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

Abstract

The $\Lambda \Lambda$-$\Xi N$-$\Sigma \Sigma$ coupling in ${}_{\Lambda \Lambda }^6$He is studied with the [$\alpha$ + $\Lambda$ + $\Lambda$] + [$\alpha$ + $\Xi$ + $N$] + [$\alpha$ + $\Sigma$ + $\Sigma$] 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 ($B$=$N$, $\Lambda$, $\Xi$ and $\Sigma$). We find that the calculated $\Delta B_{\Lambda \Lambda }$ of ${}_{\Lambda \Lambda }^6$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, $\Delta B_{\Lambda \Lambda }^{exp}=1.01\pm 0.20_{-0.11}^{+0.18}$ MeV. Characteristics of the $S=-2$ sector in the NSC97 potentials are discussed in detail.

18 pages, 4 figures