The results of low energy crossed molecular beam experiments to determine differential elastic scattering cross sections over a wide angular range for symmetric rare gas pairs are presented. The scattering data are interpreted by finding parameters for a piecewise analytic potential form which is constrained to agree with semi‐empirical calculations of long range force constants. The validity of determining potentials from rainbow extrema locations and relative amplitudes as well as wide angle scattering is discussed and the restrictions imposed by the quantization of orbital angular momentum are also mentioned. The utility of second virial coefficient calculations is discussed. A discussion of reduced potential forms for the various systems suggests that a common form does not exist: the validity of a simple, universally valid combination rule is also questioned.