Theoretical models development basic assumptions

The basic theoretical models to describe the interaction of ionized particles with matter were developed early in the 20th century by Bohr [1,2], Bethe [3] and Bloch [4] (BBB). These models provide the general framework to almost any consideration on the energy loss of swift particles in matter. The first two of these models are based on widely different assumptions, the Bohr description is fully classical, representing the atomic electrons by classical oscillators, while the Bethe model is based on quantum perturbation theory (first-order Born approximation). 

Since the introduction of the isolated binary collision model there has been considerable controversy over its applicability. A number of theoretical papers have challenged its basic assumptions and proposed corrections due to collective effects (usually within the weak coupling approximation of Section II.B), while others have supported and extended the model. In this section, we outline the development of the controversy over the binary collision approximation, which is not resolved even today. 

Another example of a process in which a charge is moved across an interface is interfacial electron transfer reactions. As in the case of ion transfer, experimental data on electron transfer across liquid-liquid interfaces are very limited. For this process, however, there exists a theoretical framework developed within a dielectric continuum model,which built on the fundamental theory of electron transfer in bulk media. Computer simulations, which complement experiments and theory, have not yet dealt with chemically realistic systems but, instead, considered idealized molecules to test the basic assumptions of the continuum model. 

It is helpful to contrast the view we adopt in this book with the perspective of Hill (1986). In that case, the normative example is some separable system such as the polyatomic ideal gas. Evaluation of a partition function for a small system is then the essential task of application of the model theory. Series expansions, such as a virial expansion, are exploited to evaluate corrections when necessary. Examples of that type fill out the concepts. In the present book, we establish and then exploit the potential distribution theorem. Evaluation of the same partition functions will still be required. But we won t stop with an assumption of separability. On the basis of the potential distribution theorem, we then formulate additional simplified low-dimensional partition function models to describe many-body effects. Quasi-chemical treatments are prototypes for those subsequent approximate models. Though the design of the subsequent calculation is often heuristic, the more basic development here focuses on theories for discovery of those model partition functions. These deeper theoretical tools are known in more esoteric settings, but haven t been used to fill out the picture we present here. 

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