Correlation Functions of Dense Gases and Liquids

One of the most useful approaches to the theory of dense gases and liquids is the study of correlation (or distribution) functions. We here apply a theoretical method for calculating all the correlation functions in an inhomogeneous system. We reproduce the virial expansion in an inhomogeneous system by using the solution of the one-point correlation function or the density function. Then, we derive the pair correlation function by using the two-point correlation function. We also reveal the solution of the direct correlation function in the Ornstein-Zernike equation. We find that the direct correlation function expanded in a power series in the density relates to the virial expansion.