Structure and stability of bosonic clouds: alkali atoms with negative scattering length

We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density when non locality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number $N$ of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system as the strength of the effective interaction increases with $N$.