Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

Combining the measured binding energies of four of the most weakly bound rovibrational levels of the ${}^{87}{\mathrm{Rb}}_2$ molecule with results of two other recent high-precision experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. We predict scattering lengths, clock shifts, and Feshbach resonances with an unprecedented level of accuracy. Two of the Feshbach resonances occur at easily accessible magnetic fields in mixed-spin channels. One is related to a $d$-wave shape resonance.