We report calculations of the ground-state energies and geometries for clusters of different sizes(up to 80 particles),where individual particles interact simultaneously via a short-ranged attractive potential,modeled with a generalization of the Lennard-Jones potential,and a long-ranged repulsive Yukawa potential.We show that for specific choices of the parameters of the repulsive potential,the ground-state energy per particle has a minimum at a finite cluster size.For these values of the parameters in the thermodynamic limit,at low temperatures and small packing fractions,where clustering is favored and cluster-cluster interactions can be neglected,thermodynamically stable cluster phases can be formed.The analysis of the ground-state geometries shows that the spherical shape is marginally stable.In the majority of the studied cases,we find that above a certain size,ground-state clusters preferentially grow almost in one dimension.
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