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So far there has been no reliable method to calculate the Casimir force atseparations comparable to the root-mean-square of the height fluctuations ofthe surfaces. Statistical analysis of rough gold samples has revealed thepresence of peaks considerably higher than the root-mean-square roughness.These peaks redefine the minimum separation distance between the bodies and canbe described by extreme value statistics. Here we show that the contribution ofthe high peaks to the Casimir force can be calculated with a pairwise additivesummation, while the contribution of asperities with normal height can beevaluated perturbatively. This method provides a reliable estimate of theCasimir force at short distances, and it solves the significant, so farunexplained discrepancy between measurements of the Casimir force between roughsurfaces and the results of perturbation theory. Furthermore, we illustrate theimportance of our results in a technologically relevant situation.

Roughness correction to the Casimir force at short separations: Contact distance and extreme value statistics