Resolving structural transitions in spherical dust clusters

Finite systems in confining potentials are known to undergo structural transitions similar to phase transitions. However, these systems are inhomogeneous, and their "melting" point may depend on the position in the trap and vary with the particle number. Focusing on three-dimensional Coulomb systems in a harmonic trap a rich physics is revealed: in addition to radial melting we demonstrate the existence of intrashell disordering and inter-shell angular melting. Our analysis takes advantage of a novel melting criterion that is based on the spatial two and three-particle distribution functions and the associated reduced entropy which can be directly measured in complex plasma experiments.