# Beyond-PFA Casimir Force between two spheres at finite temperature. (arXiv:1802.01326v1 [quant-ph])

A recent experiment [J.L. Garrett et al., Phys. Rev. Lett {\bf 120}, 040401

(2018)] measured for the first time the gradient of the Casimir force between

two gold spheres at room temperature. The theoretical analysis of the data was

carried out using the standard Proximity Force Approximation (PFA). A fit of

the data, using a parametrization of the force valid for the sphere-plate

geometry, was used by the authors to place a bound on deviations from PFA.

Motivated by this work, we compute the Casimir force between two gold spheres

at finite temperature. The semi-analytic formula for the Casimir force that we

construct is valid for all separations, and can be easily used to interpret

future experiments in both the sphere-plate and sphere-sphere configurations.

We describe the correct parametrization of the corrections to PFA for two

spheres that should be used in data analysis.