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We investigate the ground state properties of a one-dimensional two-componentultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solutionis used to calculate the many-body wave function of the system. Then weevaluate the single-particle reduced density matrix and two-particle densitydensity correlations of the system for different interaction strengths. We findthat the momentum density distributions of the strongly interactingtwo-component Fermi gas is distinct from that of free spinless Fermi gasalthough their position density distributions are similar. This interactingsystem may be experimentally accessible using ultra-cold atoms.

Exact results of two-component Fermi gas in a hard wall trap