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Theoretical methods m3c

The modularisation process
The creation of the modules Theoretical methods was more difficult than the creation of the modules Experimental methods. In the original versions, the presentation of the theoretical methods is less localised than that of the experimental methods. The module A08-m3ci1 is derived mainly from the section 3.Potential curves, A08-m3ci2 from 8.Rotational coupling and A08-m3cii from 4.Calculations. The section 1.Introduction of the original A08 also contains some information on the theoretical methods, which is mostly repeated in the following sections, as does the section 7.Discussion. Most of the information represented in A05-m3c is derived from the section 1.Introduction in the original version of A05.

The boundaries of the module: entanglement
In the domain of experimental molecular dynamics, the theoretical methods are generally used to interpret the experimental results. The theoretical methods described in A05-m3c, for example, are used to explain the experimental cross sections (by comparing the experiment and the general theory in a qualitative interpretation) and, in particular, to calculate the theoretical cross sections based on the experimental results in a quantitative interpretation. The usage of the theoretical methods on the (experimental) results, and the fruits of that usage are presented in the Interpretation module. This makes it difficult to separate theoretical methods and the interpretation, which is reflected in the fact that the modules Theoretical methods and Interpretation overlap and are strongly linked.

We have represented the information on the theoretical model in the Methods module, rather than in the Interpretation module, to stress the fact that it is part of the `theoretical toolbox' of models and theoretical assumptions and approximations available at that time. We have also considered the following alternatives:

1.
To present in the Interpretation everything that happens later in the problem-solving process than the stage in which the experimental results are obtained. In this approach the experimental work is primary, and the theory is dedicated to the enhancement (namely the interpretation) of the experiment. This approach, however, leads to an intractable Interpretation module. In such an Interpretation module would be gathered a) the description of the model for the interpretation, b) the application of the model in terms of calculations, c) the outcome of these calculations, and d) the comparison of the results of the calculations with the results of the measurements. Therefore, we have decided not to accumulate everything associated with the interpretation of the experimental results in the Interpretation module.

2.
To ignore the fact that the experimental results are used to generate the theoretical results (the calculated differential cross sections) and to reconstruct parallel experimental and theoretical problem-solving processes, where the experimental and theoretical results, obtained via the two methods, are finally compared at the point where the two parallel courses join again in an interpretation. This approach better fits the philosophical idea of science as a programme with predictions and testing. However, the two courses are not parallel logically speaking, as the experimental results are used as input in the calculations.

3.
To present the model on the microscopic level in the Interpretation module, but to treat it on the mesoscopic level as part of the theoretical toolbox. In this manner, the fact that the theory is used to interpret the experimental results would be emphasised, hopefully without encumbering the Interpretation module too much, because this would take into account that the basic model is mesoscopic information anyway. Nevertheless, we prefer to stress the fact that the theoretical method are methods, so that readers can search for a particular theoretical method under that heading, regardless of the purpose for which it is used.  

The criterion given in the guidelines for the presentation of a theoretical method in this module, is that the information should not depend on the experimental results (see appendix A). This implies that a model that is newly developed on the basis of experimental results, rather than used in the response to another problem, is presented in the Interpretation, rather than in the module Theoretical methods. This criterion works, in spite of the fact that in the original article the presentation of some theoretical methods often does depend on the experimental results, although the theoretical methods themselves don't. In A05, for example, the atom-atom model for molecular collisions and the calculation methods for the differential cross section are clarified using figures of the potential curves and of the deflection function. These figures are based on experimental results. At this stage, however, the theoretical methods take into account only the general shapes and not the exact results. This is emphasised by the fact that in the original article A05 these theoretical methods are presented in the section 1.Introduction, rather than in the section 4.Discussion. Part of that account is also included in article A08, in the section 3.Potential curves. In the modular version, the model is presented in full in a mesoscopic module Theoretical methods .

Another example of a potential entanglement of the Theoretical methods and the Interpretation is the argumentation in the Theoretical methods A05-m3c supporting the standpoint that the model is not really applicable in the situation at hand, because vibration is neglected. That is not a conclusion of the article: the authors were already aware of it and stated it in the Introduction of the original article (The authors just tried to get a qualitative insight into the harpoon reaction using this, admittedly inadequate, theoretical model; in article A08, they addressed this problem by considering a more simple system for which the assumptions are valid.). In this discussion, the value of the electron affinity is used as an argument supporting the standpoint that the effect of vibration is large in this reaction and thereby that the model is not applicable. The electron affinity is calculated in the Interpretation, i.e. `later' on in the problem-solution pattern (and later in the original article). For the sake of coherence, this argument has to be provided with the rest of the argumentation on the applicability of the model. We include the argument and the entire argumentation in the Theoretical methods module A05-m3c, thus grouping all information concerning the model that was available to the authors before they started the experiment, including a discussion of its relevance to the problem at hand. The `forward reference', firstly, is not very disturbing even in the original version, as it concerns only a simple value put into this module. Secondly, it is even less disturbing in the modular version, where the input value has been linked to the place it was obtained, thus sparing the reader some searching within the article. That link explicitly expresses the fact that the value of the electron affinity used in A05-m3c is input from the module Quantitative interpretation A05-mbi.
Within the module: internal structure
Once the information that is to be represented in the Theoretical methods is collected, the next question is how to structure that module using the physics characterisation. How do we deal with a conglomerate of theories, models, approximations that are all part of the `theoretical toolbox'? For example, in the Theoretical methods A08-m3c we discuss: the Landau-Zener with the potential curves, deflection functions, differential cross sections, the stationary phase approximation, the uniform approximation, JWKB phase shifts, and rotational coupling.

We have compromised between two following extremes:

1.
To put everything in the same elementary module, because the information is inter-dependent; However, that module would be very complicated, addressing many different issues
2.
To put each issue in a separate constituent module. This would lead to constituent modules that need to overlap quite seriously, if they are to be self-contained. In addition, the coherence of the constituents would be obscured.
We have created a complex module Theoretical methods that consists of two components. The constituent module A08-mci focuses on the transition probability. That module in its turn consists of two constituent modules, each focusing on a specific case of the transition probability: A08-m3ci1 on the probability associated to the Landau-Zener coupling and A08-m3ci2 on the one associated to the rotational coupling. The elementary module A08-m3cii presents the methods used for the following step: the calculation of the differential cross section based on the deflection function, with the stationary-phase approximation, the uniform approximation and JWKB shifts. The internal structure of this elementary module has been indicated typographically (using headings), to clarify the function of the different parts.

The resulting module
Because the module Theortical methods presents the existing methods that are used in the article at hand, it is to be expected that those methods are already described elsewhere. In the original articles, the authors have also made that assumption. The information about the theoretical methods is not complete and the reader is assumed to know quite a lot about it. In the module version, A05-m3c and well as A08-m3c are complemented, by means of links, with mesoscopic modules  and macroscopic  which do cater for less informed readers. This allows the modular version to meet the communication criterion that the details of the background must be made available.

In fact, most of the theoretical methods can be given in a mesoscopic or macroscopic module. The Theoretical methods modules A05-m3c and A08-m3c refer to the same mesoscopic accounts of the atom-atom model in MESO-m3c-mod and of the scattering theory for differential cross sections MESO-m3c-diff. However, the articles still contain non-trivial microscopic Theoretical methods modules, in which we summarise which theoretical tools have been used, how the different theoretical tools cohere, and in which we argued their applicability to the situation at hand.


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