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{≤}rₛ{≤}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 {Δ}l=4, where l is the angular-momentum quantum number. This critical size is on the order of N{~}10³ valence electrons for all metallic densities; in the specific case rₛ=4, the result is N=1640, in excellent agreement with the experimentally observed transition in Na clusters to ``shells of atoms'' in the range 1400N2000.