$\mathrm{\Lambda }\mathrm{\Lambda }$-$\mathrm{\Xi }N$-$\mathrm{\Sigma }\mathrm{\Sigma }$ coupling in ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He with the Nijmegen soft-core potentials

The $\mathrm{\Lambda }\mathrm{\Lambda }$-$\mathrm{\Xi }N$-$\mathrm{\Sigma }\mathrm{\Sigma }$ coupling in ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6$He is studied with the [$\alpha$ + $\mathrm{\Lambda }$ + $\mathrm{\Lambda }$] + [$\alpha$ + $\mathrm{\Xi }$ + $N$] + [$\alpha$ + $\mathrm{\Sigma }$ + $\mathrm{\Sigma }$] model, where the $\alpha$ particle is assumed as a frozen core. We use the Nijmegen soft-core potentials, NSC97e and NSC97f, for the valence baryon-baryon part, and the phenomenological potentials for the $\alpha -B$ parts ($B$=$N$, $\mathrm{\Lambda }$, $\mathrm{\Xi }$ and $\mathrm{\Sigma }$). We find that the calculated $\Delta B_{\Lambda\Lambda}$of$^{~6}_{\Lambda\Lambda}$He for NSC97e and NSC97f are, respectively, 0.6 and 0.4 MeV in the full coupled-channel calculation, the results of which are about half in comparison with the experimental data, $\mathrm{\Delta }{B}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{exp}=1.01\pm 0.20_{-0.11}^{+0.18}$ MeV. Characteristics of the $S=-2$ sector in the NSC97 potentials are discussed in detail.