$^{6}_{ΛΛ}$He as a $ΛΛ$ interaction constraint

Abstract

The Nijmegen OBE potential D is SU(3) rotated to model the strangeness -2 sector of the baryon-baryon force. Soft core repulsion is introduced to regularize the singular nature of the OBE functions. The strength of the $^1$S$_0$ $t=0$ interaction is adjusted to model three scenarios: (1) a bound state, (2) a narrow virtual, or antibound, state, and (3) an unbound state in which the force is weakly attractive. Using a separable approximation to these potentials, the binding energy of $^{6}_{ΛΛ}$He is calculated in an $ΛΛα$ model. The resultant binding energies suggest that the strength of the $^1$S$_0$ $t=0$ $ΛΛ$ and the $nn$ interactions should be similar, if the coupling between the $ΛΛ$ and $ΞN$ channels is taken into consideration.