Representation of pair correlations in nematics

A complete expansion of equilibrium pair correlation functions for a uniaxi al nematic phase composed of axially symmetric, non-polar and chiral molecu les is proposed. Full advantage is taken of the symmetry of the nematic sta te and of the molecules. The explicit analysis and classification of the te rms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Bern e mesogen. The theory is contrasted with the commonly used approach employi ng invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy i s resolved.