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We theoretically investigate the equation of state and Tan's contact of anon-degenerate three dimensional Bose gas near a broad Feshbach resonance,within the framework of large-$N$ expansion. Our results agree with thepath-integral Monte Carlo simulations in the weak-coupling limit and recoverthe second-order virial expansion predictions at strong interactions and hightemperatures. At resonance, we find that the chemical potential and energy aresignificantly enhanced by the strong repulsion, while the entropy does notchange significantly. With increasing temperature, the two-body contactinitially increases and then decreases like $T^{-1}$ at large temperature, andtherefore exhibits a peak structure at about $4T_{c0}$, where $T_{c0}$ is theBose-Einstein condensation temperature of an ideal, non-interacting Bose gas.These results may be experimentally examined with a non-degenerate unitary Bosegas, where the three-body recombination rate is substantially reduced. Inparticular, the non-monotonic temperature dependence of the two-body contactcould be inferred from the momentum distribution measurement.

Equation of state and contact of a strongly interacting Bose gas in the normal state