The self-diffusion coefficient of a granular gas in the homogeneous cooling
state is analyzed near the shearing instability. Using mode-coupling theory, it
is shown that the coefficient diverges logarithmically as the instability is
approached, due to the coupling of the diffusion process with the shear modes.
The divergent behavior, which is peculiar of granular gases and disappears in
the elastic limit, does not depend on any other transport coefficient. The
theoretical prediction is confirmed by molecular dynamics simulation results
for two-dimensional systems
