The scattering structure functionSN(q) of a large flexible ring polymer withNmonomers in a good solvent is calculated as a universal expansion in the variableq2RG2gsim;, where RG2gsim; denotes the mean square radius of gyration of the ring. To solve the interacting polymer problem, the methods of renormalized field theory are applied directly to Fixmanrsquo;s cluster expansion. The results are obtained using the approximation of expanding in egr;equiv;4minus;(dimension of space) and indicate that the selfhyphen;repulsion has a greater influence on the large distance behavior of a ring polymer when compared with a linear polymer. In particular, we find that the radius of gyration ratio RG2gsim;ring/RG2gsim;lineis a universal quantity and to first order in egr; is equal to 0.568. For ideal polymers, the ratio is known to be 0.5.
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