Force-range correction in the three-body problem: Application to three-nucleon systems

A non-relativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length a is much larger than the range l of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the |a| → ∞ limit and finite-l/a corrections to observables of interest. Here we use such an effectivetheory treatment to consider the impact of corrections linear in the two-body effective range, r s on the three-boson bound-state spectrum and recombination rate for |a| |r s |. We do this by first deriving results appropriate to the strict limit |a| → ∞ in coordinate space. We then extend these results to finite a using once-subtracted momentum-space integral equations. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.

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“…(This potential had been conjectured, but not derived in Ref. [17].) Specifically, we found that the perturbing potential is…”

Section: Discussionmentioning

confidence: 85%

“…The form of Eq. (50), but not the specific pre-factor of the 1/R 3 potential, was proposed by Efimov on dimensional grounds [17]. The momentum-space evaluation of first-order (in r s /|a|) effects in Ref.…”

Section: B the Linear Range Correction In The Unitary Limitmentioning

confidence: 99%

Range corrections to three-body observables near a Feshbach resonance

2009

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“…That approach is controlled by the parameter R/a 2 . A first assessment of the impact that taking R/a 2 = 0 has on universality predictions was carried out by Efimov [10,11], and these calculations were recently systematized using EFT by Hammer & Mehen [12] and Bedaque et al [4], both of whom showed that the O(R/a 2 ) corrections to universality came from the physics of two-body scattering alone. This means that, up to corrections of O(R 2 /a 2 2 ), the low-energy properties of the three-body system are determined by two numbers: the ratios R/a 2 and a 3 /a 2 .…”

Section: Introductionmentioning

confidence: 99%

The Three-Boson System at Next-to-Next-to-Leading Order

2006

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We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a 2 , with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3 /a 3 2 ). Since corrections of O(R/a 2 ) and O(R 2 /a 2 2 ) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.

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“…About forty years ago the Efimov effect was suggested as an anomaly appearing in a three-body system when at least two of the two-body subsystems simultaneously have short-ranged bound states at zero energy (Efimov 1970, Efimov 1971. The three-body system then has infinitely many bound states with exponentially decreasing binding energies and correspondingly increasing mean square radii.…”

Section: Efimov Physicsmentioning

confidence: 99%

“…In particular, the study of (Massignan & Stoof 2008) provide results that are close to the experimental data. On the nuclear physics side, finite-range corrections for three-nucleon systems have been considered by Efimov himself about two decades ago (Efimov 1991).…”

Section: Measurable Consequences In Physics Systemsmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Force-range correction in the three-body problem: Application to three-nucleon systems

Cited by 48 publications

References 7 publications

Range corrections to three-body observables near a Feshbach resonance

Range corrections to three-body observables near a Feshbach resonance

The Three-Boson System at Next-to-Next-to-Leading Order

Comparing and contrasting nuclei and cold atomic gases

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