Inelastic neutron scattering response function

Because there is no general microscopic theory of liquids, the analysis of inelastic neutron scattering experiments must proceed on the basis of model calculations. Recently1 we have derived a simple interpolation model for single particle motions in simple liquids. This derivation, which was based on the correlation function formalism, depends on dispersion relation and sum rule arguments and the assumption of simple exponential decay for the damping function. According to the model, the linear response in the displacement, yft), satisfies the equation... 

This approximate expression is similar to the response function (5.138) which we wrote down by analogy with the expressions (5.136,137) for e(o)), except that the harmonic frequency o).(q) has been replaced by the pseudo-harmonic frequency o)-(q) and r.(q) has been replaced by r.(q). From the ex-perimental point of view, we see that o)j(q) and Fj(q) are to be determined from the measured positions and half-widths of the infrared absorption bands, the Raman lines, or the peaks of inelastic neutron scattering spectra. Examples of infrared experimental data are shown in Fig.5.14. The pseudoharmonic frequencies d).(q) defined by (5.144) should not be confused with... 

Certainly the clearest conclusion from the examples of this chapter is the total absence of sharp features in the inelastic response function of anomalous lanthanide and metallic actinide materials. This contrasts strongly with the sharp dispersionless crystal-field excitations observed in most lanthanide compounds, in which the exchange interactions are weak (fig, 2), and with the sharp spin-wave excitations found in systems with strong exchange interactions. In many of the early studies with neutron inelastic scattering, for example of the heavy lanthanides or transition metals and their compounds, the width of the excitations was never an issue. It was almost always limited by the instrumental resolution, although it should be stressed that this resolution is relatively poor compared to that obtained by optical techniques. However, the situation is completely different in the materials discussed in this chapter. Now the dominant factor is often the width indeed in some materials the width of the over-damped response function is almost the only remaining parameter with which to characterize the response. 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

Fig. 52. Background corrected neutron spectra for USn, as a function of temperature obtained with E, = l2.5meV and with =3.1 meV (upper three frames). The full line represents the results of a lit and the cross-hatched area, the low-energy magnetic response. The spectrum in the lower frame is taken with i=50meV. The hatched area represents phonon and mirltiple inelastic scattering. (From JLoewenhaupt and Loong 1990.)...

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