The third virial coefficient of unitary Bose gas

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 b₃ and the third virial coefficient a₃ 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 ν = π/6), one can push the full analytical estimate of b₃ and a₃ up to an error that is in practice negligible. (author)