Three-body Faddeev calculations for and hypernuclei*

Abstract

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.

The charge and mass symmetry breaking in the KK K¯ system

“…The increase of ξ leads to the increase or decrease of the two-body energies of the K 0 K − and K + K − pair, respectively. At the same time, the binding energy of the K 0 K + K − system remains unchanged up to a value of ξ = 0.03, as is demonstrated in figure 2 and can be seen from equation (17). A similar situation was demonstrated in the previous subsection when the mass scaling parameter ζ increases up to the value of ζ = 0.06.…”

“…By adding the algebraic equations in (17), we obtain E = E 0 . In other words, in the first order of perturbation theory, the average potential gives E = E 0 .…”

“…However, the method of hyperspherical harmonics, the variational method in the harmonic-oscillator basis, and the variational method complemented with the use of explicitly correlated Gaussian basis functions has been successfully employed for the solution of a fewbody problem in atomic, nuclear, high energy physics, and even in condensed matter physics [7]. Some recent studies for the application of the Faddeev technique in momentum space and configuration spaces across various physics sectors including atomic physics [8], condensed matter physics [9][10][11], and nuclear physics [12][13][14][15][16][17]. It should be mentioned that the recent literature on the subject is not limited by the cited works.…”

Studying Omega-nucleon-nucleon three-body states by realistic nucleon-nucleon and first principles Lattice QCD Omega-nucleon potentials in the cluster model

“…In addition because Ωd systems is deeply bound, increasing our knowledge about its properties could help future theoretical and experimental studies. Therefore, in addition to cross-check of the binding energies and their convergence, we also investigate the geometrical properties of Ωd (T = 0) 5/2 + state in cluster model based in expansion on hyperspherical harmonics (HH method) [18][19][20] . We should emphasize that, here we have not evaluated the contributions of coupling to inelastic channels, i.e.…”