A Unified Explanation of Magic Numbers in Small Clusters
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 clusters1 the numbers 13, 19, 25, 55, 71, 87, 147, while for Ar and Kr the numbers2 14, 16, 19, 21, 23, 27, and 14, 16, 19, 22, 25, 27, 29, 39, 75, 87, respectively, and for Na the numbers3 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, one3 for the last set of above numbers (Na clusters; magic numbers as a result of decoupled 3s electrons driven by a central potential) and another1 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.
KeywordsSmall Cluster Hard Sphere Magic Number Equilibrium Geometry Unify Explanation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Plenum Press, New York 1987