Abstract
Analytical relationships for the surface and curvature energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. By modifying the cluster shape from a spheroid to a semi-spheroid (including the flat surface of the end cup) the most stable shape was changed from a sphere to a superdeformed prolate semi-spheroid. Potential energy surfaces vs. deformation and the number of atoms, N, illustrate this property independent of N.