d_0/d_0$. Finally, at separations $d>100\; nm$ the force is rather weak, and the error is dominated by thermomechanical noise as it was explained in former studies [@Zwo08b].

Evaluation of the force based on the Lifshitz theory requires the use of the optical properties of the interacting materials as input data. The optical properties of gold films were measured in air with ellipsometry in the wavelength range $137\;nm-33\;\mu m$ [@Sve08]. Outside of this interval at low frequencies ($\lambda
>33\;\mu m$) the data were extrapolated according to the Drude model with the plasma frequency $\omega_p=7.84\pm 0.07\; eV$ and the relaxation frequency $\gamma=49.0\pm 2.1\; meV$. The Drude parameters were determined from the measured part of the dielectric function [@Sve08]. At high frequencies ($\lambda <137\; nm$) the method of extrapolation did not play any role, and the data were taken from the handbook [@HB].

Theory {#Sec3}
======

Gold-gold interaction in the Lifshitz theory {#Sec3.1}
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First we are going to calculate the interaction energy between two plates $E_{pp}^{flat}$. To be more precise it must be the free energy if we consider the interaction at finite temperature $T$. Here, however, we will neglect the thermal effect because our intention is to calculate the force in 