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We analyze the universality of the Unitary Fermi Gas in its ground state froma Wilsonian renormalization point of view and compute the effective rangedependence of the Bertsch parameter $\xi$ exactly. To this end we construct aneffective block-diagonal two-body separable interaction with the Fermi momentumas a cut-off which reduces the calculation to the mean field level. Theinteraction is separable in momentum space and is determined by Tabakin'sinverse scattering formula. For a vanishing effective range we get $\xi =\frac{176}{9 \pi }-\frac{17}{3} = 0.56$. By using phase-equivalent similaritytransformations we can show that there is a class of exact solutions with anyvalue in the range $ 0.56 \ge \xi \ge -1/3$.

An exact solution to the Bertsch problem and the non-universality of the Unitary Fermi Gas