Neutron skins of atomic nuclei: per aspera ad astra

The complex nature of the nuclear forces generates a broad range and diversity of observational phenomena. Heavy nuclei, though orders of magnitude less massive than neutron stars, are governed by the same underlying physics, which is enshrined in the nuclear equation of state. Heavy nuclei are expected to develop a neutron-rich skin where many neutrons collect near the surface. Such a skin thickness is strongly sensitive to the poorly-known density dependence of the symmetry energy near saturation density. An accurate and model-independent determination of the neutron-skin thickness of heavy nuclei would provide a significant first constraint on the density dependence of the nuclear symmetry energy. The determination of the neutron-skin thickness of heavy nuclei has far reaching consequences in many areas of physics as diverse as heavy-ion collisions, polarized electron and proton scattering off nuclei, precision tests of the standard model using atomic parity violation, and nuclear astrophysics. While a systematic and concerted experimental effort has been made to measure the neutron-skin thickness of heavy nuclei, a precise and model-independent determination remains elusive. The measurement of parity-violating asymmetries provides a clean and model-independent determination of the weak form factor of the nucleus which is dominated by the neutron distribution. However, measuring parity-violating asymmetries of the order of a part per million is both challenging and time-consuming. Alternative observables sensitive to the symmetry energy have been proposed and measured succesfully in recent experimental campaigns. These data are valuable, but interpretations contain implicit model dependence that hinder the clean determination of the neutron-skin thickness. How to move forward at a time when many new facilities are being commissioned and how to strengthen the synergy with other areas of physics are primary goals of this review