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 $S=-2$.

Purpose: The aim is to describe the ingredients of the $S=-2$ 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 $S=-2$ are based on the SU(3) extension of the ESC potentials for the strangeness $S=0$ and $S=-1$ 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 $S=-2$ 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 $S=-1$ sectors information from the Nagara event and the scarce experimental results on the $\mathrm{\Xi }N$ cross sections have been used as (mild) constraints to determine the free parameters in the simultaneous fit of the deuteron and the $NN\oplus YN$ scattering data. Therefore, the potentials for the $S=-2$ sectors are almost completely determined by the fits to the $NN, YN$ data, and SU(3) symmetry.

Results: Various properties of the $S=-2$ potentials are illustrated by giving results for scattering lengths, bound states, phase parameters, and total cross sections. The well-depth $U_{\mathrm{\Xi }}$ is calculated and $\mathrm{\Xi }N G$-matrix interactions are derived and applied to ${\mathrm{\Xi }}^{-}$-capture reactions. Here, a phenomenological $\mathrm{\Xi }N$ interaction is added to describe the experiments. Furthermore, the ESC16 model supplemented with phenomenological SU(3) symmetric gaussian interactions is analyzed, and attractive $\mathrm{\Xi }N$ 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 $S=-2$ 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 $U_N,U_{\mathrm{\Lambda }},U_{\mathrm{\Sigma }}$, and $U_{\mathrm{\Xi }}$ and hypernuclear $S=-2$ reactions phenomenological additions are needed.

• Received 18 April 2020
• Revised 29 August 2020
• Accepted 30 October 2020

DOI:https://doi.org/10.1103/PhysRevC.102.054003