Analysis of ultracold Rb + Yb collisions

We present predictions for s-wave scattering lengths and bound state energies for all 14 isotopic combinations of Rb and Yb. Groups at NIST/JQI (Porto \textit{et al.}) and in D\"{u}sseldorf (G\"{o}rlitz \textit{et al.}) are currently pursuing experiments using this system. The D\"{u}sseldorf group has recently observed phase separation at thermal temperatures of the co-trapped $^{87}$Rb + $^{174}$Yb system, indicating a very strong interaction. In contrast, they observed low thermalization rates in co-trapped $^{87}$Rb + $^{170}$Yb, indicating a very weak interaction. These two data points provide bounds on scattering lengths. The universal properties of van der Waals potentials, using our estimate of the C$_{6}$ coefficient, and mass scaling then allows a determination of the number of bound states in the potential, all s-wave scattering lengths, and energies of weakly-bound states. The calculated scattering lengths range from very large and positive to very large and negative, with every qualitatively different regime in-between represented.