Structure and Madelung energy of spherical Coulomb crystals

With the help of molecular-dynamics computer simulations, we study the equilibrium configurations of systems of N=2–5000 strongly correlated charged particles under the influence of a radial harmonic external confining force and their mutual Coulomb forces. The temperature is well below the crystallization point; i.e., the ratio of Coulomb to kinetic energy is as large as Γ=${10}^9$. The particles arrange in concentric spherical shells with approximately constant intershell distances. On the surfaces plane hexagonal structures are well pronounced. The calculated radii, occupation numbers, and energies per particle are compared with results of classical geometrical and shell models with homogeneously charged shells corrected for hexagonal surface occupation. The closed-shell particle numbers also agree well with those of multilayer icosahedra. From the computer simulations we extract a Madelung (excess) energy of -0.8926, which is close to the theoretical value of the shell model corrected for plane hexagonal surfaces, -0.8923, but larger than the one of the infinite geometrical lattice, -0.8944, and of the bcc value of -0.8959. Surface-energy effects are positive and of the order of ${\mathit{N}}^{\mathrm{-}1/3}$.