van der Waals interaction as a summable asymptotic series

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients C-2k of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density. with outer radius R and thickness t. The result is C-2k = -c(k) (t/R)root 4 pi rho[(2R)(2)](k). The c(k) approach a limiting constant value, so the infinite series for the van der Waals interaction at separation d, -C-6/d(6) - C-8/d(8)- ..., can be summed analytically, diverging only for d <= 2R. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with R fixed by the true static dipole polarizability. Once t/R is fixed, all the higher coefficients are determined by just C-6 and C-8. Finally, we compare the exact C-2k to those from a pair interaction model, which works for solid spheres (t = R) but not for fullerenes. DOI:10.1103/PhysRevA.86.062714