Crystallization and melting of a system of charges in a liquid helium cluster

A system of like (positive or negative) charges forming 'snowballs' or 'bubbles' in a three-dimensional liquid helium cluster is investigated. The charges are confined inside the cluster by an 'image potential' produced by the polarization of liquid helium. The stability of a multiply charged helium cluster is considered. Computer simulations are used to investigate the crystallization and melting of the system of charges depending on the dimensionless parameter T* = kBTεR/e2, where kB is the Boltzmann constant, T is the temperature, ε is the dielectric constant of liquid helium, R is the cluster radius, and e is a unit charge. Various characteristics, including symmetry groups and moments, have been found for equilibrium configurations of charges in a cluster with N = 1-100 charges. At small N ∼ 10, Thomson's model of successive filling of 'belts' of charges can be used to describe the structure of equilibrium configurations of charges. At large N, the description of the structure formed by charges using the idea of a quasi-two-dimensional 'closed triangular lattice' with topological defects is more adequate. Formally, this description is valid starting from N = 4. The melting of a 'lattice' of charges is described. A number of our conclusions can be generalized to clusters of other noble gases