Abstract
We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this renormalized interaction to a degenerate unitary Bose gas to study its stationary properties and elementary excitations using the mean-field theory and the hyperspherical method. Since the scattering length is no longer a relevant length scale at unitarity, universal properties are obtained that depend only on the average particle density. Our treatment shows that the universal relations for the total energy and for the two-body contact are $E/N=12.67\hbar^2\langle n^{2/3}\rangle/2m$ and $C_{2}/N=11.8\langle n^{1/3}\rangle$ respectively.
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