  Near equilibrium, the rate of relaxation to equilibrium and the transport
properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC)
are determined by three collision integrals, $\mathcal{G}^{12}$,
$\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals
conserve momentum and energy during bogolon collisions, but only $
\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the
contribution of only two collision integrals, $ \mathcal{G}^{22}$ and $
\mathcal{G}^{12}$. In this work, we show that the third collision integral $
\mathcal{G}^{31}$ makes a significant contribution to the bogolon number
relaxation rate and needs to be retained when computing relaxation properties
of the BEC. We provide values of relaxation rates in a form that can be applied
to a variety of dilute Bose-Einstein condensates.
