Scales and Universality in Few-Body Systems

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

doi:10.1007/s00601-011-0236-7

Cited by 44 publications

(70 citation statements)

References 162 publications

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“…This is known as the Efimov effect and its characteristics have been the subject of intense investigation both experimentally [4][5][6][7] and theoretically [8][9][10][11][12]. In recent years the study of the Efimov effect has been extended to what is now called Efimov physics and refers to the physics of shallow states.…”

Section: Introductionmentioning

confidence: 99%

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N-boson spectrum from a discrete scale invariance

2014

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We present an analysis of the N -boson spectrum computed using a soft two-body potential, the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length a close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground state of the system with one less particle. It is governed by a unique universal function (ξ ), already known in the case of three bosons. In the three-particle system the angle ξ , determined by the ratio of the two-and three-body binding energies E 3 /E 2 = tan 2 ξ , characterizes the discrete scale invariance of the system. Extending the definition of the angle to the N -body system as E N /E 2 = tan 2 ξ , we study the N -boson spectrum in terms of this variable. The analysis of the results, obtained for up to N = 16 bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of N is observed at fixed values of a. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length a and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

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Section: Introductionmentioning

confidence: 99%

“…These correlations indicate a limitation in the number of scales that governs the dynamics of the system [12].…”

Section: Introductionmentioning

confidence: 99%

N-boson spectrum from a discrete scale invariance

2014

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“…The theoretical formulation is a little elaborate but available in details in the literature [7,8]. We shall here only specify our notation and present the Faddeev equations in momentum space.…”

Section: A Faddeev Equationsmentioning

confidence: 99%

Mean-square radii of two-component three-body systems in two spatial dimensions

et al. 2016

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We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons (A) and one distinguishable particle (B). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, A = mB/mA, between particles B and A are varied from 0.01 to 100 providing a number of bound states decreasing from 8 to 2. Energies and mean-square radii of these states are analyzed for small A by use of the Born-Oppenheimer potential between the two heavy A-particles. For large A the radii of the two bound states are consistent with a slightly asymmetric threebody structure. When A approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound AB-dimers and one loosely bound A-particle.

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“…The aim is to establish the validity or limitations of universal scaling relations predicted by the zero-range model. These universal scaling relations are a consequence of the dominance of long-range Efimov potential over the properties of the halo [28][29][30], and they are expressed as model-independent correlations between low-energy observables [13,15], where the short-range physics is parameterized by one three-body s-wave observable, like, e.g., the two-neutron separation energy.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the properties of the low-energy parameters open the possibility to use concepts from the Efimov physics [11,12] already applied to cold atoms (see Refs. [13,14]), namely universality and model independence, which characterizes the large extension of the halo structure [15].…”

Section: Introductionmentioning

confidence: 99%

Emergent universality in the two-neutron halo structure of C22

2016

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The structure of the two-neutron halo 22 C is investigated by means of a renormalized zero-range three-body model, with interactions in the s-wave channel, and a finite-range model with two-and three-body forces provided by the hyperspherical adiabatic expansion method. In both models the halo wave function in configuration space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The halo-matter density is computed for 22 C with different three-body forces and low-energy parameters, with two-neutron separation energy within the range 50 keV S 2n 1000 keV. The halo-neutron density depends weakly on the neutron-20 C scattering length as long as its absolute value is larger than the neutron-neutron one. The halo-neutron density is then analyzed by means of the root-mean-square radius, the probability density, and also the geometry, taking into account the angle between the two Jacobi coordinates. The results of finite-range and zero-range two-neutron-core models are compared. The effects in the halo structure of short-range and long-range three-body forces are studied, and the emergent universal behavior of the halo-neutron density and its geometry is pointed out.

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Scales and Universality in Few-Body Systems

Cited by 44 publications

References 162 publications

N-boson spectrum from a discrete scale invariance

N-boson spectrum from a discrete scale invariance

Mean-square radii of two-component three-body systems in two spatial dimensions

Emergent universality in the two-neutron halo structure of C22

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