Zimm model in good solvent

So far we have been considering the 0 condition. The excluded volume interaction is taken into account if we add a potential 

If such a potential is introduced, the Langevin equation again becomes nonlinear. However, on the same level of the approximation as the preaveraging approximation, we can treat the problem simply by assuming the linear Langevin equation 

To calculate Cp. we have to know the distribution of R -R of the excluded volume chain. Since this is not yet known precisely, we assume, for the sake of simplicity, that the distribution of R - R is the same as the distribution of the end-to-end vector of the excluded volume chain with n—m segments, and has the following functional formr f 

On the other hand the parameter kp can be determined from the equilibrium distribution of Xp as 

To calculate (Jfp)eq, it is convenient to rewrite eqn (4,18) using integration by parts, so that 

---