To understand the electronic shell and supershell structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals a surprisingly simple dependence of the supershells on the jellium density. It is shown how this can be understood in the framework of a periodic-orbit expansion by analytically extending the well-known semiclassical treatment of a spherical cavity to more realistic potentials.

• Received 28 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.2678