On Direct and Pair Correlation Functions of the Crystalline State and the Crystal‐Liquid Phase Boundary

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Abstract
Assuming a non‐constant single particle density suitable to describe a bulk crystalline state and a crystal‐liquid phase boundary, the coupled ORNSTEIN‐ZERNIKE and PERCUS‐YEVICK equation to determine the direct and the pair correlation for a one‐component LENNARD‐JONES system are approximately solved. A hard core reference system is defined within a perturbation treatment; the corrections resulting from the true interaction can be calculated straighforward if the hard core solutions are known. The approximation involves a new class of exact solutions for the limiting case of strongly localized single particle densities.