  We study the diffusion of tracers (self-diffusion) in a homogeneously cooling
gas of dissipative particles, using the Green-Kubo relation and the
Chapman-Enskog approach. The dissipative particle collisions are described by
the coefficient of restitution $\epsilon$ which for realistic material
properties depends on the impact velocity. First, we consider self-diffusion
using a constant coefficient of restitution, $\epsilon=$const, as frequently
used to simplify the analysis. Second, self-diffusion is studied for a
simplified (stepwise) dependence of $\epsilon$ on the impact velocity. Finally,
diffusion is considered for gases of realistic viscoelastic particles. We find
that for $\epsilon=$const both methods lead to the same result for the
self-diffusion coefficient. For the case of impact-velocity dependent
coefficients of restitution, the Green-Kubo method is, however, either
restrictive or too complicated for practical application, therefore we compute
the diffusion coefficient using the Chapman-Enskog method. We conclude that in
application to granular gases, the Chapman-Enskog approach is preferable for
deriving kinetic coefficients.
