  We calculate the Casimir force and its gradient between a spherical and a
planar gold surface. Significant numerical improvements allow us to extend the
range of accessible parameters into the experimental regime. We compare our
numerically exact results with those obtained within the proximity force
approximation (PFA) employed in the analysis of all Casimir force experiments
reported in the literature so far. Special attention is paid to the difference
between the Drude model and the dissipationless plasma model at zero frequency.
It is found that the correction to PFA is too small to explain the discrepancy
between the experimental data and the PFA result based on the Drude model.
However, it turns out that for the plasma model, the corrections to PFA lie
well outside the experimental bound obtained by probing the variation of the
force gradient with the sphere radius [D. E. Krause et al., Phys. Rev. Lett.
98, 050403 (2007)]. The corresponding corrections based on the Drude model are
significantly smaller but still in violation of the experimental bound for
small distances between plane and sphere.
