Integral relations and the adiabatic expansion method for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>reactions above the breakup threshold: Helium trimers with soft-core potentials

Garrido, E.; Romero-Redondo, Carolina; Kievsky, A.; Viviani, M.

doi:10.1103/physreva.86.052709

Cited by 15 publications

(18 citation statements)

References 22 publications

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“…To this aim, we make use of the adiabatic expansion method as discussed in Refs. [21,22] for energies below the dimer breakup threshold and recently extended to energies above that threshold [23]. As it is well known, the adiabatic expansion method is a very powerful method used to describe bound states [24].…”

Section: A Elastic and Breakup Cross Sectionsmentioning

confidence: 99%

“…[23], where the inelasticity (|S 11 |) and the real part of the phase shift [Re(δ)] have been calculated at selected energies for increasing values of K max (grand-angular quantum number associated to the last adiabatic term included in the expansion of the scattering wave function). The conclusion was that the use of the integral relations produces a pattern of convergence similar to a bound-state calculation.…”

Section: A Elastic and Breakup Cross Sectionsmentioning

confidence: 99%

“…Following the method described in [23], we have computed σ e and σ b for the TBG + H3B potential (λ = 1 case). The results are given by the solid and dashed curves in Fig.…”

Section: A Elastic and Breakup Cross Sectionsmentioning

confidence: 99%

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Recombination rates from potential models close to the unitary limit

2013

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We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length a. To this aim, we use the hyperspherical adiabatic expansion and we extract the S matrix through the integral relations recently derived. The results are compared to the universal form, α ≈ 67.1 sin 2 [s 0 ln(κ * a) + γ ], for different values of a and selected values of the three-body parameter κ * . A good agreement with the universal formula is obtained after introducing a particular type of finiterange corrections, which have been recently proposed [A. Kievsky and M. Gattobigio, Phys. Rev. A 87, 052719 (2013)]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length.

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Section: A Elastic and Breakup Cross Sectionsmentioning

confidence: 99%

Section: A Elastic and Breakup Cross Sectionsmentioning

confidence: 99%

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Recombination rates from potential models close to the unitary limit

2013

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“…In the adiabatic hyper-spherical representation of this mass imbalanced three-body system, it happens that the coupling between the lowest adiabatic channel, which asymptotically goes to the atom-dimer channel, with the breakup channels is weak (see e.g. [24]). In addition, asymptotically the lowest adiabatic hyper-spherical potential is attractive, while the breakup channels have a barrier around ρ ∼ |a HL |.…”

mentioning

confidence: 99%

“…[23], which was extended to energies above the breakup threshold in Ref. [24]. The Gaussian potential with r 0 being the interaction range is given by…”

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confidence: 99%

Probing Efimov discrete scaling in an atom-molecule collision

et al. 2018

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The discrete Efimov scaling behavior, well-known in the low-energy spectrum of three-body bound systems for large scattering lengths (unitary limit), is identified in the energy dependence of atommolecule elastic cross-section in mass imbalanced systems. That happens in the collision of a heavy atom with mass mH with a weakly-bound dimer formed by the heavy atom and a lighter one with mass mL mH . Approaching the heavy-light unitary limit the s−wave elastic cross-section σ will present a sequence of zeros/minima at collision energies following closely the Efimov geometrical law. Our results open a new perspective to detect the discrete scaling behavior from low-energy scattering data, which is timely in view of the ongoing experiments with ultra-cold binary mixtures having strong mass asymmetries, such as Lithium and Caesium or Lithium and Ytterbium.The Efimov effect [1] refers to a discrete scaling symmetry, which emerges in the quantum three-body system at the unitary limit (when the two-body scattering lengths diverge). The optimal condition to observe this discrete scaling symmetry in cold atomic laboratories is now found for heteronuclear three-atom systems with large mass asymmetry and large interspecies scattering lengths. In the Efimov (unitary) limit, the shallow three-body levels are geometrically spaced, namely the ratio between the binding energies of the n and n + 1 levels is given by B = exp (2π/s 0 ), where s 0 is a universal constant, which depends only on the mass ratio and not on the details of the interaction. The energy ratio for three identical bosons is exp (2π/s 0 ) ≈ 515, decreasing for the case of two heavy particles and light one. When m L /m H = 0.01, for example, the value of this energy ratio goes to exp (2π/s 0 ) = 4.698 [2].The Efimov geometric scaling factor has been measured in a cold-atom experiment with mass-imbalance mixtures of Caesium ( 133 Cs) and Lithium ( 6 Li) gases by different groups [3,4]. The ratio between the positions of two successive peaks in the three-body recombination rate, obtained by varying the large negative scattering lengths (a HL ), was found in close agreement with the theory. Complementary to this finding, a fingerprint of the Efimov scaling can be found in the s−wave ultracold atom-molecule cross-section by varying the incident momentum energy k instead of the scattering lengths. Natural, but not yet evidenced experimentally or theoretically. What we expect is beyond the trimer crossing the corresponding continuum, which creates the resonant enhancement of the inelastic collisions of Caesium atoms with Caesium dimers, as observed by Knoop et al. [5].Furthermore, there is an evident strong interest in ultra-cold heteronuclear atom-molecule collisions by experimental groups [6][7][8]. Trap setups with ultra-cold degenerated mixtures of alkali-metal-rare-earth molecules with strong mass-imbalanced systems as Ytterbium and Lithium ( 174,173 Yb− 6 Li) have also been reported in Refs. [9,10]. We should mention that on the theory side [11], reactions at ...

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Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

Chen

Phillips

2013

Few-Body Syst

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We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, . The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N 2 LO) in the /a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N 2 LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N 2 LO phase-shift predictions will receive higher-order corrections of < 0.2%. In contrast, the prediction of SREFT for the binding energy of the "deep" trimer of Helium-4 atoms displays poor convergence.

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Integral relations and the adiabatic expansion method for1+2reactions above the breakup threshold: Helium trimers with soft-core potentials

Cited by 15 publications

References 22 publications

Recombination rates from potential models close to the unitary limit

Recombination rates from potential models close to the unitary limit

Probing Efimov discrete scaling in an atom-molecule collision

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

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