  A Hartree-Fock and Hartree-Fock-Bogoliubov study of a few body system of
spatially separated charge carriers was carried out. Using these variational
states, we compute an approximation to the correlation energy of a finite
system of electron-hole pairs. This energy is shown as a function of the
Coulomb coupling and the interplane distance. We discuss how the correlation
energy can be used to theoretically determine the formation of indirect
excitons in semiconductors which is relevant for collective phenomena such as
Bose-Einstein condensation (BEC).
