Spatial monomer distribution for a flexible polymer in a good solvent

We calculate the fourth moment 〈r4〉 of the average monomer–monomer separation in a flexible linear polymer in the excluded volume limit. The ratio 〈r4〉/〈r2〉2 is a universal number expressible in terms of the exponents γ and ν. The ratio is 8% smaller for the excluded volume chain than for the ideal chain. To account for the excluded volume interaction we use field theory methods to renormalize the Mayer–Fixman cluster expansion. Our approximation method of expanding in dimension of space minus four introduces an estimated uncertainty of 1%. The end point moment ratio 〈r4e〉/〈r2e〉2 behaves similarly.