Efimov Physics and Connections to Nuclear Physics

Abstract

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by continuous scale invariance, which is broken into discrete scale invariance when three or more particles come into play. This symmetry induces a universal behavior for different systems that is independent of the details of the underlying interaction and rooted in the smallness of the ratio ℓ[Formula: see text] a B ≪ 1, where the length a B is associated with the binding energy of the two-body system [Formula: see text], and ℓ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the onset of system-specific nonuniversal effects. In this review, we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which a B → ∞, and we show that nuclear systems belong to this class of universality. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Four-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scattering

“…Cold 4 He atoms constitute one of the simplest quantum systems exhibiting the phenomenon of the Efimov physics [1,2]; see Refs. [3,4] for recent reviews.…”

“…Cold 4 He atoms constitute one of the simplest quantum systems exhibiting the phenomenon of the Efimov physics [1,2]; see Refs. [3,4] for recent reviews. In contrast to atomic systems of alkali metals, no external fine-tuning is needed since the interatomic 4 He interaction supports a single shallow dimer bound state in the S-wave.…”

“…[3,4] for recent reviews. In contrast to atomic systems of alkali metals, no external fine-tuning is needed since the interatomic 4 He interaction supports a single shallow dimer bound state in the S-wave. Consequently, the two-atom scattering length is large compared to the interaction or effective range, ensuring conditions for the realization of the Efimov physics.…”

“…It manifests itself by the existence few-body states. In systems consisting of N = 3 (4) atoms of 4 He this leads to two bound trimer (tetramer) states, a more tightly bound ground state and a shallow excited state located near the twocluster breakup threshold.…”

“…The system of three 4 He atoms has been studied in a large number of works employing realistic interaction models, and a good agreement between different theoretical methods has been achieved, not only for binding energies but also for the atom-dimer scattering length [5][6][7][8][9][10][11][12]. Several existing calculations for the ground state 4 He tetramer also agree well, but significant differences show up in the excited tetramer binding energy [5,7,10,11]. The latter is correlated with the atom-trimer scattering length, the few existing results being in sizable disagreement, thereby calling for further studies with alternative methods.…”