  We consider the Bose-Einstein condensation of atoms in a trap where the
density of particles is so high that the low density approach of Gross and
Pitaevskii will not be applicable. For this purpose we use the slave boson
representation which is valid for hard-core bosons at any density. This
description leads to the same results as the Gross-Pitaevskii approach in the
low density limit, but for higher densities, it predicts the depletion of the
order parameter field condensate in the regions where the density of the atomic
cloud is high.
