  We present a theoretical study of the ground state of a Bose-Einstein
condensate with repulsive inter-particle interactions in a double-well
potential, using a restricted variational principle. Within such an approach,
there is a transition from a single condensate to a fragmented condensate as
the strength of the central barrier of the potential is increased. We determine
the nature of this transition through approximate analytic as well as numerical
solutions of our model in the regime where the inter-particle interactions can
be treated perturbatively. The degree of fragmentation of the condensate is
characterized by the degrees of first-order and second-order spatial coherence
across the barrier.
