France'
- '$^2$MESA+ Research Institute, University of Twente, P.O. 217, 7500 AE Enschede, The Netherlands'
author:
- 'I. Pirozhenko$^1$, A. Lambrecht$^1$, and V. B. Svetovoy$^2$'
title: Sample dependence of the Casimir force
---

Introduction\[Sec1\]
====================

The Casimir force [@Cas48] between uncharged metallic plates attracts considerable attention as a macroscopic manifestation of the quantum vacuum [@Mil94; @Mos97; @Mil01; @Kar99; @Bor01]. With the development of microtechnologies, which routinely control the separation between bodies smaller than 1 $\mu m$, the force became a subject of systematic experimental investigation. Modern precision experiments have been performed using different techniques such as torsion pendulum [@Lam97], atomic force microscope (AFM) [@Moh98; @Har00], microelectromechanical systems (MEMS) [@Cha01; @Dec03a; @Dec03b; @Dec05; @Ian04; @Ian05] and different geometrical configurations: sphere-plate [@Lam97; @Har00; @Dec03b], plate-plate [@Bre02] and crossed cylinders [@Ede00]. The relative experimental precision of the most precise of these experiments is estimated to be about 0.5% for the recent MEMS measurement [@Dec05] and 1% for the AFM experiments [@Har00; @Cha01].

In order to come to a valuable comparison between the experiments and the theoretical predictions, one has to calculate the force with a precision comparable to the experimental accuracy. This is a real challenge to the theory because the force is 