Bubble Nuclei, Neutron Stars and Quantum Billiards A

We briefly review the significance of quantum corrections in the total energy of systems with voids: bubble nuclei, atomic clusters and the inhomogeneous phase of neutron stars. It was suggested a long time ago that very large nuclei might not undergo a Coulomb explosion if they acquire a new topology, that of a bubble or a torus 1. When a void is formed, while the density and therefore the total volume is kept unchanged, the surface area of such a nucleus naturally increases and that leads to an increased surface energy and less binding. However, at the same time the average distance between protons increases as well and the total Coulomb energy then decreases. The balancing of these two types of energy and the fact that configurations with larger binding energy than the familiar compact geometries exists is the reason why bubble–like and torus–like nuclei could in principle be someday observed. It was realized however that shell effects play a crucial role in stabilizing these new shapes 2. During the last decade many experimentalists have tried to manufacture highly charged metallic clusters, but, again, Coulomb repulsion prevented their creation. The idea that objects with a different topology, in particular bubble–like charged metallic clusters could be a possible route to create highly charged metallic clusters was recently put forward 3 , and again the stabilizing role of the shell corrections was noted as playing a decisive role. There was an aspect of bubble systems, which for mysterious reasons never caught the attention of previous authors:Where should one position a bubble inside a nucleus? Symmetry considerations seem to suggest that a spherical