Bose-Einstein Condensation of Atoms in a Trap
  We point out that the local density approximation (LDA) of Oliva is an adaptation of the Thomas-Fermi method, and is a good approximation when $\varepsilon = \hbar\omega/kT <<1$. For the case of scattering length $a > 0$, the LDA leads to a quantitative result (14') easily checked by experiments. Critical remarks are made about the physics of the many body problem in terms of the scattering length $a$. 
T. T. Chou, Chen Ning Yang, and L. H. Yu