The kinetic and interaction energies of a trapped Bose gas: beyond the mean field

The kinetic and interaction energies of a three-dimensional (3D) dilute ground-state Bose gas confined in a trap are calculated beyond a mean-field treatment. They are found to depend on the pairwise interaction trough two characteristic lengths: the first, a, is the well-known scattering length and the second, b, is related to the latter by b = a - lambdapartial derivativea/partial derivativelambda with lambda being the coupling constant. Numerical estimations show that the pairwise interaction energy of a dilute gas of alkali atoms in a trap is negative (in spite of the positive scattering length); its absolute value is found by about the order of magnitude larger than that of the mean-field interaction energy that corresponds to the last term in the Gross-Pitaevskii (GP) functional. (C) 2002 Published by Elsevier Science B.V.