  We theoretically analyze dissociation of a harmonically trapped Bose-Einstein
condensate of molecular dimers and examine how the spatial inhomogeneity of the
molecular condensate affects the conversion dynamics and the atom-atom pair
correlations in the short-time limit. Both fermionic and bosonic statistics of
the constituent atoms are considered. Using the undepleted molecular-field
approximation, we obtain explicit analytic results for the asymptotic behavior
of the second-order correlation functions and for the relative number squeezing
between the dissociated atoms in one, two and three spatial dimensions.
Comparison with the numerical results shows that the analytic approach employed
here captures the main underlying physics and provides useful insights into the
dynamics of dissociation for conversion efficiencies up to 10%. The results
show explicitly how the strength of atom-atom correlations and relative number
squeezing degrade with the reduction of the size of the molecular condensate.
