Shell Correction Energy for Bubble Nuclei

The positioning of a bubble inside a many fermion system does not affect the volume, surface, or curvature terms in the liquid drop expansion of the total energy. Besides possible Coulomb effects, the only other contribution to the ground state energy of such a system arises from shell effects. We show that the potential energy surface is a rather shallow function of the displacement of the bubble from the center and in most cases the preferential position of a bubble is off-center. Systems with bubbles are expected to have bands of extremely low lying collective states, corresponding to various bubble displacements.