Electronic shell and supershell structures in trivalent-metal clusters exhibit large discrepancies with the results of the conventional jellium model. For gallium the beat location in the supershell pattern is found around Ne=2500 valence electrons, in disagreement with the jellium model prediction Ne=1150. The discrepancies can be explained by a slight softness increase of the effective electronic potential at the surface. Theoretical calculations, taking into account ion pseudopotentials, within both local and nonlocal approaches, show that this softness arises to a large extent from the non-Coulombic short-range electron-ion interaction.
