Ultracold physics with 3, 4, or 5 atoms

Recent studies will be reviewed [1-3], which utilize hyperspherical coordinates to treat few-body systems, concentrating on processes such as recombination, in which the initial state has 3 or more free particles in the continuum. Of particular interest are ultracold species with large two-body scattering lengths, for which universal behavior has been seen experimentally [4] that goes beyond the ordinary universality associated with the Efimov effect. The so-called three-body parameter, now understood to be universal for systems having van der Waals interactions, is readily interpreted using this theoretical framework, and predictions are made concerning A$+$A$+$B collisions as well as the homonuclear case A$+$A$+$A. Various aspects of the work presented have been carried out in collaboration with Jia Wang, Yujun Wang, Jose D'Incao, Javier von Stecher, and Brett Esry. \\[4pt] [1] J. Wang et al., Phys. Rev. Lett. \textbf{108}, 263001 (2012)\\[0pt] [2] J. Wang et al., Phys. Rev. A \textbf{84}, 052721 (2011)\\[0pt] [3] Y. Wang et al. arXiv:1207.6439 (2012).\\[0pt] [4] M. Berninger et al., Phys. Rev. Lett. \textbf{107}, 120401 (2011).