  We examine the basic mode structure of atomic Cooper pairs in an
inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasi-particle
vacuum, the single particle density matrix and the anomalous density matrix
share the same set of eigenfunctions. These eigenfunctions correspond to
natural pairing orbits associated with the BCS ground state. We investigate
these orbits for a Fermi gas in a spherical harmonic trap, and construct the
wave function of a Cooper pair in the form of Schmidt decomposition. The issue
of spatial quantum entanglement between constituent atoms in a pair is
addressed.
