  Two-dimensionality of the scattering events in a Bose-Einstein condensate
introduces a logarithmic dependence on density in the coupling constant
entering a mean-field theory of the equilibrium density profile, which becomes
dominant as the s-wave scattering length gets larger than the condensate
thickness. We analyze quantitatively the role of the form of the coupling
constant in determining the transverse profile of a condensate confined in a
harmonic pancake-shaped trap at zero temperature. We trace the regions of
experimentally accessible system parameters for which the cross-over between
different dimensionality behaviors may become observable through in situ
imaging of the condensed cloud with varying trap anisotropy and scattering
length.
