Star orbits in metal clusters

A possibility that classical five-point star orbits play a dominant role for shell structures of large metal clusters is investigated quantum mechanically. With a soft Woods-Saxon spherical potential a signature of the five-point star orbit is found in the level densities. Quantum numbers of degenerate levels in the soft Woods-Saxon potential differ by 2 and 5 in radial nodes and angular momenta, respectively. Unlike the experimental observation the peaks in the mass spectrum are not equally spaced as a function of ${\mathit{N}}^{1/3}$. The self-consistent jellium model does not reproduce the degeneracy associated with the five-point star orbits. It is demonstrated that by covering high-density metal clusters with a layer of a low-density metal the potential can be made softer.