Analytical treatment of interacting Fermi gas in arbitrary dimensional   harmonic trap
  We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that Thomas-Fermi approximation agrees well with exact results for any dimension even though system is dilute and small, i.e. when the Thomas-Fermi approximation is generally expected to fail. In the high temperature (classical) region, we find interaction energy decreases in proportion to T^(-d/2), where T is temperature and d is dimension of the system. Effect of interaction in the ground state in two and three-dimensional systems is also discussed. 
Hiroyuki Yoshimoto and Susumu Kurihara