  In many phenomenologically interesting models of thermal leptogenesis the
heavy neutrinos are non-relativistic when they decay and produce the baryon
asymmetry of the Universe. We propose a non-relativistic approximation for the
corresponding rate equations in the non-resonant case, and a systematic way for
computing relativistic corrections. We determine the leading order coefficients
in these equations, and the first relativistic corrections. The
non-relativistic approximation works remarkably well. It appears to be
consistent with results obtained using a Boltzmann equation taking into account
the momentum distribution of the heavy neutrinos, while being much simpler. We
also compute radiative corrections to some of the coefficients in the rate
equations. Their effect is of order 1% in the regime favored by neutrino
oscillation data. We obtain the correct leading order lepton number washout
rate in this regime, which leads to large (~ 20%) effects compared to previous
computations.
