Physics and Chemistry of Small Clusters pp 151-155 | Cite as

# A Unified Explanation of Magic Numbers in Small Clusters

## Abstract

Small clusters with specific numbers of atoms, called magic numbers, exhibit particular stability properties in comparison to other cluster sizes. The identification of magic numbers in the literature, however, is rather confusing, since different sets of such numbers have been reported for different kind of atoms. For example, for Xe clusters^{1} the numbers 13, 19, 25, 55, 71, 87, 147, while for Ar and Kr the numbers^{2} 14, 16, 19, 21, 23, 27, and 14, 16, 19, 22, 25, 27, 29, 39, 75, 87, respectively, and for Na the numbers^{3} 2, 8, 20, 40, 58, 92 have been reported. The theoretical explanation of magic numbers in the literature is not unique as well. It follows two independent reasonings, one^{3} for the last set of above numbers (Na clusters; magic numbers as a result of decoupled 3s electrons driven by a central potential) and another^{1} for the other three sets (Xe, Ar, Kr clusters; magic numbers as a result of packing of spheres). Moreover, even for the same kind of clusters, theoretically expected magic numbers are not supported experimentally and experimentally observed numbers are not covered by theoryl.

## Keywords

Small Cluster Hard Sphere Magic Number Equilibrium Geometry Unify Explanation## Preview

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## References

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