Correlation Function and Invariant

By way of introduction we here summarize a few results of general validity, before focusing on the nonparticulate two-phase system that will be discussed in the rest of Section 5.3. For the present we stipulate only that the system of study is characterized by its scattering length density distribution p(r), which is not restricted in any way. The intensity of scattering I(q) is then given by 

The correlation function rn(r), according to (5.61), can be obtained by taking the inverse Fourier transform of the scattered intensity I(q), which, however, must be measured in absolute units if T (r) is to be obtained also in absolute units. When the intensity is known only in arbitrary (relative) units, y(r) can still be obtained in view of the normalization condition y (0) = 1. 

The invariant Q was defined, in Section 1.5.4, as the quantity that represents the total scattering power of the sample, and it can be evaluated by integrating the observed intensity I(q) over the whole reciprocal space, as indicated by Equation (1.85), or in the case of an isotropic material by 

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