Structure of spherical three-dimensional Coulomb crystals

An analysis of the structural properties of three-dimensional Coulomb clusters confined in a spherical parabolic trap is presented. Based on extensive high-accuracy computer simulations the shell configurations and energies for particle numbers in the range $60⩽N⩽160$ are reported. Further, the intrashell symmetry and the lowest metastable configurations are analyzed for small clusters and a different type of excited state that does not involve a change of shell configuration is identified.

Figure 1

(Color online) Binding energy ${\Delta }_2$ (right axis) and mean Voronoi symmetry parameter (MVSP, left axis) for the two outermost cluster shells. (a) $N⩽80$; (b) $80⩽N⩽160$.

Figure 2

Voronoi construction for the cluster $N=17$ for the two energetically lowest states with shell configuration $N=\{1,16\}$. White (gray) areas are hexagons (pentagons), indicating the number of nearest neighbors of the corresponding particle (black dot). (a) ground state; (b) first excited (“fine structure”) state; (c) arrangement of the four particles surrounded by hexagons; the two states differ by rotation of the edge $AB$, black (white) circles correspond to case (a) [(b)].