made to the determination of the equation of state of gases and liquids at low temperatures. The method utilizes the "nearest neighbor" expansion, which is a special case of Brueckner's "linked cluster" expansion. A description is given of condensation, mixed phases, the critical point and the critical temperature. It is shown that even the lowest-order approximation, which involves a relatively simple calculation, yields a physically reasonable theory of these phenomena, as well as the equation of state of the liquid phase. Specific calculations are presented for a system both above and below the critical temperature, and a description of collective phenomena in a quantum-mechanical system is given. The physical basis of the approach rests in a technique for inter-changing the order in which averages are taken, and putting "fluctuations" into higher-order terms, which in turn may be handled by the same method. At low temperatures, when the thermal de Broglie wavelength of the particles is large so that they are effectively "spread over large distances," such fluctuations due to particle-particle encounters are expected to be small.