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We report on measurements of three-body recombination rates in an ultracold gas of Li atoms in the extremely nonuniversal regime where the two-body scattering length vanishes. We show that the rate is well defined and can be described by two-body parameters only: the scattering length and the effective range . We find the rate to be energy independent, and, by connecting our results with previously reported measurements in the universal limit, we cover the behavior of the three-body recombination in the whole range from weak to strong two-body interactions. We identify a nontrivial magnetic field value in the nonuniversal regime where the rate should be strongly reduced.

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