Self-Binding Transition in Bose Condensates with Laser-Induced ``Gravitation''

In our recent publication (D. O'Dell, et al, Phys. Rev. Lett. 84, 5687 (2000)) we proposed a scheme for electromagnetically generating a self-bound Bose-Einstein condensate with 1/r attractive interactions: the analog of a Bose star. Here we focus upon the conditions neccessary to observe the transition from external trapping to self-binding. This transition becomes manifest in a sharp reduction of the condensate radius and its dependence on the laser intensity rather that the trap potential.