Mean-field quantization of several hundred electrons in sodium metal clusters

Measurements of the mass-abundance spectra of sodium clusters from supersonic expansions are presented. The spectra show evidence of a regular spherical shell structure with magic numbers ${\mathit{N}}_0$ scaling approximately with the cube root of the number of sodium atoms N, and hence the number of delocalized (valence) electrons in the cluster. Altogether, twelve shell closings are observed, adding to the previously known shell closings, ${\mathit{N}}_0$=2, 8, 20, 40, 58, 92, and 138; the 8–12th magic numbers ${\mathit{N}}_0$=196, 260, 344, 440, and 558. The implications of shell structure in such large systems are discussed.