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The statistical properties of patch electric fields due to a polycrystallinemetal surface are calculated. The fluctuations in the electric field scale like1/z^2, when z >> w, where z is the distance to the surface, and w is thecharacteristic length scale of the surface patches. For typical thermallyevaporated gold surfaces these field fluctuations are comparable to the imagefield of an elementary charge, and scale in the same way with distance to thesurface. Expressions for calculating the statistics of the inhomogeneousbroadening of Rydberg atom energies due to patch electric fields are presented.Spatial variations in the patch fields over the Rydberg orbit are found to beinsignificant.

Energy shifts of Rydberg atoms due to patch fields near metal surfaces