Universal Behavior of Few-Boson Systems Using Potential Models

Kievsky, A.; Viviani, M.; Álvarez-Rodríguez, R.; Gattobigio, M.; Deltuva, A.

doi:10.1007/s00601-017-1228-z

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…The points correspond to the calculated values, while the solid line is a quadratic fit. The limit value for r 0 /ā → 0 is C 0 = −2.68402(3), and it is in agreement with the previous results in literature [20,35,36]. The square point shows the ratio at which āB and re are well reproduced.…”

supporting

confidence: 91%

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Subleading contributions to $N$-boson systems inside the universal window

Recchia,

Kievsky,

Girlanda

et al. 2022

Preprint

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We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guidance, we construct a series of potential terms which have a decreasing importance in the description of the binding energy of the systems. The leading order potential terms consist in a two-body term, usually attractive, plus a three-body term, usually repulsive; this last term is required to prevent the collapse of systems with more than two particles. At this order, the parametrization of the two-body potential is done to obtain a correct description of the scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a three-body datum. We investigate the role of the cut-off in the leading order description and we extend the exploration beyond the leading order by including the next-to-leading order terms in both, the two-and three-body potentials. We use the requirement of the stability of the N -body system, whose energy is variationally estimated, to introduce the three-body forces. The potential parametrization, as a function of the cut-off, is fixed to describe the energy of 4 He clusters up to seven particles within the expected accuracy. Finally, we also explore the possibility to describe at the same time the atom-dimer scattering length.

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supporting

confidence: 91%

“…As already noted in Refs. [20,35,36], the scaling limit is well defined C 0 → −2.68402(3); moreover, at fixed r 0 , this is the value at which the scattering length is infinite. Varying the ratio r 0 /ā, the effective range, the binding length, and r B could differ from the LM2M2 values.…”

Section: A Two-body Forcementioning

confidence: 94%

Subleading contributions to $N$-boson systems inside the universal window

Recchia,

Kievsky,

Girlanda

et al. 2022

Preprint

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“…This has been confirmed experimentally [6,14], which therefore raises the question, whether this pattern continues for higher N . Theoretical calculations for N = 5, 6 have been made, which predict that the pattern of two N + 1 state accompany each universal N ground state at least for N ≤ 6 [15][16][17][18][19][20][21][22][23][24]. Experimental evidence that two Borromean pentamer (N = 5) states does accompany the ground tetramer state have been reported [25].…”

Section: A Efimov Physics Beyond Three Bosonsmentioning

confidence: 99%

Window for Efimov physics for few-body systems with finite-range interactions

Rasmussen¹,

Jensen²,

Fedorov³

2017

J. Phys. B: At. Mol. Opt. Phys.

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We investigate the two lowest-lying weakly bound states of N ≤ 8 bosons as functions of the strength of two-body Gaussian interactions. We observe the limit for validity of Efimov physics. We calculate energies and second radial moments as functions of scattering length. For identical bosons we find that two (N − 1)-body states appear before the N -body ground states become bound. This pattern ceases to exist for N ≥ 7 where the size of the ground state becomes smaller than the range of the two-body potential. All mean-square-radii for N ≥ 4 remain finite at the threshold of zero binding, where they vary as (N − 1) p with p = −3/2, −3 for ground and excited states, respectively. Decreasing the mass of one particle we find stronger binding and smaller radii. The identical particles form a symmetric system, while the lighter particle is further away in the ground states. In the excited states we find the identical bosons either surrounded or surrounding the light particle for few or many bosons, respectively. We demonstrate that the first excited states for all strengths resemble two-body halos of one particle weakly bound to a dense N -body system for N = 3, 4. This structure ceases to exist for N ≥ 5.

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