  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.
