Long polymers in good solvent : ε-expansion of the ratio of the radius of gyration to the end to end distance

Abstract

The ratio of the radius of gyration to the mean square end to end distance of an isolated long chain is given to second order in e = 4 — d, where d is the space dimension. Our method of calculation is based on the direct renormalization idea introduced by J. des Cloizeaux. In dimension three (e = 1), our result can be compared with the result of computer experiments made by C. Domb and F. F. Hioe.