Separation of coherent and incoherent neutron contributions

We have shown that the cross-section (q) of a macroscopic sample which scatters neutrons is the sum of coherent and incoherent contributions 

The cross-section Z(q) is proportional to the number of particles I (q) falling on the detector 

Unfortunately, XA is not known with great precision. When the coherent and incoherent contributions are of the same order, the term on the left has a value which is uncertain then, it is necessary to obtain 2Tcoll(ij) in a different way. For this purpose two successive experiments are performed in such a way that the weights of the coherent and incoherent contributions are different in each experiment. The constants Kk associated with these experiments remain unknown, but their ratio is considered as known. The first experiment is always the same we described it earlier. The second experiment can be performed in various ways. We shall describe three of them the first two are the most frequently used, the third one seems more efficient but is not so common. 

We shall use the indices 1 and 2 to denote what concerns the first and the second experiment. 

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