  The four-particle system is the simplest few-body system containing the
fundamental physics involved in ultracold fermionic gases. We have made recent
efforts to solve the quantum four-body problem in the adiabatic hyperspherical
representation. Our approach yields a set of coupled potential curves that can
in turn be solved for all elastic and inelastic processes. These rates may play
an important role in the lifetime of molecules in ultracold fermi gases. We
believe this will lead to a deeper understanding of ultracold fermi systems and
the physics of the BCS-BEC crossover.
