  This paper presents the Thomas-Fermi approach generalized to consider the
particle correlations in many-body systems with non-Coulomb interaction
potentials. The key points of the generalization consist in using integral
formulation and extracting the pair distribution function. The latter has been
found to obey the integral equation which, in the classical limit, is reduced
to the well-known equation of Bogoliubov. So, the approach presented gives the
way of taking into account interactions in the quantum many-body systems beyond
the weak coupling perturbation theory.
