# Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation

## TL;DR

This study compares exact numerical calculations of the Casimir force between gold surfaces with the proximity force approximation, highlighting discrepancies between Drude and plasma models and experimental bounds.

## Contribution

It provides the first detailed numerical comparison beyond PFA for Casimir forces, analyzing Drude and plasma models at zero frequency.

## Key findings

- Corrections to PFA are too small to explain experimental discrepancies with Drude model.
- Plasma model corrections to PFA exceed experimental bounds at small distances.
- Drude model corrections are smaller but still violate experimental bounds at close separations.

## Abstract

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.