Three-Body Recombination into Deep Bound States in a Bose Gas with Large Scattering Length

An effective field theory for the three-body system with large two-body scattering length $a$ is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant $\alpha$ is calculated to first order in the short-distance interactions that allow the recombination. For $a<\mathrm{}0\mathrm{}$, the dimensionless combination $m\alpha /\left(ħa^4\right)$ is a periodic function of $\ln |a|$ that exhibits resonances at values of $a$ that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when $a$ becomes large and negative.