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