Probing the ΞN interaction through inversion of spin-doublets in ΞNαα nuclei

Abstract

We propose to obtain information on the spin-isospin dependence of the $\mathrm{\ensuremath{\Xi}}N$ interaction through the energy levels of $\mathrm{\ensuremath{\Xi}}N\ensuremath{\alpha}$ and $\mathrm{\ensuremath{\Xi}}N\ensuremath{\alpha}\ensuremath{\alpha}$ systems, with $\ensuremath{\alpha}$ being a spectator to attract the $\mathrm{\ensuremath{\Xi}}N$ pair without changing its spin-isospin structure. By using the Gaussian expansion method with the state-of-the-art $\mathrm{\ensuremath{\Xi}}N$ potential obtained from lattice QCD calculations, it is found that $\mathrm{\ensuremath{\Xi}}N\ensuremath{\alpha}\ensuremath{\alpha}$ has spin-doublet bound states with ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ and ${2}^{\ensuremath{-}}$ in both isospin triplet and singlet channels. The inversion of the ${1}^{\ensuremath{-}}\ensuremath{-}{2}^{\ensuremath{-}}$ spin-doublet between the iso-triplet and the iso-singlet is found to be strongly correlated with the relative strengths of the $\mathrm{\ensuremath{\Xi}}N$ interaction in the $^{11}\mathrm{S}_{0}, ^{13}\mathrm{S}_{1}, ^{31}\mathrm{S}_{0}$, and $^{33}\mathrm{S}_{1}$ channels. The $({K}^{\ensuremath{-}},{K}^{+})$ and $({K}^{\ensuremath{-}},{K}^{0})$ reactions on the $^{10}\mathrm{B}$ target are proposed to produce those bound states.