Casimir forces beyond the proximity approximation

¹ Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Complesso Universitario MSA Via Cintia, I-80126 Napoli, Italy, EU
² INFN Sezione di Napoli - I-80126 Napoli, Italy, EU
³ Laboratoire de Physique Théorique et Modèles Statistiques, CNRS UMR 8626, Bât. 100, Université Paris-Sud F-91405 Orsay cedex, France, EU
⁴ Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology Cambridge, MA 02139, USA
⁵ Massachusetts Institute of Technology, Department of Physics - Cambridge, MA 02139, USA

Received: 2 December 2011
Accepted: 24 January 2012

Abstract

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere/plate Casimir force at all separations.