Lambda-Lambda bond energy from the Nijmegen potentials

Abstract

The $\Lambda\Lambda$ bond energy $\Delta B_{\Lambda \Lambda}$ in $\Lambda\Lambda$ hypernuclei is obtained from a $G$-matrix calculation which includes the coupling between the $\Lambda\Lambda$, $\Xi N$ and $\Sigma\Sigma$ channels, as well as the effect of Pauli blocking to all orders. The Nijmegen NSC97e model is used as bare baryon-baryon interaction in the strangeness $S=-2$ sector. The $\Lambda\Lambda$-$\Xi N$ coupling increases substantially the bond energy with respect to the uncoupled $\Lambda\Lambda$ case. However, the additional incorporation of the $\Sigma \Sigma$ channel, which couples simultaneously to $\Lambda\Lambda$ and $\Xi N$ states, has a surprisingly drastic effect and reduces the bond energy down to a value closer to that obtained in an uncoupled calculation. We find that a complete treatment of Pauli blocking reduces the repulsive effect on the bond energy to about half of what was claimed before.