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 eta of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function psi(0). We find that for a < 0 and eta << 1 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 eta >> 1 a negative scattering length prevents the formation of the condensate. If a > 0, then an increase of density is accompanied by the evolution of psi 0 to a comparatively wide quasihomogeneous distribution.