Density dependence of the electronic supershells in the homogeneous jellium model

We present the results of self-consistent calculations of the electronic shell and supershell structures for clusters having up to 6000 valence electrons. The ionic background is described in terms of a homogeneous jellium. The calculations were performed for a series of different electron densities, resembling Cs, Rb, K, Na, Li, Au, Cu, Tl, In, Ga, and Al, respectively. By analyzing the occupation of the energy levels at the Fermi energy as a function of cluster size, we show how the shell and supershell structures for a given density arise from the specific arrangement of energy levels. We investigate the electronic shells and supershells obtained for different electron densities. Using a scaling argument, we find a surprisingly simple dependence of the position of the supernodes on the electron density.