  We study the effects of many-body correlations in trapped ultracold atomic
Bose gases. We calculate the ground state of the gas using a ground-state
auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702
(2004)]. We examine the properties of the gas, such as the energetics,
condensate fraction, real-space density, and momentum distribution, as a
function of the number of particles and the scattering length. We find that the
mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result
of the kinetic energy as a function of the scattering length. We present
detailed QMC data for the various quantities, and discuss the behavior of GP,
modified GP, and the Bogoliubov method under a local density approximation.
