Beyond the Gross-Pitaevskii approximation: Local density versus correlatedbasis approach for trapped bosons

We study the ground state of a system of Bose hard spheres trapped in an is otropic harmonic potential to investigate the effect of the interatomic cor relations and the accuracy of the Gross-Pitaevskii equation. We compare a l ocal-density approximation, based on the energy functional derived from the low-density expansion of the energy of the uniform hard-sphere gas, and a correlated wave-function approach, which explicitly introduces the correlat ions induced by the potential. Both higher-order terms in the low-density e xpansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becom es similar to that attained in recent experiments (N similar to 10(7)). [S1 050-2947(99)00109-2].