Theory of Classical Fluids: Hyper-Netted Chain Approximation, I Formulation for a One-Component System
Theory of Classical Fluids: Hyper-Netted Chain Approximation, I Formulation for a One-Component System
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经典流体理论：超网络链近似，I 单组分系统公式
DOI：
10.1143/ptp.20.920
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发表时间：
1958
影响因子：
--
通讯作者：
T. Morita
中科院分区：
文献类型：
--
作者：
T. Morita
为了将自由能和径向分布函数的团簇展开式应用于密度不小的气体或液体，已经提出了几种方法来考虑对应于大图的项。本文提出了一种近似法，它包括过去的近似法，即第一或第二近似法，它考虑了用傅里叶变换容易计算的图，在我们的近似法中所考虑的图都是从一条线或一个环开始，用西瓜代替组成线的一系列过程所构成的图;在更换的过程中，西瓜中的一条线也可以用西瓜来代替。这种近似称为超网链近似，在这种近似下得到的自由能和径向分布函数的公式由方程给出。(29（30）(35)给出了自由能和径向分布函数的“超网链”展开式。本文给出了超网链近似的另一组公式，并与过去离子体系的理论作了比较，在以后的论文中将给出其在实际问题中的应用。
Several attemps have been presented to take account of terms corresponding to large graphs in the cluster expansion formulae for the free energy and the radial distribution function, for the purpose of applying them to a gas of not small density or to a liquid. In this paper is proposed an approximation, which includes the approximations in the past as the first or second approximation, by taking account of graphs which can be easily evaluated by means of the Fourier transformation.The graphs taken into account in our approximation are all those which can be constructed starting from a line or a ring by a sequence of the processes to replace a constituent line by a watermelon ; in the course of the replacement, a line in a watermelon is also allowed to be replaced by a watermelon. The approximation will be called the hyper-netted chain approximation.The formulae obtained in this approximation for the free energy and the radial distribution function are given by eqs. (29′)−(30′) and eq. (35), which demand the solution of a recurrence equation containing the Fourier transformations.The expansion formulae for the free energy and the radial distribution function by means of the “hyper-netted chains” are also presented. They contain the results in the hyper-netted chain approximation as their leading terms.Another set of the formulae in the hypere-netted chain approximation is given and compared with the theories for ionic system in the past.Applications to practical problems will be given in forthcoming papers.