Pair correlations inside an ideal chain

A pair correlation function (r) may be de ed as follows. We pick one monomer at randoni in the chain, and we place it at the origin. Then we ask, what is the number density of other monomers at a distance r from the frrst, and we average the result over all choices of the frrst monomer. The Fourier transform of g(r) 

The function (r) has an integral which is just the total number of monomers per chain N 

The functions (r) and (q) obey simple scaling rules g(r) = Ng r/R ) where g is an universal function. 

The structure of g(q) for ideal chains was discussed first by Debye,and thus we call g(q) the Debye function gi (q). 

Focusing on the limit r R , we can reach the form of g(r) by a simple argument. In a sj re of radius r we have a certain number of monomers n, related to r by the random walk scaling law no r. The function g(r) scales like the density of monomers in the sphoe  

---