Bogolyubov condition

A. Problem of Bound States—Generalization of the Bogolyubov Condition... 

We solve these equations using the Bogolyubov condition ... 

Clearly, it is necessary to generalize the Bogolyubov condition (2.4). It is obvious in generalizing (2.4) to assume that in systems with two-particle bound states, the pair 1 and 2 moved independently of all other particles as t—> -< . Then it is possible to write... 

Let us now consider the Bogolyubov condition for the three-particle density operator. In generalizing (2.4), the Bogolyubov condition now takes the form (if three-particle bound states are absent)... 

As in Section II, the initial values F12(t0) and F123(/0) for the binary and the three-particle density operators must be determined. For this purpose we have to generalize the Bogolyubov condition of the weakening of initial correlations given by (2.4) for systems that do not support the formation of bound states. 

To use this solution it is necessary to solve two problems. The first problem is the determination of F12(/0). Usually, for deriving a closed equation for F,(f), Bogolyubov s condition of the complete weakening of the initial correlation is used. This is given by8... 

F c2 is the contribution to F12(f) for pairs in scattering states, and Fb2 is the part for pairs in bound states. Now, in the sense of Bogolyubov, we use for the scattering states the condition of the total weakening of initial correlation ... 

The next problem is the determination of the initial value of the three-particle density operator. Using the generalized Bogolyubov asymptotic condition in the approximation (3.39), we obtain finally... 

By considering under what conditions of ionic strength the denominator 1 + BaVl can be approximated to unity, the Debye-Hiickel limiting law has been shown above to be a good approximation for dilute solutions. However, there was at that time no theoretical justification for this except for the arguments put forward by Kramers. However, the modern work of Kirkwood, Bogolyubov et al. (Section 10.18) has fully justified the limiting law. 

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