In this work we introduce a theoretical model for the description of doubly charged xenon clusters. It is based on the assumption that the charges migrate inside the cluster by isotropic hopping through a Hubbard Hamiltonian. The Xe atoms are considered classical polarizable particles. For their interaction we use a 2-body potential to which we add charge-charge, charge-dipole, and dipole-dipole interactions. The calculations ate carried out within the ground state approximation. We perform molecular-dynamics calculations on doubly charged clusters of up to 55 atoms. We investigate the role that the quantum degree of freedom plays on the critical size far the appearance of the doubly charged clusters. The incorporation of the quantum hopping results in a fragmentation energy barrier for clusters larger than the experimentally observed critical size, so that the calculated critical appearance size is in agreement with experiment. (C) 1997 American Institute of Physics. [S0021-9606(97)02347-7].