${}_{\Lambda \Lambda }^6$He as a $\Lambda \Lambda$ 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 ${}_{\Lambda \Lambda }^6$He is calculated in an $\Lambda \Lambda \alpha$ model. The resultant binding energies suggest that the strength of the ${}^1$S${}_0$ $t=0$ $\Lambda \Lambda$ and the $nn$ interactions should be similar, if the coupling between the $\Lambda \Lambda$ and $\Xi N$ channels is taken into consideration.

27 pages,2 eps figures

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