A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme

Hadizadeh, M. R.; Radin, M.; Mohseni, Kamran

doi:10.1038/s41598-020-58577-4

Cited by 9 publications

(9 citation statements)

References 54 publications

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“…The cluster structure of light hypernuclei [53,54] has been studied with different methods, including the generator coordinate method [55], orthogonality condition model [56], Gaussian expansion method [57,58], and Tohsaki-Horiuchi-Schuck-Röpke wave function approach [59]. The Faddeev-Yakubovsky (FY) equations are extensively used to study the structure of three-and four-body bound states, with identical and non-identical particles, in different sectors of physics [60][61][62][63][64][65]. FY equations are solved with different techniques such as direct projection in momentum space [66], hyperspherical harmonics (HH) [67], adiabatic hyperspherical [68], and variational methods [69,70].…”

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confidence: 99%

Three-body Faddeev calculations for and hypernuclei*

Etminan

Hadizadeh²

2022

Chinese Phys. C

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We study the ground-state properties of $\prescript{6}{YY}{\text{He}}$ double hyperon for $\lla$ and $\ooa$ nuclei in a three-body model $(Y+Y+\alpha)$. We solve two coupled Faddeev equations corresponding to three-body configurations $(\alpha Y,Y)$ and $(YY, \alpha)$ in configuration space with the hyperspherical harmonics expansion method by employing the most recent hyperon-hyperon interactions obtained from lattice QCD simulations. Our numerical analysis for $\lla$, using three $\Lambda\Lambda$ lattice interaction models, leads to a ground state binding energy in the domain $(-7.468, -7.804)$ MeV and the separations $\langle r_{\Lambda-\Lambda} \rangle$ and $\langle r_{\alpha-\Lambda} \rangle$ in the domains $(3.555, 3.629)$ fm and $(2.867 , 2.902 )$ fm, correspondingly. The binding energy of double-$\Omega$ hypernucleus $\ooa$ leads to $-67.21$ MeV and consequently to smaller separations $\langle r_{\Omega-\Omega} \rangle = 1.521$ fm and $\langle r_{\alpha-\Omega} \rangle = 1.293 $ fm. Besides the geometrical properties, we study the structure of ground-state wave functions and show that the main contributions are from the $s-$wave channels. Our results are consistent with the existing theoretical and experimental data.

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confidence: 99%

Three-body Faddeev calculations for and hypernuclei*

Etminan

Hadizadeh²

2022

Chinese Phys. C

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“…The definitions and notation shown in this appendix follow Refs. [19,20]. The shifted momentum arguments appearing in Eq.…”

Section: Appendix a Definitionsmentioning

confidence: 99%

“…Kamada and Glöckle have shown that relativistic and boosted potentials can be obtained directly from nonrelativistic potentials by solving a quadratic equation using an iterative scheme [18]. Once the boosted potential is obtained, the 2B T −matrix in the rest frame of the threebody system can be computed as required for the kernel of the relativistic Faddeev equations [19,20].…”

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Three-boson stability for boosted interactions towards the zero-range limit

Mohseni,

Chaves,

da Costa

et al. 2021

Preprint

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We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Glöcke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.

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“…To do so, we formulated the quadratic operator relation between the nonrelativistic and relativistic NN potentials in momentum space leading to a 3D integral equation 10 . We successfully implemented this iterative approach to calculate the matrix elements of boosted 2B potential from the MT potential to study the relativistic effects in a 3B bound state 11 . Our numerical results showed that the relativistic effects lead to a 2% reduction in 3B binding energy using MT potential.…”

Section: Introductionmentioning

confidence: 99%

Relativistic nucleon–nucleon potentials in a spin-dependent three-dimensional approach

Hadizadeh

Radin

Nazari

2021

Sci Rep

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The matrix elements of relativistic nucleon–nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2N) spin-singlet state, and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy.

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A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme

Cited by 9 publications

References 54 publications

Three-body Faddeev calculations for and hypernuclei*

Three-body Faddeev calculations for and hypernuclei*

Three-boson stability for boosted interactions towards the zero-range limit

Relativistic nucleon–nucleon potentials in a spin-dependent three-dimensional approach

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