When a few tens of charged particles are trapped in a spherical electrostatic potential at low temperature they form concentric shells resembling atoms. These ``artificial atoms can be easily controlled by varying the confinement strength. We analyze
such systems for the case that the particles are bosons and find superfluid behavior which even persists in the solid state. This novel state of matter is a mesoscopic supersolid.
In small confined systems predictions for the melting point strongly depend on the choice of quantity and on the way it is computed, even yielding divergent and ambiguous results. We present a very simple quantity which allows to control these proble
ms -- the variance of the block averaged interparticle distance fluctuations.
