van der Waals interaction as a summable asymptotic series

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients C₂ₖ of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density ρ with outer radius R and thickness t. The result is C₂ₖ=-cₖ(t/R)√4πρ[(2R)²]ᵏ. The cₖ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation d, -C₆/d⁶-C₈/d⁸-⋯, 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 C₆ and C₈. Finally, we compare the exact C₂ₖ to those from a pair interaction model, which works for solid spheres ($t=R$) but not for fullerenes.