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Integral Equation Theory for Pair Correlation Functions in a Crystal

A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving parts are calculated using the integral equation theory of homogeneous fluids. The symmetry broken part of the direct pair correlation function is calculated from a series written in powers of order parameters and that of the total pair correlation function from the Ornstein- Zernike equation. The results found for a two-dimensional hexagonal lattice show that the method provides accurate and detailed informations about the pair correlation functions in a crystal.