  The properties of a balanced two-component Fermi gas in a one-dimensional
harmonic trap are studied by means of the coupled cluster method. For few
fermions we recover the results of exact diagonalization, yet with this method
we are able to study much larger systems. We compute the energy, the chemical
potential, the pairing gap, and the density profile of the trapped clouds,
smoothly mapping the crossover between the few-body and many-body limits. The
energy is found to converge surprisingly rapidly to the many-body result for
every value of the interaction strength. Many more particles are instead needed
to give rise to the non-analytic behavior of the pairing gap, and to smoothen
the pronounced even-odd oscillations of the chemical potential induced by the
shell structure of the trap.
