Correlation Functions for Isotropic Motion

In accordance with equations (3.15), the memory functions / (s) and y (s) in the dynamic equations are given by their one-sided transforms 

In this case the theory, apart from the characteristic Rouse relaxation time r, contains three more parameters, namely the relaxation time r of the medium, the measure B of the increase in the resistance of the particle when it moves among the chains, and the measure of internal viscosity E associated with resistance to the deformation of the coil due to the present of ambient macromolecules. 

We use expression (4.22) to specify the quantities (4.4) and calculate equilibrium correlation functions (4.14) for the case, when m = 0, 

are the relaxation times of the macromolecule in a monomer viscous fluid - Rouse relaxation times 

The dynamic equations determine the two relaxation branches, while one of them contains the small relaxation times t, the other - the large ones r+ which practically for long macromolecules coincide with the relaxation time Ta. Further on, it is convenient to consider asymptotic formulae for small and large mode numbers separately, so that for these branches, one has approximations 

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