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We study normal state properties of an interacting Fermi gas in an isotropicharmonic trap of arbitrary dimensions. We exactly calculate the first-orderperturbation terms in the ground state energy and chemical potential, andobtain simple analytic expressions of the total energy and chemical potential.At zero temperature, we find that Thomas-Fermi approximation agrees well withexact 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 hightemperature (classical) region, we find interaction energy decreases inproportion to T^(-d/2), where T is temperature and d is dimension of thesystem. Effect of interaction in the ground state in two and three-dimensionalsystems is also discussed.Comment: 15 pages, 4 figure

Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap