An exact result for the incoherent scattering function in dilute suspensions

The effect of a square well potential added to the hard core repulsion, between particles in a dilute suspension, on their self-diffusion coefficient is investigated on the basis of the results, obtained by Batchelor, for the mobility of these particles. Hydrodynamic interactions are neglected. It is found that a moderately strong attractive potential leads to an increase of the self-diffusion coefficient, whereas a repulsive potential has the opposite effect. The exact result for the incoherent scattering function is given. The results for the self-diffusion coefficient are recovered in the long time limit. The short time behavior is also discussed and some conclusions are drawn.