Binding and structure of tetramers in the scaling limit

Hadizadeh, M. R.; Yamashita, M. T.; Tomio, Lauro; Delfino, A.; Frederico, T.

doi:10.1103/physreva.85.023610

Cited by 33 publications

(28 citation statements)

References 61 publications

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“…Based on a zero-range model, Refs. [35][36][37] report some sensitivity of four-body energies to a four-body scale, but these results do not contradict the absence of a four-body interaction at LO in Pionless EFT. The absence of an essential four-body parameter has also been verified in the context of potential models with a short range [38][39][40][41] and of renormalization-group analyses [42][43][44].…”

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confidence: 70%

Nuclear Physics Around the Unitarity Limit

et al. 2017

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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. DOI: 10.1103/PhysRevLett.118.202501 For the purposes of nuclear physics, QCD, the theory of strong interactions, has essentially two independent parameters, namely the up and down quark masses. Their average controls the pion mass and consequently, the range of the nuclear force R ∼ M −1 π ≃ 1.4 fm. Their difference, plus electromagnetism, generates small differences in masses and interactions between neutrons and protons. At the physical point, the two-nucleon (NN) scattering length in the 3 S 1 channel is a t ≃ 5.4 fm, with the deuteron as a shallow bound state (B D ≃ 2.224 MeV); in the 1 S 0 channel, a s ≃ −23.7 fm, and a shallow virtual bound state exists at B NN Ã ≃ 0.068 MeV. With relatively small changes in quark masses, these states become, respectively, unbound and bound [1][2][3][4]. In the physics of cold atoms near Feshbach resonances, external magnetic fields play a role similar to the quark masses and allow the scattering length to be tuned arbitrarily [5].Approximate correlations B D;NN Ã ≈ 1=ðM N a 2 t;s Þ, with M N ≃ 940 MeV the nucleon mass, hold because the size of all these scales is unnatural compared to the typical interaction range R. The NN system therefore appears close to the unitarity (or unitary) limit, where both states cross zero energy, the scattering lengths become infinite (1=a t;s ¼ 0), and cross sections saturate the unitarity bound. It has indeed been suggested that this happens not far from the physical point [6]. While this presumed proximity has been discussed qualitatively for a long time, it has traditionally not played any special role in constructing nuclear forces, and it is neither assessed nor exploited in order to simplify the description of nuclei. As an exception, Refs. [7,8] use potential models to map out correlations between observables in three-and fournucleon systems as the limit is approached at fixed a t =a s .Here, we argue that the typical particle binding momentum Q A of the A-nucleon system satisfies 1=a s;t < Q A < 1=R so that a combined expansion in Q A R and 1=ðQ A a s;t Þ converges quickly and quantitatively reproduces the physical systems. With this, the gross features of states in the nuclear chart are determined by a very simple le...

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confidence: 70%

Nuclear Physics Around the Unitarity Limit

et al. 2017

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“…In contrast, in Refs. [57,58,59] a contact model suggested the emergence of a fourbody scale. However, a subtraction procedure was employed which has no transparent connection to field theory.…”

Section: More Bodies But No More Scales?mentioning

confidence: 99%

Unitarity and Discrete Scale Invariance

Kolck

2017

Few-Body Syst

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International audienceWhile the complexity of some many-body systems may stem from a profusion of distinct scales, as we approach two-body unitarity (through experimental control or as a theoretical limit) rich structures exist even though there is no more than one essential scale. I comment, from the point of view of effective field theory, on some current problems in the transition from few to many bodies in bosonic and multi-state fermion systems, where order emerges from the discrete scale invariance associated with a single, contact three-body force

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“…Then, the SQ is transformed back to a prolonged ET, and repeatedly. The mode associated with the transformation is named the ET-SQ-ET mode (or the H-type oscillation named in [20]). Since the wave functions of 2 − and 4 − appear as nodes at the ET and SQ, the ET-SQ-ET mode contains three nodes and therefore is an excited mode.…”

Section: Shape-densitiesmentioning

confidence: 99%

Universal Prohibited Zones in the Coordinate Space of Few-Body Systems

Bao

2013

Few-Body Syst

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In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be equivalent to the operation of another element. Making use of the matrix representations of the groups, the equivalence leads to a set of homogeneous linear equations imposing on the wave functions. When the matrix of these equations is non-degenerate, the wave functions will appear as nodal surfaces in these zones. In this case, these zones are prohibited. In this paper, tightly bound 4-boson systems with three types of interaction have been studied analytically and numerically. The existence of the universal prohibited zones has been revealed, and their decisive effect on the structures of the eigenstates is demonstrated. PACS 03.65.-w · 03.65.Ge · 02.20.-a · 21.45.-v · 36.40.Mr

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Binding and structure of tetramers in the scaling limit

Cited by 33 publications

References 61 publications

Nuclear Physics Around the Unitarity Limit

Nuclear Physics Around the Unitarity Limit

Unitarity and Discrete Scale Invariance

Universal Prohibited Zones in the Coordinate Space of Few-Body Systems

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