Quantum-mechanical calculation of the van der Waals interaction between small metallic spheres

We give the first microscopic calculation of the leading terms in the van der Waals interaction energy between two very small metallic particles, treating their electronic excitations in the quantum-mechanical Infinite Barrier Model and the Random Phase Approximation. The results are very close to those obtained for the corresponding classical spheres, provided that we describe them by their effective radii calculated to satisfy the electrostatic zero-force sum-rule. We examine the higher order terms and the exact results at short distances in the plasmon-pole approximation, and discuss the convergence of the multipole expansions.