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Ultracold atoms are increasingly used for high precision experiments that canbe utilized to extract accurate scattering properties. This calls for astronger need to improve on the accuracy of interatomic potentials, and inparticular the usually rather inaccurate inner-range potentials. A boundarycondition for this inner range can be conveniently given via the accumulatedphase method. However, in this approach one should satisfy two conditions,which are in principle conflicting, and the validity of these approximationscomes under stress when higher precision is required. We show that a bettercompromise between the two is possible by allowing for an adiabatic change ofthe hyperfine mixing of singlet and triplet states for interatomic distancessmaller than the separation radius. A mass scaling approach to relateaccumulated phase parameters in a combined analysis of isotopically relatedatom pairs is described in detail and its accuracy is estimated, taking intoaccount both Born-Oppenheimer and WKB breakdown. We demonstrate how numbers ofsinglet and triplet bound states follow from the mass scaling.

Predicting scattering properties of ultracold atoms: adiabatic accumulated phase method and mass scaling