The long range forces in AFM on Au(111), measured experimentally are explained as due to interaction with the image potential in the tip and the multiple images in both tip and sample of a single electron localized transiently on the Au(111) surface in front of the tipdue to the presence of the AFM tip and the image screening it provides.
Force versus relative tip-sample separation measured on Au(111) in the non-contact dynamic mode of atomic force microscopy in ultra-high vacuum conditions: black dots and crosses for W-tip on Au(111) (G. Cross et al. Phys. Rev. Lett. 80, 4685, 1998).
Full curve: theoretical data with the QND method for the force (nN) between the Au(111) surface and a W/W(110) tip versus the tip-sample distance. The tungsten atom at the tip apex is above a Au atom in the sample surface.
D. Drakova and G. Doyen, Phys. Stat. Sol. (b) 242, p R103 (2005).