  In this paper we have presented the calculation of pair correlation functions
in a nematic phase for a model of spherical particles with the long-range
anisotropic interaction from the mean spherical approximation(MSA) and the
Percus-Yevick (PY) integral equation theories. The results found from the MSA
theory have been compared with those found analytically by Holovko and
Sokolovska (J. Mol. Liq. $\bf 82$, 161(1999)). A free energy functional which
involves both the symmetry conserving and symmetry broken parts of the direct
pair correlation function has been used to study the properties of the nematic
phase. We have also examined the possibility of constructing a free energy
functional with the direct pair correlation function which includes only the
principal order parameter of the ordered phase and found that the resulting
functional gives results that are in good agreement with the original
functional. The isotropic-nematic transition has been located using the grand
thermodynamic potential. The PY theory has been found to give nematic phase
with pair correlation function harmonic coefficients having all the desired
features. In a nematic phase the harmonic coefficient of the total pair
correlation function $h({\bf x_1},{\bf x_2})$ connected with the correlations
of the director transverse fluctuations should develop a long-range tail. This
feature has been found in both the MSA and PY theories.
