Nuclear physics around the unitarity limit

In the unitarity (or unitary) limit, where the two-nucleon S-wave channels have infinite scattering lengths and zero-energy bound states, only one dimensionful parameter is left and set by the triton binding energy. While the proximity of the real world to this idealized scenario has been discussed qualitatively for a long time, it has traditionally not played any special role in constructing nuclear forces. Here it is argued that at least light nuclei may reside in a sweet spot: bound weakly enough to be insensitive to the details of the interaction, but dense enough to be insensitive to the exact values of the large two-body scattering lengths as well, so that a systematic expansion around the unitarity limit converges. With this, the gross features of states in the nuclear chart are determined by a very simple leading-order interaction, whereas - much like the fine structure of atomic spectra - observables are moved to their physical values by small perturbative corrections. Explicit evidence in favor of this conjecture is shown for the binding energies of three and four nucleons.