THE ROLE OF DIMENSIONALITY IN THE STABILITY OF A CONFINED CONDENSED BOSE-GAS

We study analytically the ground-state stability of a Bose-Einstein co ndensate (BEG) confined in an harmonic trap with repulsive or attracti ve zero-range interaction by minimizing the energy functional of the s ystem. In the case of repulsive interaction the BEC mean radius grows by increasing the number of bosons, instead in the case of attractive interaction the BEC mean radius decreases by increasing the number of bosons: to zero if the system is one-dimensional and to a constant min imum radius, with a maximum number of bosons, if the system is three-d imensional.