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Realistic effective interactions for halo nuclei

We study halo nuclei using a two-frequency shell-model approach employing wave functions of two different oscillator constants $\hbarω_{in}$ and $\hbarω_{out}$, the former for the inner orbits and the latter for the halo (outer) orbits. An initial application has been made for the halo nuclei $^6$He and $^6$Li, with $0s_{1/2}$ taken as the inner and ( $0p_{3/2}$, $0p_{1/2}$) as the halo orbits. Starting from the Paris NN interaction, we have derived a G-matrix folded-diagram effective interaction for this two-frequency model space, using an essentially exact treatment for the Pauli exclusion operator for the G-matrix. While keeping $\hbarω_{in}$ fixed, we have performed calculations with different choices for $\hbarω_{out}$, treating it as a variation parameter. For $\hbarω_{in}=19.7 MeV$ and $\hbarω_{out}=8.2 MeV$, our calculated valence energies for $^6$He and $^6$Li are -2.77 and -3.55 Mev, respectively, both in good agreement with experiments. The importance of certain three-body-force diagrams is discussed.