Yvan Castin, Félix Werner
By unitary Bose gas we mean a system composed of spinless bosons with s-wave interaction of infinite scattering length and almost negligible (real or effective) range. Experiments are currently trying to realize it with cold atoms. From the analytic solution of the three-body problem in a harmonic potential, and using methods previously developed for fermions, we determine the third cumulant (or cluster integral) b_3 and the third virial coefficient a_3 of this gas, in the spatially homogeneous case, as a function of its temperature and the three-body parameter R_t characterizing the Efimov effect. A key point is that, converting series into integrals (by an inverse residue method), and using an unexpected small parameter (the three-boson mass angle nu=pi/6), one can push the full analytical estimate of b_3 and a_3 up to an error that is in practice negligible.
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http://arxiv.org/abs/1212.5512
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