BOSE-EINSTEIN CONDENSATION IN A TRAP - THE CASE OF A DENSE CONDENSATE

We consider the Bose-Einstein condensation of atoms in a trap where th e density of particles is so high that the low-density approach of Gro ss [J. Math. Phys. (N.Y.) 4, 195 (1963)] and Pitaevskii (V. L. Ginsbur g and L. P. Pitaevskii, Zh. Eksp. Teor. Fit. 34, 1240 (1958) [Sov. Phy s. JETP 7, 1858 (1958)]) will not be applicable. For this purpose we u se the slave boson representation which is valid for hard-core bosons at any density. This description leads to the same results as the Gros s-Pitaevskii approach in the low-density limit, but for higher densiti es, it predicts the depletion of the condensate in the regions where t he density of the atomic cloud is high.