The surfaces of compact systems: from nuclei to stars

While providing information from worlds separated by five-to-six orders of magnitude in dimensions and in energy, the pairing properties (electrical resistance and viscosity), the electromagnetic response (spectrum of colours), the resilience to stress (elasticity), the ability to deform (plasticity), etc., associated with clusters of atoms and with atomic nuclei have surprisingly similar properties, once the proper scalings are done, and demonstrate the many analogies that can be drawn between different finite many-body systems. These analogies can be further extended to cosmic and to customer tailored nanometre materials. Femtometre materials, like the inner crust of a neutron star (pulsar), are made out of the same protons and neutrons which make infinite nuclear matter. However in pulsars, protons and neutrons are arranged in the form of finite nuclei immersed in a sea of free neutrons. This is the reason why these celestial objects rotate, conduct heat, emit neutrinos, etc., very differently from infinite nuclear matter. In fact, these phenomena reflect the properties of the corresponding atomic nuclei which form the pulsar. Among these properties, those associated with the nuclear surface are most important. Nanostructured materials are made out of atoms as their more common forms, but the atoms are arranged in nanometre or sub-nanometre-size clusters, which become the constituent grains, or building blocks, of new materials like, e.g., C₆₀ fullerene. Because these tiny grains respond to light, mechanical stress and electricity quite differently from micron- or millimetre-sized grains, nanostructured materials display an array of novel attributes. At the basis of the new phenomena we find again the surface of the building blocks used to produce the new materials. A proper understanding of the interweaving of the single-particle motion with the static and dynamic deformations of the surface of finite many-body systems is likely to provide the key to open a whole new world of interdisciplinary research in such disparate fields as isolated atomic nuclei and clusters, new materials and compact stellar objects. The concepts and the experimental evidence needed to tool this key will be reviewed. Special emphasis will be set on the open questions still remaining to be answered to reach this goal.