Three-body Faddeev calculations for ΛΛα and ΩΩα hypernuclei

چکیده مقاله

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.