  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.
