  Bose-Einstein condensates with tunable interatomic interactions have been
studied intensely in recent experiments. The investigation of the collapse of a
condensate following a sudden change in the nature of the interaction from
repulsive to attractive has led to the observation of a remnant condensate that
did not undergo further collapse. We suggest that this high-density remnant is
in fact the absolute minimum of the energy, if the attractive atomic
interactions are nonlocal, and is therefore inherently stable. We show that a
variational trial function consisting of a superposition of two distinct
gaussians is an accurate representation of the wavefunction of the ground state
of the conventional local Gross-Pitaevskii field equation for an attractive
condensate and gives correctly the points of emergence of instability. We then
use such a superposition of two gaussians as a variational trial function in
order to calculate the minima of the energy when it includes a nonlocal
interaction term. We use experimental data in order to study the long range of
the nonlocal interaction, showing that they agree very well with a
dimensionally derived expression for this range.
