  We introduce a density-functional formalism based on the Parsons-Lee and the
generalized van der Waals theories in order to describe the thermodynamics of
anisotropic particle systems with steric interactions. For ellipsoids of
revolution, the orientational distribution function is obtained by minimizing
the free energy functional and the equations of state are determined. The
system exhibits a nematic-isotropic discontinuous transition, characterized by
a phase separation between nematic and isotropic phases at finite as well low
packing fractions. The model presents a phase behavior which is in good
agreement with Monte-Carlo simulations for finite aspect ratios.
