Exact Casimir-Polder potential between a particle and an ideal metal   cylindrical shell and the proximity force approximation
  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 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects. 
V.B. Bezerra, E.R. Bezerra de Mello, G.L. Klimchitskaya, V.M.   Mostepanenko, A.A. Saharian
hep-th quant-ph