BOSONIC CLOUDS WITH ATTRACTIVE INTERACTION BEYOND THE LOCAL INTERACTION APPROXIMATION

We study the properties of a Bose-Einstein condensed cloud of atoms wi th negative scattering length confined in a harmonic trap. When a real istic non local (finite range) effective interaction is taken into acc ount, we find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density. This state is self-bound but its density can be quite low if the number N of ato ms is not too big. The transition between the two classes of solutions as a function of N can be either sharp or smooth according to the rat io between the range of the attractive interaction and the length of t he trap. A tight trap bads to a smooth transition. In addition to the energy and the shape of the cloud we study also the dynamics of the sy stem. In particular, we study the frequencies of collective oscillatio n of the Bose condensate as a function of the number of atoms both in the local and in the non local case. Moreover, we consider the dynamic s of the cloud when the external trap is switched off.