Abstract
We calculate the first-order perturbation correction to the ground-state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With $c$ denoting the interaction strength, we find that, for a large number of particles $N$, the $1/c$ correction to the ground-state energy increases as ${N}^{5/2}$, in contrast to the unperturbed Tonks-Girardeau value that is proportional to ${N}^{2}$. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground-state energy and reproduces the zero temperature thermodynamics obtained by a local-density approximation.
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