Theory of inelastic neutron scattering

1 Theory of inelastic neutron scattering from solids 

As described above, inelastic neutron scattering measures the energy that the system can exchange with the neutron and the probability of each exchange (see equation 6.5). Given that we are interested only in hydrogen, we can initially restrict ourselves to incoherent scattering, i.e. those terms in equation 

Incoherent inelastic scattering from a proton in a harmonic potential well the Einstein oscillator model 

The simplest analytic model for an isolated proton in a lattice assumes that it is situated in a potential well centred on an interstitial site. This model is particularly appropriate to protons in a transition metal lattice, where the electron from the hydrogen atom can be accommodated in the d-band of the metal, but is also applicable to many other cases as well - e.g. to molecular hydrogen trapped in ion-exchanged zeolites (see Section 6.8.2 below). The model assumes that there are no interactions between neighbouring hydrogen atoms and that there is little coupling with the lattice modes. This implies that M/wjp 1 where m is the mass of the proton and M is the mass of the lattice atom. In transition metals, with face-centred cubic (FCC), body-centred cubic (BCC) or hexagonal close packed (HCP) lattices, the proton normally sits on either octahedral or tetrahedral sites. In more complex intermetallic 

Perturbation analysis of anharmonic and anisotropic effects in inelastic 

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