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

الأصل · EN

We analyze the universality of the Unitary Fermi Gas in its ground state from a Wilsonian renormalization point of view and compute the effective range dependence of the Bertsch parameter ξ exactly. 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 ξ= 176/9 π-17/3 = 0.56. By using phase-equivalent similarity transformations we can show that there is a class of exact solutions with any value in the range 0.56 ≥ ξ≥ -1/3.