A simple analytic expression for the first cumulant of the dynamic structure factor of a polymer coil in the Rouse model is derived. The obtained formula is exact within the usual assumption of the continuum distribution of beads along the chain. It reflects the contributions to the scattering of light or neutrons from both the internal motion of the polymer and its diffusion, and is valid in the whole region of the wave-vector change at the scattering.
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