Complete roughness and conductivity corrections for Casimir force measurement

Abstract

We consider detailed roughness and conductivity corrections to the Casimir force in the recent Casimir force measurement employing an atomic force microscope. The roughness of the test bodies---a metal plate and a sphere---was investigated with the atomic force microscope and the scanning electron microscope, respectively. It consists of separate crystals of different heights and a stochastic background. The amplitude of roughness relative to the zero roughness level was determined and the corrections to the Casimir force were calculated up to the fourth order in a small parameter (which is this amplitude divided by the distance between the two test bodies). Also the corrections due to finite conductivity were found up to fourth order in relative penetration depths of electromagnetic zero-point oscillations into the metal. The theoretical result for the configuration of a sphere above a plate taking into account both corrections is in excellent agreement with the measured Casimir force.