Extended-soft-core Baryon-Baryon ESC08 model III. S=-2 Hyperon-hyperon/nucleon Interaction

This paper presents the Extended-Soft-Core (ESC) potentials ESC08c for baryon-baryon channels with total strangeness S=-2. The potential models for S=-2 are based on SU(3) extensions of ESC potential models for the S=0 and S=-1 sectors, which are fitted to experimental data. Flavor SU(3)-symmetry is broken only kinematically by the masses of the baryons and the mesons. For the S=-2 channels no experimental scattering data exist, and also the information from hypernuclei is rather limited. Nevertheless, in the fit to the S=0 and S=-1 sectors information from the so called NAGARA event and the $\Xi$-well-depth has been used as constraints to determine the free parameters in the simultaneous fit of the $NN \oplus YN \oplus YY$ data. Therefore, the potentials for the S=-2 sector are determined mainly by the NN-, YN-data, and SU(3)-symmetry.Various properties of the potentials are illustrated by giving results for scattering lengths, effective ranges, bound states, elastic and inelastic phase parameters, and total cross sections. Notably is the prediction of a bound state D$^*$ in the $\Xi N(^3S_1,I=1)$-channel with a binding energy $B_E=1.56$ MeV. This state is deuteron-like, i.e. a member of the $\{10^*\}$-decuplet. As for the normal deuteron $D= pn(^3S_1-^3D_1)$ the strong tensor force is responsible for this state. The features of $\Xi$ hypernuclei predicted by ESC08c are studied on the basis of the G-matrix approch. The well-depth $U_\Xi= -7.0$ MeV, and the $\Xi -\Lambda\Lambda$ conversion width is $\Gamma_\Xi^c= 4.5$ MeV.