  For standard leptogenesis from the decay of singlet right-handed neutrinos,
we derive source terms for the lepton asymmetry that are present in a finite
density background but absent in the vacuum. These arise from cuts through the
vertex correction to the decay asymmetry, where in the loop either the Higgs
boson and the right-handed neutrino or the left-handed lepton and the
right-handed neutrino are simultaneously on shell. We evaluate the source terms
numerically and use them to calculate the lepton asymmetry for illustrative
points in parameter space, where we consider only two right-handed neutrinos
for simplicity. Compared to calculations where only the standard cut through
the propagators of left-handed lepton and Higgs boson is included, sizable
corrections arise when the masses of the right-handed neutrinos are of the same
order, but the new sources are found to be most relevant when the decaying
right-handed neutrino is heavier than the one in the loop. In that situation,
they can yield the dominant contribution to the lepton asymmetry.
