Abstract
Light nuclei fall within a regime of universal physics governed by the fact that the two-nucleon scattering lengths are large compared to the typical nuclear interaction range set by one-pion exchange. This places nuclear physics near the so-called unitarity limit in which the scattering lengths are exactly infinite. Effective field theory provides a powerful theoretical framework to capture this separation of scales in a systematic way. It is shown here that the nuclear force can be constructed as a perturbative expansion around the unitarity limit and that this expansion has good convergence properties for both the binding energies of A=3,4 nuclei as well as for the radii of these states.
Highlights
Δ0(k) denotes the S-wave scattering phase shift for two particles with relative momentum k
In the two-body sector, universality relates scattering parameters to shallow bound and virtual states. This is a consequence of Eq (1) and the principle of analyticity: the effective range expansion (ERE) provides an expansion of the S matrix, so whenever poles at complex momenta—in particular bound and virtual states, which reside at purely imaginary momenta—fall within the radius of convergence of the expansion, they are described by the same parameters
The unitarity expansion may seem like merely a minor departure from standard Pionless effective field theory (EFT)
Summary
Nuclear physics at very low energies hosts a fascinating emergent phenomenon: out of the tremendously complicated dynamics of quarks and gluons, governed by the strong interaction (Quantum Chromodynamics, QCD) that is highly nonperturbative in this regime, arise strikingly simple features for systems of few nucleons. [14,15,16] that for physical values of the NN scattering lengths the triton can be interpreted as the single remaining bound state of such an Efimov tower More recently it was established in a model-independent way [17] that a virtual state in the threenucleon (3N ) system, known to exist for a long time [18,19], is an S-matrix pole that would be an excited Efimov state instead if nature were just slightly closer to the unitarity limit. This makes the zero-range theory well defined by regularizing the otherwise divergent interaction via the introduction of a cutoff scale Λ Both the value of Λ and the particular form of the regulator function are arbitrary and renormalization, discussed below, ensures that observables are independent of these choices.
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