  In this paper, we study the three-body recombination rate of a homogeneous
dilute Bose gas with a Feshbach resonance at zero temperature. The ground state
and excitations of this system are obtained. The three-body recombination in
the ground state is due to the break-up of an atom pair in the quantum
depletion and the formation of a molecule by an atom from the broken pair and
an atom from the condensate. The rate of this process is in good agreement with
the experiment on $^{23}$Na in a wide range of magnetic fields.
