SHELL EFFECTS IN PLANAR ELECTRON CLUSTERS

We investigate the electronic shell structure of planar metal clusters , having in mind clusters on insulating surfaces with an interface ene rgy such that the cluster covers the surface in a monolayer. In this f irst survey we concentrate on the shell effects of such a planar elect ron cloud using the Ultimate Jellium Model where the structural effect s of the positive background are completely eliminated. An axially sym metric electron cloud shows shell effects which are, however, somewhat smaller than those of fully free three-dimensional clusters. The free variation of the shape for planar clusters on surfaces, leading to ma ny triaxial clusters, diminishes the shell effects even further, leadi ng to the existence of hybrid-deformed clusters and a lack of energeti cally favored ''magic'' clusters in an intermediate size range N appro ximate to 10-30. In contrary to the situation for free clusters the sm all shell energies have a minor effect on the energetics of the ground state. As a consequence, electronic shell effects are only one ingredi ent amongst others to determine the kinetics of cluster growth on (ins ulating) substrates. With a bold rescaling assumption, we can relate a xially symmetric planar clusters to the planar electron cloud in a neu tral quantum dot, having the consequence that shell effects persist to play a role in these systems.