Bose-Einstein Condensation in Trapped Atomic Gases

We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio {η} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ψ₀. We find that for $a<0$ and η1 it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For η1 a negative scattering length prevents the formation of the condensate. If $a>0$, then an increase of density is accompanied by the evolution of ψ₀ to a comparatively wide quasihomogeneous distribution.