Some applications of the Faddeev–Yakubovsky equations to the cold-atom physics

Carbonell, J.; Deltuva, A.; Lazauskas, Rimantas

doi:10.1016/j.crhy.2010.12.001

Cited by 6 publications

(2 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To guide the eye, the lower and higher dark blue circles are connected by a dark blue vertical dashed line. a B = 182.22 a 0 , the value a AD = 217 a 0 is obtained, which has to be compared with the LM2M2 value for this quantity of 218.4 a 0 (83). Thus, the Gaussian characterization of the universal window can accurately take into account finite-range effects.…”

Section: The Three-boson System: Scattering Statesmentioning

confidence: 99%

Efimov Physics and Connections to Nuclear Physics

Kievsky

Gattobigio

Girlanda

et al. 2021

Annu. Rev. Nucl. Part. Sci.

View full text Add to dashboard Cite

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.

show abstract

Section: The Three-boson System: Scattering Statesmentioning

confidence: 99%

Efimov Physics and Connections to Nuclear Physics

Kievsky

Gattobigio

Girlanda

et al. 2021

Annu. Rev. Nucl. Part. Sci.

View full text Add to dashboard Cite

show abstract

“…Therefore the gaussian characterization of the unitary window indicates, for that value of the r 0 /a B ratio, the atomdimer scattering length to be a AD = 1.19 a B . Using the LM2M2 value, a B = 182.22 a 0 , we obtain a AD = 217 a 0 , to be compared to the LM2M2 value for this quantity of 218.4 a 0 [30]. So, a gaussian potential constructed to describe simultaneously the dimer and excited state of the trimer reproduces also the value of the atom-dimer scattering length within a 1% error.…”

Section: The Three-body Case a Three Equal Bosonsmentioning

confidence: 84%

Gaussian characterization of the unitary window for N=3 : Bound, scattering, and virtual states

et al. 2020

View full text Add to dashboard Cite

The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having 1/2 spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering and virtual states.

show abstract

Formation of the Positronium Antihydride Molecules ($$\bar{\textrm{H}}\textrm{Ps}$$) in Low Energy, 5-Body Collisions of Antihydrogen Ion $$\bar{\textrm{H}}^+$$ with Positronium Atoms Ps

Froelich,

Yamashita,

Kino

et al. 2024

Few-Body Syst

View full text Add to dashboard Cite

In this paper we present the first pilot calculation of the elastic and inelastic cross sections for the 5-body scattering of antihydrogen ions with positronium atoms. These cross sections have not been calculated before and are not known experimentally. In particular, we focus on the collisional rearrangement reactions $$\bar{{ \mathrm H}}^+ + \textrm{Ps} \rightarrow {\bar{\textrm{H}}}\textrm{Ps} +{\mathrm{e^+}}$$ H ¯ + + Ps → H ¯ Ps + e + which deplete the $$\bar{\textrm{H}}^+$$ H ¯ + ions and result in stable atomcules $$\bar{\textrm{H}}\textrm{Ps}$$ H ¯ Ps . To better understand the mechanism of this rearrangement, we study the 3-dimensional, angle resolved positron densities of the 3- and 4-body fragments in the initial and final states of the rearrangement collision.

show abstract

Some applications of the Faddeev–Yakubovsky equations to the cold-atom physics

Cited by 6 publications

References 49 publications

Efimov Physics and Connections to Nuclear Physics

Efimov Physics and Connections to Nuclear Physics

Gaussian characterization of the unitary window for N=3 : Bound, scattering, and virtual states

Formation of the Positronium Antihydride Molecules ($$\bar{\textrm{H}}\textrm{Ps}$$) in Low Energy, 5-Body Collisions of Antihydrogen Ion $$\bar{\textrm{H}}^+$$ with Positronium Atoms Ps

Contact Info

Product

Resources

About