Static-coherent-scattering function for a single polymer chain: Conformational space renormalization of polymers. V

The static-coherent-scattering function $S(\overrightarrow{\mathrm{k}},N)$ for a single polymer chain consisting of $N$ units with full excluded-volume effect is calculated by the renormalized perturbation method in chain conformation space. $S(\overrightarrow{\mathrm{k}},N)$ is given in a closed form to order $\epsilon$($=4-d,d$ being the spatial dimension) as a function of $x=k^2〈S^2〉$ with $〈S^2〉$ the radius of gyration. It is found that $I\left(x\right)=\frac{S(\overrightarrow{\mathrm{k}},N)}{S(\overrightarrow{0},N)}$ is very close to the $I_0$ without any excluded-volume effect; the difference between $I\mathrm{}\left(x\right)\mathrm{}$ and $I_0\mathrm{}\left(x\right)\mathrm{}$ is sufficiently small to probably preclude experimental measurement. However, there still remains the possibility of observing the excluded-volume effect on the dissymmetry coefficients which magnifies the difference between $I\mathrm{}\left(x\right)\mathrm{}$ and $I_0\mathrm{}\left(x\right)\mathrm{}$.