Hartree-Fock calculations of Bose-Einstein condensation of Li-7 atoms in a harmonic trap for T>0

A self-consistent mean-field (Hartree-Fock) theory for bosons for temperature T > 0 is used to compute the spatial distribution of Li-7 atoms in a harmonic trap. In light of recent experimental observations at Rice University, the goal is to establish the extent to which Bose-Einstein condensation (BEG) is possible with Li-7 atoms, and to deduce the most effective signature of BEC from observations of the spatial profile. Our Hamiltonian, which includes the anisotropic external trap field and atom atom interactions, is equivalent to that used previously for trapped atomic hydrogen. However, the attractive atom-atom interaction creates a localized well near the origin and precludes use of the usual local-density approximation. Eigenfunctions for the lowest orbitals are obtained by iteration. The total density is obtained from a sum with Bose population factors for these explicitly computed orbitals, together with analytic sums for unperturbed (ideal gas) orbitals for higher-lying states. For a small range of temperatures near T-c, it is found that the atomic cloud exhibits a spatially localized ''condensate peak'' composed primarily of atoms in the ground state. For lower T, such that more than 800-1200 atoms are in the ground state, the calculations become numerically unstable as found previously for T = 0. Computational results for the collisional spin-flip ejection rate for T near T-c and an estimate of the fluctuation in the number of atoms in the condensate are presented.