Mean-field theory of an atomic Bose-Einstein condensate

Mean-field theory for an atomic Bose-Einstein condensate is re-examined and two new boundary conditions are introduced that take account of the impenetrability of the atomic cores. The dominant part of the resulting effective atom-atom interaction arises from the attractive part of the potential and it is seen to differ substantially from that (proportional to the scattering length) used in Gross-Pitaevskii theory. This difference is described in detail for the case of a 'hard-sphere plus attractive square-well' model potential. The consequences of the new interaction in the quantum dynamics of a rubidium condensate are studied and it is shown that, while a stable stationary S state does not exist, the condensate is contained in its trap in a state of quasi-equilibrium with small rapid variations in space and time