In this paper we discuss the statics of small assemblies of soft, rare-gas type atoms (N=4 to 13) interacting under simple two-body central forces such as the Lennard-Jones and Morse type. Our main concern is to characterize the problem of isomer multiplicity in small packed structures and to devise practical algorithms for the discovery of a representative majority, if not all, stable soft-packing structures for clusters of atoms in the above size-range. We illustrate one such possible 'Aufbau algorithm' by demonstrating the existence of no less than 988 distinct, stable minimum configurations for 13 Lennard-Jones atoms and of correspondingly smaller numbers in the range N=7 to 12. The minimal structures obtained may be classified broadly into 'crystallographic' and 'non-crystallographic' types, the latter predominating among those of greatest binding energy. A surprising result is that, when the softer (α=3) Morse potential is used, the great majority of the Lennard-Jones minima are not supported and only a much smaller class of distinct structures survive. Moreover, broadly speaking, crystallographic configurations are favoured by the softer potential, in confirmation of the intuitive view that relatively hard potentials dispose to amorphous structure. These results, representing the probable structures of free condensation nuclei near 0 K, provide an interesting statistical morphology for small nuclei, as well as being a necessary first step in the construction of a statistical thermodynamics valid at finite temperatures.
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