Assuming a spherical mean field for electrons in metal clusters, single-particle level densities and electronic binding energies are calculated for clusters with up to 4000 valence electrons. Two phenomenological mean-field potentials, simulating microscopically calculated ones, are used. A global beating pattern, which envelopes individual shell oscillations, emerge from the calculations. The semiclassical interpretation of such a supershell structure, as proposed by Balian and Bloch in terms of interference of amplitudes associated with classical closed orbits, is found to be valid in the present case. Thermal effects, which tend to smear out shell and, therefore, supershell structures, are investigated qualitatively. Consequences of the shell structure are not obscured for cluster sizes up to several thousand atoms under the experimentally accessible temperature of 100–1000 K.

• Received 5 April 1990

DOI:https://doi.org/10.1103/PhysRevB.42.9377