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We develop a variational theory of the crossover from the one-dimensional(1D) regime to the 3D regime for ultra-cold Bose gases in thin waveguides.Within the 1D regime we map out the parameter space for fermionization, whichmay span the full 1D regime for suitable transverse confinement.Comment: 4 pages, 2 figure

Crossover from One to Three Dimensions for a Gas of Hard-Core Bosons