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To this end we construct an effective block-diagonal two-body separable interaction with the Fermi momentum as a cut-off which reduces the calculation to the mean field level. The interaction is separable in momentum space and is determined by Tabakin's inverse scattering formula. For a vanishing effective range we get $\\xi = \\frac{176}{9 \\pi }-\\frac{17}{3} = 0.56$. 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