Incoherent scattering, inelastic coherent

The scattering of neutrons by any molecular system can be elastic or inelastic, coherent or incoherent. The elastic coherent scattering of a labeled polymer in a background matrix can be extracted from the data in a properly designed experiment. 

Here is the momentum transferred from the neutron and x is one of the reciprocal lattice vectors of the palladium lattice. Thus, the incoherent scattering sees all the vibration modes but the coherent scattering selects one particular phonon for a particular experimental value of Q. It is now clear that both the incoherent and coherent one-phonon scattering will depend on the shape of the optical dispersion curves and hence will be influenced by hydrogen-hydrogen interactions. Indeed, one of the first observations of inelastic scattering from a hydride [10] interpreted the shape of the optical peak in terms of a frequency distribution broadened by H-H interactions. 

Inelastic coherent and incoherent scattering are proportional to the space and time Fourier transforms of, respectively, the pair-correlation and the selfcorrelation functions. Analogous to dynamic light scattering, these are used to probe polymer dynamics (Arbe et al., 2(X)3 Richter, 2003 Stepanek et al., 2002 Annis et al., 2001). 

The inelastically scattered photons may or may not be scattered in phase. If they retain a phase relationship with one another the scattered radiation is coherent. If the inelastically scattered photons are emitted with random phases, as in spontaneous Raman and fluorescence, the radiation is said to be incoherently scattered. Because incoherent scattering seems to have the most immediate potential for applications in aerosol studies it will be emphasized in what follows. However, the case of coherent scattering by molecules embedded in particles is also of potential significance and will also be considered briefly in the next section. 

In standard inelastic (coherent or incoherent time-of-flight) scattering experiments, increasing the resolution (the precision of the determination of energy transfers) by a given factor x costs... 

With these parameters in hand, we then started to treat the on-resonance spectrum. It is very difficult to find a proper model to describe the mixture of elastic and inelastic (coherent and incoherent) scattering. The simplest approach, which ignores hyperfine interactions, was derived in Ref. 34. Here, we used a simple exponential decay to simulate the elastic scattering contribution. Then Eq. (12.10) becomes... 

But the fingerprint also contains information on the macroscopic properties of a specimen. The half-value widths of the reflections are inversely proportional to the crystallite sizes, and directly proportional to the concentration and magnitude of structural defects. The coherent scattered component of the background results from amorphous constituents in the specimen, while the incoherent scattering is chiefly due to inelastic atomic scattering. 

One can distinguish elastic-inelastic and coherent-incoherent scattering processes [8]. Indeed, neutron sources are very expensive and quite rare compared to optical sources such as black bodies or lasers. However, neutrons give information that cannot be obtained with other techniques. Some interesting properties are featured below. 

The interaction between the incident electron beam and the object produces elastic and inelastic scattering. The coherent term of elastic scattering is responsible for the electron diffraction pattern. An additional incoherent term due to interaction with the nucleus of the atom is responsible for the real absorption factor. It produces a peak near 0 = 10 radian (i.e., very near the incident beam). From 100 to 400 kV, s varies in the range 0.01 to 0.06 A. ... 

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