  We introduce a major theoretical generalization of existing techniques for
handling the three-body problem that accurately describes the interactions
among four fermionic atoms. Application to a two-component Fermi gas accurately
determines dimer-dimer scattering parameters at finite energies and can give
deeper insight into the corresponding many-body phenomena. To account for
finite temperature effects, we calculate the energy-dependent complex
dimer-dimer scattering length, which includes contributions from elastic and
inelastic collisions. Our results indicate that strong finite-energy effects
and dimer dissociation are crucial for understanding the physics in the
strongly interacting regime for typical experimental conditions. While our
results for dimer-dimer relaxation are consistent with experiment, they confirm
only partially a previously published theoretical result.
