Abstract: | The scattering law S(k, w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ώ(κ) of S(k, w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse-Zimm model) using the “spring-bead” model ignoring memory effects. For small $ left( {kasqrt N ll 1} right) $ and large (ka >> 1) values of k we find OHacgr; = 0.195 κ2/β aŋo,$ sqrt N $ and OHacgr; = κ2/βξ respectively, indicating that the width is governed mainly by the viscosity ŋo for small κ values and by the friction coefficient ξ for large κ values. For intermediate κ values which are of importance in neutron scattering we find that in the Rouse limit Ώ = κ4a2/12βξ. When the hydrodynamic effects are included, Ώ(κ) becomes 0.055 κ3/βeng;o. Using the Rouse-Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Ώ(κ). The implications of the theoretical predictions for scattering experiments are discussed. |