Casimir force for a sphere in front of a plane beyond Proximity Force Approximation

TL;DR

This paper calculates the first two terms of the asymptotic expansion for the Casimir force between a sphere and a plane at small separations, considering both Dirichlet and Neumann boundary conditions.

Contribution

It provides a more accurate approximation of the Casimir force beyond the Proximity Force Approximation for sphere-plane configurations.

Findings

Derived the first two terms of the asymptotic expansion for small separations.

Extended analysis to both Dirichlet and Neumann boundary conditions.

Abstract

For the configuration of a sphere in front of a plane we calculate the first two terms of the asymptotic expansion for small separation of the Casimir force. We consider both Dirichlet and Neumann boundary conditions.