Nuclear Physics Around the Unitarity Limit

TL;DR

This paper proposes that nuclear structure features can be understood through a perturbative expansion around the unitarity limit, where two-nucleon interactions exhibit zero-energy bound states, linking nuclear properties to a single scale related to the triton binding energy.

Contribution

It introduces a novel approach to nuclear physics by expanding around the unitarity limit, simplifying the understanding of nuclear structure through a single scale parameter.

Findings

Nuclear features emerge from a perturbative expansion near the unitarity limit.

Observables are close to their physical values with small corrections.

Light nuclei are weakly bound and insensitive to interaction details.

Abstract

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system.