  The study of heavy quarkonium suppression in heavy-ion collisions represents
an important source of information about the properties of the quark-gluon
plasma produced in such collisions. In a previous paper, we have considered how
to model the evolution of a quarkonium in such a way that the solution of the
resulting equations evolves toward the correct thermal equilibrium distribution
for an homogeneous and static medium. We found that it is crucial to take into
account the energy gap between singlet and octet configurations when the
temperature is not much greater than this energy gap. In this manuscript, we
explore in more detail the phenomenological consequences of this observation in
the more realistic situation of an expanding system. We consider two different
scenarios, based on the same approximation scheme, but on different choices of
parameters. In the first case, we rely on a Hard Thermal Loop approximation,
while the second case is based on a recent determination of the static
potential in lattice QCD. In both cases, we compute the decay width and the
nuclear modification factor, both taking the energy gap into account and
ignoring it. We find that the impact on the predictions is as large in the
expanding medium as it is in the static case. Our conclusion is that this
energy gap should be taken into account in phenomenological studies.
