SPHERICAL SUPERSHELLS IN METAL-CLUSTERS AND THE TRANSITION TO PROTOCRYSTALLINE STRUCTURE

One-electron calculations of spherical supershell structure are presented for metal clusters with up to 8000 valence electrons over the range of metallic densities 2 less-than-or-equal-to r(s) less-than-or-equal-to 6, using potentials adapted from self-consistent bulk surface calculations. Good agreement is obtained with detailed trends in the experimental data and with corresponding self-consistent cluster jellium calculations throughout. In the T = 0 limit, aspherical perturbations anticipated from the incipient ionic lattice are shown to eradicate the supershell structure at a cluster size corresponding to near-degeneracy at the Fermi level between valence-electron states differing by DELTA-l = 4, where l is the angular-momentum quantum number. This critical size is on the order of N approximately 10(3) Valence electrons for all metallic densities; in the specific case r(s) = 4, the result is N = 1640, in excellent agreement with the experimentally observed transition in Na clusters to "shells of atoms" in the range 1400 < N < 2000.