Higher-order conductivity corrections to the Casimir force

Full text follows: Considerable recent attention has been focused on the new experiments on measuring the Casimir force. To be confident that experimental data fit theory at a level of several percent, a variety of corrections to the ideal expression for the Casimir force should be taken into account. One of the main corrections at small separations between interacting bodies is the one due to finite conductivity of the boundary metal. This correction has its origin in non-zero penetration depth δ0 of electromagnetic vacuum oscillations into the metal (for a perfect metal of infinitely large conductivity δ0 = 0). The other quantity of the dimension of length is the space separation a between two plates or a plate and a sphere. Their relation δ0/a is the natural perturbation parameter in which powers the corrections to the Casimir force due to finite conductivity can be expanded. Such an expansion works good for all separations a >> δ0 (i.e. for separations larger than 100-150 nm). The first-order term of this expansion was calculated almost forty years ago, and the second-order one in 1985 [1]. These two terms are not sufficient for the comparison of the theory with precision modern experiments. In this talk we report the results of paper [2] where the third- and fourth-order terms in δ0 /a expansion of the Casimir force were calculated first. They gave the possibility to achieve an excellent agreement of a theory and experiment. (author)