The self-diffusion constant for large heavy particles

We construct a closed-form expression for the self-diffusion constant, D, for a hard-sphere particle whose mass and radius are large compared to the corresponding bath-particle quantities. The expression yields the Stokes-Einstein law at high bath-particle densities and the Boltzmann form for low densities. In addition, the first density correction to D is obtained and the higher-order density corrections are shown to diverge. The second density correction diverges as −log(k0R), where k0 is a cutoff wavevector and R is the radius of the particle.