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 $\ensuremath{\rho}$ with outer radius $R$ and thickness $t$. The result is ${C}_{2k}=\ensuremath{-}{c}_{k}(t/R)\sqrt{4\ensuremath{\pi}\ensuremath{\rho}}{[{(2R)}^{2}]}^{k}$. The ${c}_{k}$ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation $d$, $\ensuremath{-}{C}_{6}/{d}^{6}\ensuremath{-}{C}_{8}/{d}^{8}\ensuremath{-}\ensuremath{\cdots}$, can be summed analytically, diverging only for $d\ensuremath{\le}2R$. 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.