Calculations of Bose-Einstein Condensation of ^7Li atoms in a Harmonic Trap

A self-consistent mean-field theory for bosons for T>0 is used to reconcile predictions of collapse with recent observations of Bose-Einstein condensation of 7Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the anisotropic external trap field and atom-atom interactions are obtained by an iteration process. A sum over the Bose distribution, and the ``alternating direction implicit'' algorithm are used. Near Tc, the ensemble exhibits a localized condensate composed of atoms in the few lowest states. For lower T, numerical instability indicates collapse to a more dense phase.