Pair Distribution for a Cell-Model Liquid

The pair distribution function for a cell-model liquid has been derived by Lund in an earlier work in the form of an integral equation which depends upon the cell-center distribution function and the cell model. From this integral equation an approximate integral equation is obtained by substituting a function, linearly dependent upon the molecular pair distribution function and a variable parameter λ, for the cell-center distribution function. This approximate integral equation is solved for the molecular pair distribution and λ is shown to depend upon the difference between temperature and the critical temperature. Although the exact numerical solution of the molecular pair distribution is not practical because of a great number of arbitrary constants of integration, the stability of phase can be noted above and below the critical point. The solution for the molecular pair distribution function is shown to agree with the Ornstein-Zernike theory in the neighborhood of the critical point.