Ground-state properties of a trapped Bose gas beyond the mean-field approximation

We study the effect of interatomic correlations beyond the mean-field approximation on the ground-state properties of a trapped Bose gas interacting through a repulsive potential. To this end we employ a variational procedure that is based on the energy functional derived, in the local-density approximation, using the low-density expansion for the ground-state energy of the homogeneous gas. We also make analytic estimates of the corrections due to the higher-order terms in the expansion. We find that corrections are of the order of $1%.$ However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.