Scattering by a Gaussian Chain

2 Scattering by a Gaussian Chain It is possible to calculate 5 i(k) in the whole range of k for a Gaussian chain without approximations. A continuous version of Eq. 2.59 is needed for the definition of 5i(k). 

The density autocorrelation function for two segments on the Gaussian chain is given as 

After some calculations (see Appendix 2.C), Eq. 2.80 with r = 0 simplifies to 

This relationship can also be intuitively obtained in the following discussion. When r Rg, a partial chain of n segments is contained in the sphere of a radius r = bn /2. The average segment density within the sphere is 

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