We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the K-39-Rb-87 isotopic pair is combined with preexisting observations of resonance patterns for K-40-Rb-87. Inter-isotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet and triplet potentials and establishes precisely near-threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the validity of the Born-Oppenheimer approximation at the present level of accuracy.
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