Scattering by a Polymer Chain

Scattering by a larger molecule is stronger, because beams scattered by different parts of the molecule can interfere constructively. We consider here how the 

These photons enter the monomers to cause polarization on each of them. Because monomers are located at different positions along the beam path, the Ej that causes the polarization at a given time is different from monomer to monomer. Therefore, compared at the same time, the phase of the oscillating polarization is different for each monomer. The scattered radiation E, caused by the polarization on the ith monomer at r, at time t, and traveling with a wave vector ks is given by 

The photodetector detects the total amplitude of the radiation scattered by different monomers. The total electric field of the scattered light is E i + Es2 + + E. Before adding all of them, we first consider the sum of E, and 

Thus we find that the complex amplitude of the light scattered by the whole chain is modified by a factor of 2 =iexp(i ii). The square of the magnitude of the factor determines how the beams scattered by the N monomers interfere. Thus the intensity of the light scattered by the whole chain is proportional to 

If the monomers are isotropic particles with the same polarizability a, the intensity I of horizontally scattered light (6 = ttII in Eq. 2.45) is 

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