Extended-soft-core baryon-baryon model ESC16. III. S=−2 hyperon-hyperon/nucleon interactions

Abstract

Background: This is the third of a series of papers on baryon-baryon (BB) interactions, where the baryons are the lowest lying baryon states with spin and parity ${J}^{P}={(1/2)}^{+}$. The paper presents the extended-soft-core (ESC) model ESC16 for BB channels with strangeness $S=\ensuremath{-}2$.Purpose: The aim is to describe the ingredients of the $S=\ensuremath{-}2$ ESC16 potentials, to apply these two-body interactions to BB scattering and via $G$-matrix calculations to hypernuclear systems, and to compare with the presently available experimental information.Methods:The potentials for $S=\ensuremath{-}2$ are based on the SU(3) extension of the ESC potentials for the strangeness $S=0$ and $S=\ensuremath{-}1$ sectors, which are fitted to experimental nucleon-nucleon ($NN$), hyperon-nucleon ($YN$), and hyperon-hyperon ($YY$) data. Flavor SU(3) symmetry is broken only `kinematically' by the masses of the baryons and the mesons. For the $S=\ensuremath{-}2$ channels almost no experimental scattering data exist, and the information from hypernuclei is also rather limited. Nevertheless, in the fit to the $S=0$ and $S=\ensuremath{-}1$ sectors information from the Nagara event and the scarce experimental results on the $\mathrm{\ensuremath{\Xi}}N$ cross sections have been used as (mild) constraints to determine the free parameters in the simultaneous fit of the deuteron and the $NN\ensuremath{\bigoplus}YN$ scattering data. Therefore, the potentials for the $S=\ensuremath{-}2$ sectors are almost completely determined by the fits to the $NN, YN$ data, and SU(3) symmetry.Results: Various properties of the $S=\ensuremath{-}2$ potentials are illustrated by giving results for scattering lengths, bound states, phase parameters, and total cross sections. The well-depth ${U}_{\mathrm{\ensuremath{\Xi}}}$ is calculated and $\mathrm{\ensuremath{\Xi}}N G$-matrix interactions are derived and applied to ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$-capture reactions. Here, a phenomenological $\mathrm{\ensuremath{\Xi}}N$ interaction is added to describe the experiments. Furthermore, the ESC16 model supplemented with phenomenological SU(3) symmetric gaussian interactions is analyzed, and attractive $\mathrm{\ensuremath{\Xi}}N$ interactions are obtained. Combined with three-body forces derived from the ESC meson-pair vertices and the Fujita-Miyazawa interaction, yields good baryon well depths.Conclusions: The ESC16 $S=\ensuremath{-}2$ potentials, with kinematically broken SU(3) symmetry, provide a basis for realistic calculations in nuclear and hypernuclear physics. For a successful description of the well depth's ${U}_{N},{U}_{\mathrm{\ensuremath{\Lambda}}},{U}_{\mathrm{\ensuremath{\Sigma}}}$, and ${U}_{\mathrm{\ensuremath{\Xi}}}$ and hypernuclear $S=\ensuremath{-}2$ reactions phenomenological additions are needed.