Nuclear inelastic scattering intensity

Fig. 15. Basic equipment for measuring a nuclear inelastic scattering spectrum. Detector 1 measures the intensity of the incoherent nuclear forward scattering, which proceeds both elastically and inelas-tically detector 2 measures only the intensity of the coherent nuclear forward scattering, which proceeds elastically. Figure according to Ruffer and Chumakov (224).

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

Fig. 15. Scattered intensity of time-of-flight spectra plotted against energy transfer, E, for polycrystalline CeAlj. Thick continuous line shows result of fit constructed from various components indicated by fainter lines flat background, nuclear elastic line, inelastic magnetic lines at = 5.2meV and 7.5 meV, respectively (Murani et al. 1977).

Since an oscillating dipole moment is a source of new waves generated at each molecule, (8.5) shows that an elastically scattered wave at the frequency w is produced (Rayleigh scattering) but also inelastically scattered components with the frequencies (w-w ) (Stokes waves) and superelastically scattered waves with the frequencies (w+w ) (anti-Stokes components). The microscopic contributions from each molecule add up to macroscopic waves with intensities which depend on the population N(E ) of the molecules in the initial level Ej, on the intensity of the incident radiation and on the expression (9Qij/9q )q which describes the dependence of the polarizability components on the nuclear displacements. 

Inelastic neutron scattering spectroscopy is characterized by completely different intensities because the neutron scattering process is entirely attributable to nuclear interactions [110] Each atom features its nuclear cross section, which is independent of its chemical bonding. Then the intensity for any transition is simply related to the atomic displacements scaled by scattering cross sections. And because the cross section of the proton is about one order of magnitude greater than that for any other atom, the method is able to record details of quantum dynamics of proton transfer. 

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