Zero-point vibrational energies of spherical Coulomb crystals

Thanks to their well-pronounced shell structures, spherical Coulomb crystals possess zero-point vibrational energies {epsilon(SCC)(N)} that are dominated by one component. This shell-additive contribution, which arises from particle motions within individual shells, is readily modeled with a superposition of modified Thomson problems with no adjustable parameters. On the other hand, the negative-valued shell-pair contribution, which has its origin in the correlation of particle motions involving different shells, is accurately approximated with a simple expression involving two fitted constants. The sum of these two quantities underestimates the actual values of {epsilon(SCC)(N)} by less than 1.7%, the residual error being due to the higher multipole-multipole intershell interactions and geometry relaxation due to the intershell correlation. Overall, {epsilon(SCC)(N)} scale like N(3/2), the proportionality constant reaching the limiting value of approximately 1.1 for large numbers of particles N.