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

Ultracold atoms are increasingly used for high precision experiments that can be utilized to extract accurate scattering properties. This calls for a stronger need to improve on the accuracy of interatomic potentials, and in particular the usually rather inaccurate inner-range potentials. A boundary condition for this inner range can be conveniently given via the accumulated phase method. However, in this approach one should satisfy two conditions, which are in principle conflicting, and the validity of these approximations comes under stress when higher precision is required. We show that a better compromise between the two is possible by allowing for an adiabatic change of the hyperfine mixing of singlet and triplet states for interatomic distances smaller than the separation radius. A mass scaling approach to relate accumulated phase parameters in a combined analysis of isotopically related atom pairs is described in detail and its accuracy is estimated, taking into account both Born-Oppenheimer and WKB breakdown. We demonstrate how numbers of singlet and triplet bound states follow from the mass scaling.