  We study the Bose-Einstein condensation for a cloud of $^7$Li atoms with
attractive nonlocal (finite-range) interaction in a harmonic trap. In addition
to the low-density metastable branch, that is present also in the case of local
interaction, a new stable branch appears at higher densities. For a large
number of atoms, the size of the cloud in the stable high-density branch is
independent of the trap size and the atoms are in a macroscopic quantum
self-trapped configuration. We analyze the macroscopic quantum tunneling
between the low-density metastable branch and the high-density one by using the
istanton technique. Moreover we consider the decay rate of the Bose condensate
due to inelastic two- and three-body collisions.
