Curve representing P r

In the preceding sections, we showed that the probability distribution P(r) of the vector r joining the end points of a polymer in a good solvent is given by the scaling law 

Unfortunately, P(r) has never been measured in three dimensions for a real polymer. There exist only results of calculations concerning rather short chains drawn on lattices (N = 18 for a cubic lattice). We must content ourselves with rather coarse estimations. 

As the coefficients ft and D are not very well-known for d = 3, we choose to determine them by requiring that f(x) obeys the definition conditions (13.1.130) which give 

Moreover, a calculation of P(r) to first order in e was performed for any r, by Oono et al.19 who used the formalism of field theory. This calculation can be made directly as we show in Appendix K. The Fourier transform P(k) of P(r) to 

A Fourier transformation in d-dimensional space gives the corresponding value of P(r) [see eqn (K.2)] 

---