A simplified version of the WCA theory allows us to start from an observed structure factor and derive a core potential and gradient at an effective collision diameter. The quality of fit and internal consistency checks indicate that the method works for liquids of inert gases, certain simple metals and the noble metals. It is less accurate, although still useful, for transition metals and lanthanides. In the latter case, there is a peaking in core diameter at Eu(4f76s2) as the series is traversed. This has no counterpart in the transition metal series which shows a steady decrease (although with an anomalously small value for Cr(3d54s1)).