Magic Numbers for Sphere Packings: Experimental Verification in Free Xenon Clusters

The existence of magic numbers for atomic microclusters has been found experimentally for the first time. The magic numbers $n^{*}$ manifest themselves in the mass spectra of free xenon clusters, nucleated in the gas phase. The observed numbers $n^{*}=13, 55, \mathrm{and} 147$ coincide with the numbers of spheres required for complete-shell icosahedra. The appearance of further magic numbers (19, 25, 71, and 87) is only partially explained by previous calculations.