Eur. Phys. J. C (2011) 71: 1614
https://doi.org/10.1140/epjc/s10052-011-1614-5

Regular Article - Theoretical Physics

Exact Casimir–Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

¹ Department of Physics, Federal University of Paraíba, C.P. 5008, CEP 58059–900, João Pessoa, Pb, Brazil
² North-West Technical University, Millionnaya Street 5, St. Petersburg, 191065, Russia
³ Noncommercial Partnership “Scientific Instruments”, Tverskaya Street 11, Moscow, 103905, Russia
⁴ Department of Physics, Yerevan State University, 1 Alex Manoogian Street, 0025, Yerevan, Armenia

^* e-mail: aram.saharian@gmail.com

Received: 27 January 2011
Revised: 28 February 2011
Published online: 9 April 2011

Abstract

We derive the exact Casimir–Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir–Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1R, where R is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.