ΛΛ 6 He and Λ 9 Be systems in the three-body cluster model treated on the basis of differential Faddeev equations

Abstract

The ΛΛ 6 He and Λ 9 Be hypernuclei are treated as the S=0, T=0 (for the former) and S=1/2, T=0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I–III model, the ΛΛ interaction potential is specified in the form \(V_{\Lambda \Lambda } = \frac{2}{3}V_{NN} \). Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the ΛΛ 6 He and Λ 9 Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a Λ 5 He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the ΛΛ 6 He hypernucleus and that scattering in the Λ Λ 5 He system is similar to neutron scattering on a deuteron.