The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic orbit expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic orbit expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials, and show that it describes the shift of the supershells as the surface of a cluster potential becomes softer.
 

Physical Review B, 58 2329-39, 1998.