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We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon (F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0. 0246E (5/2) +. . . and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E (-1) - 0. 691 +. . . . The minimum of the fermion dispersion curve is located at |p|= (2mepsilon (0) ) (1/2), where epsilon_ (0) /mu=2+O (E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.
Nishida et al. (Fri,) studied this question.