  We experimentally determined various thermodynamic quantities of interacting
two-component fermions at the zero-temperature limit from the
Bardeen-Cooper-Schrieffer (BCS) region to the unitarity limit. The obtained
results are very accurate in the sense that the systematic error is within 4%
around the unitarity limit. Using this advantage, we can compare our data with
various many-body theories. We found that an extended ${\it T}$-matrix
approximation, which is a strong-coupling theory involving fluctuations in the
Cooper channel, well reproduces our experimental results. We also found that
the superfluid order parameter ${\it \Delta}$ calculated by solving the
ordinary BCS gap equation with the chemical potential of interacting fermions
is close to the binding energy of the paired fermions directly observed in a
spectroscopic experiment and that obtained using a quantum Monte Carlo method.
Since understanding the strong-coupling properties of a superfluid Fermi gas in
the BCS-BEC (Bose-Einstein condensation) crossover region is a crucial issue in
condensed matter physics and nuclear physics, the results of the present study
are expected to be useful in the further development of these fields.
