  We calculate the short time and the long time diffusion coefficient of a
spherical tracer particle in a polymer solution in the low density limit by
solving the Smoluchowski equation for a two-particle system and applying a
generalized Einstein relation (fluctuation dissipation theorem). The tracer
particle as well as the polymer coils are idealized as hard spheres with a
no-slip boundary condition for the solvent but the hydrodynamic radius of the
polymer coils is allowed to be smaller than the direct-interaction radius. We
take hydrodynamic interactions up to 11th order in the particle distance into
account. For the limit of small polymers, the expected generalized
Stokes-Einstein relation is found. The long time diffusion coefficient also
roughly obeys the generalized Stokes-Einstein relation for larger polymers
whereas the short time coefficient does not. We find good qualitative and
quantitative agreement to experiments.
