Waites interpolation equations

In particular, in the widely-spread Waite s approach the reaction rate on intuitive grounds is represented by a sum of the mono- and bimolecular contributions 

If there were no bimolecular recombination, we would get from equation (3.2.9) that 

Therefore, whole kinetics reads as a sum of both contributions  

Equation (4.1.38) is obviously constructed in such a way that it correctly reproduces the solution of a pair problem. 

However, Waite s approach has several shortcomings (first discussed by Kotomin and Kuzovkov [14, 15]). First of all, it contradicts a universal principle of statistical description itself the particle distribution functions (in particular, many-particle densities) have to be defined independently of the kinetic process, but it is only the physical process which determines the actual form of kinetic equations which are aimed to describe the system s time development. This means that when considering the diffusion-controlled particle recombination (there is no source), the actual mechanism of how particles were created - whether or not correlated in geminate pairs - is not important these are concentrations and joint densities which uniquely determine the decay kinetics. Moreover, even the knowledge of the coordinates of all the particles involved in the reaction (which permits us to find an infinite hierarchy of correlation functions = 2. oo, and thus is 

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