  Leptogenesis with heavy neutrino flavours is discussed within a density
matrix formalism. We write the density matrix equation, describing the
generation of the matter-antimatter asymmetry, for an arbitrary choice of the
right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in
the fully flavoured regimes, this reduces to multiple-stage Boltzmann
equations. In this case we recover and extend results previously derived within
a quantum state collapse description. We confirm the generic existence of
phantom terms. However, taking into account the effect of gauge interactions,
we show that they are washed out at the production with a wash-out rate that is
halved compared to that one acting on the total asymmetry. In the N_1-dominated
scenario they cancel without contributing to the final baryon asymmetry. In
other scenarios they do not in general and they have to be taken into account.
We also confirm that there is a (orthogonal) component in the asymmetry
produced by the heavier RH neutrinos which completely escapes the washout from
the lighter RH neutrinos and show that phantom terms additionally contribute to
it. The other (parallel) component is washed out with the usual exponential
factor, even for weak washout. Finally, as an illustration, we study the two RH
neutrino model in the light of the above findings, showing that phantom terms
can contribute to the final asymmetry also in this case.
