  We have measured the interaction energy and three-body recombination rate for
a two-component Fermi gas near a narrow Feshbach resonance and found both to be
strongly energy dependent. Even for deBroglie wavelengths greatly exceeding the
van der Waals length scale, the behavior of the interaction energy as a
function of temperature cannot be described by atoms interacting via a contact
potential. Rather, energy-dependent corrections beyond the scattering length
approximation are required, indicating a resonance with an anomalously large
effective range. For fields where the molecular state is above threshold, the
rate of three-body recombination is enhanced by a sharp, two-body resonance
arising from the closed-channel molecular state which can be magnetically tuned
through the continuum. This narrow resonance can be used to study strongly
correlated Fermi gases that simultaneously have a sizeable effective range and
a large scattering length.
